From 537c3f15aaa962bd03b5a0571569526adfc95f52 Mon Sep 17 00:00:00 2001 From: WangWeiye Date: Tue, 10 Jan 2023 19:38:49 +0800 Subject: [PATCH] 20230110 afternoon --- 工具/修改题目数据库.ipynb | 2 +- 工具/关键字筛选题号.ipynb | 17 +- 工具/寻找阶段末尾空闲题号.ipynb | 4 +- 工具/批量添加题库字段数据.ipynb | 12 +- 工具/文本文件/metadata.txt | 21 +- 工具/文本文件/题号筛选.txt | 2 +- 工具/添加题目到数据库.ipynb | 10 +- 工具/题号选题pdf生成.ipynb | 15 +- 工具/题目内容编辑.ipynb | 71 --- 题库0.3/Problems.json | 825 +++++++++++++++++++++++++++++++- 10 files changed, 862 insertions(+), 117 deletions(-) delete mode 100644 工具/题目内容编辑.ipynb diff --git a/工具/修改题目数据库.ipynb b/工具/修改题目数据库.ipynb index b42d34d3..60461045 100644 --- a/工具/修改题目数据库.ipynb +++ b/工具/修改题目数据库.ipynb @@ -19,7 +19,7 @@ "source": [ "import os,re,json\n", "\"\"\"这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭, 随后运行第二个代码块\"\"\"\n", - "problems = \"30552\"\n", + "problems = \"30526,10916,10917\"\n", "\n", "def generate_number_set(string,dict):\n", " string = re.sub(r\"[\\n\\s]\",\"\",string)\n", diff --git a/工具/关键字筛选题号.ipynb b/工具/关键字筛选题号.ipynb index e0b3726a..ce51a39f 100644 --- a/工具/关键字筛选题号.ipynb +++ b/工具/关键字筛选题号.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 27, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "0" ] }, - "execution_count": 27, + "execution_count": 2, "metadata": {}, "output_type": "execute_result" } @@ -21,7 +21,7 @@ "\n", "\"\"\"---设置关键字, 同一field下不同选项为or关系, 同一字典中不同字段间为and关系, 不同字典间为or关系, _not表示列表中的关键字都不含, 同一字典中的数字用来供应同一字段不同的条件之间的and---\"\"\"\n", "keywords_dict_table = [\n", - " {\"usages\":[r\"2023届高三02班\"],\"usages2\":[r\"202209\",r\"20221[012]\"],\"usages3\":[r\"0\\.[678][\\d]{2}\"],\"usages_not\":[r\"2023届高三02班[^\\n]*0\\.[0-59][\\d]{2}\"]}\n", + " {\"content\":[\"花粉热\",r\"散点图分析[\\S\\s]*?m\",\"发动机\",\"彩色显像\"]}\n", "]\n", "\"\"\"---关键字设置完毕---\"\"\"\n", "# 示例： keywords_dict_table = [\n", @@ -31,6 +31,13 @@ "# {\"tags\":[\"第三单元\"],\"content\":[\"f\\(\",\"y=\",\"函数\"],\"usages\":[r\"0\\.9\",r\"0\\.8[3-9]\"],\"usages_not\":[r\"0\\.[0-7]\",r\"0\\.8[0-2]\"],\"usages1\":[\"2023届\"]},\n", "# {\"tags\":[\"第五单元\"],\"usages\":[r\"0\\.9\"],\"usages_not\":[r\"0\\.[0-7]\",r\"0\\.8[0-2]\"],\"usages1\":[\"2023届\"]}\n", "# ]\n", + "# 实例3: \n", + "# keywords_dict_table = [\n", + "# {\"usages\":[r\"2023届高三02班\"],\"usages2\":[r\"202209\",r\"20221[012]\"],\"usages3\":[r\"0\\.[678][\\d]{2}\"],\"usages_not\":[r\"2023届高三02班[^\\n]*0\\.[0-59][\\d]{2}\"]}\n", + " \n", + "# ]\n", + "\n", + "\n", "\"\"\"---设置输出文件名---\"\"\"\n", "filename = \"文本文件/题号筛选.txt\"\n", "\"\"\"---文件名设置完毕---\"\"\"\n", @@ -89,7 +96,7 @@ ], "metadata": { "kernelspec": { - "display_name": "mathdept", + "display_name": "Python 3.9.15 ('pythontest')", "language": "python", "name": "python3" }, @@ -108,7 +115,7 @@ "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" + "hash": "91219a98e0e9be72efb992f647fe78b593124968b75db0b865552d6787c8db93" } } }, diff --git a/工具/寻找阶段末尾空闲题号.ipynb b/工具/寻找阶段末尾空闲题号.ipynb index c740744d..8785e874 100644 --- a/工具/寻找阶段末尾空闲题号.ipynb +++ b/工具/寻找阶段末尾空闲题号.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -11,7 +11,7 @@ "text": [ "首个空闲id: 12760 , 直至 020000\n", "首个空闲id: 21441 , 直至 030000\n", - "首个空闲id: 31158 , 直至 999999\n" + "首个空闲id: 31201 , 直至 999999\n" ] } ], diff --git a/工具/批量添加题库字段数据.ipynb b/工具/批量添加题库字段数据.ipynb index 5d06d844..d23a3d2b 100644 --- a/工具/批量添加题库字段数据.ipynb +++ b/工具/批量添加题库字段数据.ipynb @@ -2,20 +2,16 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "题号: 031158 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 031159 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 031160 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 031161 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 031162 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 031163 , 字段: tags 中已添加数据: 第八单元\n", - "题号: 031164 , 字段: tags 中已添加数据: 第八单元\n" + "题号: 031201 , 字段: tags 中已添加数据: 第九单元\n", + "题号: 031202 , 字段: tags 中已添加数据: 第九单元\n", + "题号: 031203 , 字段: tags 中已添加数据: 第九单元\n" ] } ], diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index ceb5d091..01aceb77 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,22 +1,15 @@ tags -31158 -第八单元 +031201 +第九单元 -31159 -第八单元 -31160 -第八单元 +031202 +第九单元 -31161 -第八单元 -31162 -第八单元 +031203 +第九单元 + -31163 -第八单元 -31164 -第八单元 diff --git a/工具/文本文件/题号筛选.txt b/工具/文本文件/题号筛选.txt index 1b338e02..0f4b7c1f 100644 --- a/工具/文本文件/题号筛选.txt +++ b/工具/文本文件/题号筛选.txt @@ -1 +1 @@ -000023,000035,000060,000069,000087,000092,000141,000182,000230,000233,000312,000322,000360,000413,000474,000540,000655,000704,000749,000778,000795,000863,000884,000908,000939,001049,001050,001069,001072,001074,001231,001239,001242,001244,001262,001308,001309,001316,001324,001325,001328,001340,001351,001352,001353,001631,001643,001667,001668,001677,001726,001803,001853,001894,002004,002010,002017,002088,002273,002369,002372,002417,002424,002429,002434,002662,002750,002773,002775,002778,002785,002790,002791,002794,002838,002863,002871,002878,002884,002888,002893,002894,002895,002898,002905,002911,002914,002918,002966,002994,003138,003253,003281,003309,003312,003322,003337,003400,003421,003431,003567,003585,003648,003747,003777,003781,003828,003884,003959,003985,004008,004243,004409,004448,004463,004636,005016,005236,005239,005463,005508,005569,005621,005650,005720,005851,006468,006968,007911,007939,007941,007950,008392,008811,008912,008956,009200,009333,009349,009488,009490,009511,009517,009744,009858,009860,009887,009912,010060,010114,010178,010196,010453,010470,010523,010540,010631,010721,010947,011057,011078,011100,011993,012004,012015,030030,030096,030160,030202,030215,030253,030262,030280,030291,030322,030337,030398,030427,030438,030441,030462,030468,030478 \ No newline at end of file +010015,031179,031182,031188,031196 \ No newline at end of file diff --git a/工具/添加题目到数据库.ipynb b/工具/添加题目到数据库.ipynb index 92bc5c9c..c95a1837 100644 --- a/工具/添加题目到数据库.ipynb +++ b/工具/添加题目到数据库.ipynb @@ -2,21 +2,21 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "#修改起始id,出处,文件名\n", - "starting_id = 31158\n", + "starting_id = 31201\n", "origin = \"自拟题目\"\n", - "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\prostat.tex\"\n", - "editor = \"20230109\\t王伟叶\"\n", + "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目8.tex\"\n", + "editor = \"20230110\\t王伟叶\"\n", "indexed = False\n" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ diff --git a/工具/题号选题pdf生成.ipynb b/工具/题号选题pdf生成.ipynb index cb3ac48d..8fa6000a 100644 --- a/工具/题号选题pdf生成.ipynb +++ b/工具/题号选题pdf生成.ipynb @@ -2,16 +2,16 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "开始编译教师版本pdf文件: 临时文件/题库_教师用_20230108.tex\n", + "开始编译教师版本pdf文件: 临时文件/概率统计测验预选_教师用_20230110.tex\n", "0\n", - "开始编译学生版本pdf文件: 临时文件/题库_学生用_20230108.tex\n", + "开始编译学生版本pdf文件: 临时文件/概率统计测验预选_学生用_20230110.tex\n", "0\n" ] } @@ -26,13 +26,14 @@ "\"\"\"---设置题目列表---\"\"\"\n", "#留空为编译全题库, a为读取临时文件中的题号筛选.txt文件生成题库\n", "problems = r\"\"\"\n", + "031158,031159,031160,031161,031162,031163,031164,031201,031202,031203,031179,031188,031196\n", "\n", "\"\"\"\n", "\"\"\"---设置题目列表结束---\"\"\"\n", "\n", "\"\"\"---设置文件名---\"\"\"\n", "#目录和文件的分隔务必用/\n", - "filename = \"临时文件/题库\"\n", + "filename = \"临时文件/概率统计测验预选\"\n", "\"\"\"---设置文件名结束---\"\"\"\n", "\n", "\n", @@ -173,7 +174,7 @@ ], "metadata": { "kernelspec": { - "display_name": "mathdept", + "display_name": "Python 3.8.15 ('mathdept')", "language": "python", "name": "python3" }, @@ -187,12 +188,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.15" + "version": "3.8.15" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "ff3c292c316ba85de6f1ad75f19c731e79d694e741b6f515ec18f14996fe48dc" + "hash": "42dd566da87765ddbe9b5c5b483063747fec4aacc5469ad554706e4b742e67b2" } } }, diff --git a/工具/题目内容编辑.ipynb b/工具/题目内容编辑.ipynb deleted file mode 100644 index e93964ef..00000000 --- a/工具/题目内容编辑.ipynb +++ /dev/null @@ -1,71 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [], - "source": [ - "import os,re,json\n", - "with open(r\"../题库0.3/problems.json\",\"r\",encoding = \"utf8\") as f:\n", - " jsondata = f.read()\n", - "pro_dict = json.loads(jsondata)\n", - "id = input(\"输入题目id:\")\n", - "id = id.zfill(6)\n", - "content = pro_dict[id][\"content\"]\n", - "\n", - "with open(r\"模板文件/题目编辑.tex\",\"r\",encoding = \"utf8\") as f:\n", - " template_data = f.read()\n", - "\n", - "output_data = template_data.replace(\"待替换\",content)\n", - "with open(r\"临时文件/toedit.tex\",\"w\",encoding = \"utf8\") as f:\n", - " f.write(output_data)\n", - "\n", - "os.system(\"code 临时文件/toedit.tex\")\n", - "cont = input(\"继续请按回车\")\n", - "with open(r\"临时文件/toedit.tex\",\"r\",encoding = \"utf8\") as f:\n", - " edited_data = f.read()\n", - "new_content = re.findall(r\"\\\\begin{document}([\\s\\S]*?)\\\\end{document}\",edited_data)[0].strip()\n", - "pro_dict[id][\"content\"] = new_content\n", - "\n", - "jsondata_new=json.dumps(pro_dict,indent = 4,ensure_ascii=False)\n", - "with open(r\"../题库0.3/problems.json\",\"w\",encoding = \"utf8\") as f:\n", - " f.write(jsondata_new)\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3.8.8 ('base')", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.8.8" - }, - "orig_nbformat": 4, - "vscode": { - "interpreter": { - "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" - } - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 82e92220..22f81caa 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -271785,7 +271785,7 @@ }, "010916": { "id": "010916", - "content": "为了解大学校园附近餐馆的月营业收入(单位: 千元)和该店周围的大学生人数(单位: 千人)之间的关系, 抽取了$10$所大学附近餐馆的有关数据, 如下表所示.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n学生人数$x$/千人 & $2$ & $6$ & $8$ & $8$ & $12$ & $16$ & $20$ & $20$ & $22$ & $26$ \\\\ \\hline\n月营业收入$y$/千元 & $58$ & $105$ & $88$ & $118$ & $117$ & $137$ & $157$ & $169$ & $149$ & $202$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n(1) 根据以上数据, 建立月营业收入$y$与该店周围的大学生人数$x$的回归方程;\n(2) 已知某餐馆周围的大学生人数为$10000$人, 试对该店月营业收入作出预测.", + "content": "为了解大学校园附近餐馆的月营业收入(单位: 千元)和该店周围的大学生人数(单位: 千人)之间的关系, 抽取了$10$所大学附近餐馆的有关数据, 如下表所示.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline\n学生人数$x$/千人 & $2$ & $6$ & $8$ & $8$ & $12$ & $16$ & $20$ & $20$ & $22$ & $26$ \\\\ \\hline\n月营业收入$y$/千元 & $58$ & $105$ & $88$ & $118$ & $117$ & $137$ & $157$ & $169$ & $149$ & $202$ \\\\ \\hline\n\\end{tabular}\n\\end{center}\n(1) 根据以上数据, 建立月营业收入$y$与该店周围的大学生人数$x$的回归方程;\\\\\n(2) 已知某餐馆周围的大学生人数为$10000$人, 试对该店月营业收入作出预测.", "objs": [], "tags": [ "第九单元" @@ -271806,7 +271806,7 @@ }, "010917": { "id": "010917", - "content": "某运动生理学家在一项健身活动中选择了$19$位参与者, 以他们的皮下脂肪厚度来估计身体的脂肪含量, 其中脂肪含量以占体重(单位: $\\text{kg}$)的百分比表示. 得到脂肪含量和体重的数据如下表所示. 其中, 参与者$1-10$为男性, $11-19$为女性.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline\n参与者编号 & 体重$x$/$\\text{kg}$ & 脂肪含量$y$/$\\%$ & 参与者编号 & 体重$x$/$\\text{kg}$ & 脂肪含量$y$/$\\%$ \\\\ \\hline\n$1$ & $89$ & $28$ & $2$ & $88$ & $27$ \\\\ \\hline\n$3$ & $66$ & $24$ & $4$ & $59$ & $23$ \\\\ \\hline\n$5$ & $93$ & $29$ & $6$ & $73$ & $25$ \\\\ \\hline\n$7$ & $82$ & $29$ & $8$ & $77$ & $25$ \\\\ \\hline\n$9$ & $100$ & $30$ & $10$ & $67$ & $23$ \\\\ \\hline\n$11$ & $57$ & $29$ & $12$ & $68$ & $32$ \\\\ \\hline\n$13$ & $69$ & $35$ & $14$ & $59$ & $31$ \\\\ \\hline\n$15$ & $62$ & $29$ & $16$ & $59$ & $26$ \\\\ \\hline\n$17$ & $56$ & $28$ & $18$ & $66$ & $33$ \\\\ \\hline\n$19$ & $72$ & $33$ & / & / & / \\\\ \\hline\n\\end{tabular}\n\\end{center}\n(1) 分别建立男性和女性体重与脂肪含量的回归方程;\\\\\n(2) 男性和女性合在一起所构成的样本的回归方程为$y=0.021x+26.88$, 其斜率与\n(1)中所计算的斜率有差异吗? 能否对这种差异进行解释?\n(3) 计算下列情况下体重与脂肪含量的相关系数: \\textcircled{1} 男性; \\textcircled{2} 女性; \\textcircled{3} 男女合计. 这些值与(2)中所反映的信息是否一致?", + "content": "某运动生理学家在一项健身活动中选择了$19$位参与者, 以他们的皮下脂肪厚度来估计身体的脂肪含量, 其中脂肪含量以占体重(单位: $\\text{kg}$)的百分比表示. 得到脂肪含量和体重的数据如下表所示. 其中, 参与者$1-10$为男性, $11-19$为女性.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline\n参与者编号 & 体重$x$/$\\text{kg}$ & 脂肪含量$y$/$\\%$ & 参与者编号 & 体重$x$/$\\text{kg}$ & 脂肪含量$y$/$\\%$ \\\\ \\hline\n$1$ & $89$ & $28$ & $2$ & $88$ & $27$ \\\\ \\hline\n$3$ & $66$ & $24$ & $4$ & $59$ & $23$ \\\\ \\hline\n$5$ & $93$ & $29$ & $6$ & $73$ & $25$ \\\\ \\hline\n$7$ & $82$ & $29$ & $8$ & $77$ & $25$ \\\\ \\hline\n$9$ & $100$ & $30$ & $10$ & $67$ & $23$ \\\\ \\hline\n$11$ & $57$ & $29$ & $12$ & $68$ & $32$ \\\\ \\hline\n$13$ & $69$ & $35$ & $14$ & $59$ & $31$ \\\\ \\hline\n$15$ & $62$ & $29$ & $16$ & $59$ & $26$ \\\\ \\hline\n$17$ & $56$ & $28$ & $18$ & $66$ & $33$ \\\\ \\hline\n$19$ & $72$ & $33$ & / & / & / \\\\ \\hline\n\\end{tabular}\n\\end{center}\n(1) 分别建立男性和女性体重与脂肪含量的回归方程;\\\\\n(2) 男性和女性合在一起所构成的样本的回归方程为$y=0.021x+26.88$, 其斜率与(1)中所计算的斜率有差异吗? 能否对这种差异进行解释?\\\\\n(3) 计算下列情况下体重与脂肪含量的相关系数: \\textcircled{1} 男性; \\textcircled{2} 女性; \\textcircled{3} 男女合计. 这些值与(2)中所反映的信息是否一致?", "objs": [], "tags": [ "第九单元" @@ -360478,7 +360478,7 @@ }, "030526": { "id": "030526", - "content": "对下面两组数据\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline $x$ & 1 & 2 & 3 & 4 & 10 & 10 \\\\\n\\hline $y$ & 1 & 3 & 3 & 5 & 1 & 11 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n计算相关系数, 大概在$0.5$左右. 通过观察散点图, 发现对这两组大部分数据来说, 变量$x$与$y$有很强的线性相关关系, 是什么因素导致相关系数只存$0.5$左右?", + "content": "对下面两组数据\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline $x$ & 1 & 2 & 3 & 4 & 10 & 10 \\\\\n\\hline $y$ & 1 & 3 & 3 & 5 & 1 & 11 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n计算相关系数, 大概在$0.5$左右. 通过观察散点图, 发现对这两组大部分数据来说, 变量$x$与$y$有很强的线性相关关系, 是什么因素导致相关系数只有$0.5$左右?", "objs": [], "tags": [ "第九单元" @@ -373895,5 +373895,824 @@ "related": [], "remark": "", "space": "" + }, + "031165": { + "id": "031165", + "content": "试举几例具有相关关系的变量.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031166": { + "id": "031166", + "content": "判断下列两个变量之间是否具有相关关系:\\\\\n(1) 家庭月用电量与月平均气温;\\\\\n(2) 一天中的最高气温与最低气温;\\\\\n(3) 某企业生产的一种商品的销量与其广告费用;\\\\\n(4) 谷物的价格与牛肉的价格;\\\\\n(5) 在公式$L W=12$中的$L$与$W$.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031167": { + "id": "031167", + "content": "与同学一起测量脚长与身高, 并用适当方式探究它们之间是否具有相关关系.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031168": { + "id": "031168", + "content": "下列几对变量, 哪些有明显的正相关、明显的负相关、接近于$0$的相关系数?\n(1) 广告费与销售额;\\\\\n(2) 施肥量与粮食产量;\\\\\n(3) 汽车车速与司机的年龄;\\\\\n(4) 人的体重与身高.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031169": { + "id": "031169", + "content": "充气不足或过于膨胀会增加轮胎磨损, 并减少行驶里程. 对一种新型轮胎在不同压力下的行驶里程进行测试, 数据如下表:\n\\begin{center}\n\\begin{tabular}{|c|c||c|c|}\n\\hline 压力$x /(\\text{lb} / \\text{in}^2)$& 里程$y / 10^3 \\text{~km}$& 压力$x /(\\text{lb} / \\text{in}^2)$& 里程$y / 10^3 \\text{~km}$\\\\\n\\hline 30 &$29.5$& 33 &$37.6$\\\\\n\\hline 30 &$30.2$& 34 &$37.7$\\\\\n\\hline 31 &$32.1$& 34 &$36.1$\\\\\n\\hline 31 &$34.5$& 35 &$33.6$\\\\\n\\hline 32 &$36.3$& 35 &$34.2$\\\\\n\\hline 32 &$35.0$& 36 &$26.8$\\\\\n\\hline 33 &$38.2$& 36 &$27.4$\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 画出散点图;\\\\\n(2) 求出相关系数;\\\\\n(3) 将散点图与相关系数进行比照分析, 并作出适当解释.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031170": { + "id": "031170", + "content": "统计表明, 世界各国人均拥有电视机的数量与人均寿命有着较高的正相关的相关系数. 这是否说明: 国家的人均寿命与人均拥有电视机的多少有关? 运送一大批电视机到某人均寿命低的国家是否能延长该国人的寿命?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031171": { + "id": "031171", + "content": "为了探讨学生的物理成绩$y$与数学成绩$x$之间的关系, 从某批学生中随机抽取$10$名学生的成绩$(x_i, y_i)$($i=1,2, \\cdots, 10)$, 并已计算出$\\displaystyle\\sum_{i=1}^{10} x_i=758$, $\\displaystyle\\sum_{i=1}^{10} x_i^2=58732$, $\\displaystyle\\sum_{i=1}^{10} y_i=774$, $\\displaystyle\\sum_{i=1}^{10} x_i y_i=59686$. 试求:\\\\\n(1) 物理成绩$y$关于数学成绩$x$的线性回归方程;\\\\\n(2) 当数学成绩为$92$分时, 物理成绩$y$的线性回归估计值.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031172": { + "id": "031172", + "content": "某种产品的广告费支出$x$与销售额$y$之间有如下对应数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline$x / 10^6$元 & 2 & 4 & 5 & 6 & 8 \\\\\n\\hline$y / 10^6$元 & 30 & 40 & 60 & 50 & 70 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 画出散点图;\\\\\n(2) 求出线性回归方程.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031173": { + "id": "031173", + "content": "每立方米混凝土的水泥用量$x$(单位:$\\text{kg}$) 与$28$天后混凝土的抗压强度$y$(单位:$\\text{kg} / \\text{cm}^2)$之间有如下对应数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline$x / \\text{kg}$& 150 & 160 & 170 & 180 & 190 & 200 \\\\\n\\hline$y /(\\text{kg} / \\text{cm}^2)$&$56.9$&$58.3$&$61.1$&$64.6$&$68.1$&$71.3$\\\\\n\\hline \\hline$x / \\text{kg}$& 210 & 220 & 230 & 240 & 250 & 260 \\\\\n\\hline$y /(\\text{kg} / \\text{cm}^2)$&$74.1$&$77.4$&$80.2$&$82.6$&$86.4$&$89.7$\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 画出散点图;\\\\\n(2) 求出线性回归方程.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031174": { + "id": "031174", + "content": "某小吃店的日盈利$y$(单位: 百元) 与当天平均气温$x$(单位:${ }^{\\circ} \\text{C}$) 之间有如下数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|}\n\\hline$x /{}^{\\circ} \\text{C}$&$-2$&$-1$& 0 & 1 & 2 \\\\\n\\hline$y /$百元 & 5 & 4 & 2 & 2 & 1 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n甲、乙、丙$3$位同学对上述数据进行了分析, 发现$y$与$x$之间具有线性相关关系, 他们通过计算分别得到$3$个线性回归方程: \\textcircled{1} $\\hat{y}=-x+2.8$;\n\\textcircled{2} $\\hat{y}=-x+3$; \\textcircled{3} $\\hat{y}=-1.2 x+2.6$. 其中正确的是\\blank{50}. (填序号)", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031175": { + "id": "031175", + "content": "二手车车龄与其价格之间是正相关, 还是负相关? 为什么? (古董车除外)", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031176": { + "id": "031176", + "content": "车重与其每千米耗油量之间的相关系数是正还是负? 为什么?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031177": { + "id": "031177", + "content": "某工厂在某年里每月产品的总成本$y$(单位: 万元) 与月产量$x$(单位: 万件)之间有如下一组数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline$x /$万件 &$1.08$&$1.12$&$1.19$&$1.28$&$1.36$&$1.48$&$1.59$&$1.68$&$1.80$&$1.87$&$1.98$&$2.07$\\\\\n\\hline$y /$万元 &$2.25$&$2.37$&$2.40$&$2.55$&$2.64$&$2.75$&$2.92$&$3.03$&$3.14$&$3.26$&$3.36$&$3.50$\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 画出散点图;\\\\\n(2) 求相关系数;\\\\\n(3) 求线性回归方程.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031178": { + "id": "031178", + "content": "某研究所研究耕种深度$x$(单位: $\\text{cm}$) 与水稻每公顷产量$y$(单位: $\\text{t}$)的关系, 所得数据资料如下表, 试求每公顷水稻产量与耕种深度的相关系数和线性回归方程.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline 耕种深度$x / \\text{cm}$& 8 & 10 & 12 & 14 & 16 & 18 \\\\\n\\hline 每公顷产量$y / \\text{t}$&$6.0$&$7.5$&$7.8$&$9.2$&$10.8$&$12.0$\\\\\n\\hline\n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031179": { + "id": "031179", + "content": "为了解发动机的动力$x$(单位: $\\text{PH}$) 与排气温度$y$(单位:${ }^{\\circ} \\text{C}$) 之间的关系, 某部门进行相关试验, 得到如下数据:\n\\begin{center}\n\\begin{tabular}{|c|c||c|c|}\n\\hline$x / \\text{PH}$&$y /{ }^{\\circ} \\text{C}$&$x / \\text{PH}$&$y /{ }^{\\circ} \\text{C}$\\\\\n\\hline 4300 & 960 & 4010 & 907 \\\\\n\\hline 4650 & 900 & 3810 & 843 \\\\\n\\hline 3200 & 807 & 4500 & 927 \\\\\n\\hline 3150 & 755 & 3008 & 688 \\\\\n\\hline 4950 & 993 & & \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 求相关系数;\\\\\n(2) 求线性回归方程;\\\\\n(3) 估计当$x=3100$时对应$y$的值.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031180": { + "id": "031180", + "content": "为测定湖中水的清洁程度, 将一有刻度线的玻璃片放人水中直至完全看不见刻度线, 此时它与水表面的距离称为``Secchi 深度''. 为了测量湖水被水藻污染的程度, 科学家要确定水中叶绿素的总浓度. 在某一湖中, 从四月至九月每周四中午都测量 Secchi 深度和叶绿素的总浓度. 这两个变量间是正相关还是负相关? 简要说明理由.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031181": { + "id": "031181", + "content": "对下面这组数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline$x$& 1 & 2 & 3 & 4 & 10 & 10 \\\\\n\\hline$y$& 1 & 3 & 3 & 5 & 1 & 11 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n计算相关系数, 大概在$0.5$左右. 对这组数据大部分点来说, $x$与$y$之间有很强的线性相关关系. 是什么因素导致相关系数只有$0.5$左右?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031182": { + "id": "031182", + "content": "在彩色显像中, 根据以往的经验, 形成染料的光学密度$y$与析出银的光学密度$x$之间存在关系式$y=a \\mathrm{e}^{-\\frac{b}{x}}$($b>0$). 现对$y$与$x$同时做$10$次观测, 获得$10$对数据如下表, 试根据表中数据, 求出$a$与$b$的估计值.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}\n\\hline 编号 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\\\n\\hline$x$&$0.05$&$0.06$&$0.07$&$0.10$&$0.14$&$0.20$&$0.25$&$0.31$&$0.38$&$0.43$\\\\\n\\hline$y$&$0.10$&$0.14$&$0.23$&$0.37$&$0.59$&$0.79$&$1.00$&$1.12$&$1.19$&$1.25$\\\\\n\\hline\n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031183": { + "id": "031183", + "content": "下表是研究某品种小麦的施肥量与小麦产量之间关系时所获得的数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}\n\\hline 亩施肥量$x / \\text{kg}$& 0 &$2.5$& 5 &$7.5$& 10 &$12.5$& 15 &$17.5$& 20 \\\\\n\\hline 亩产量$y / \\text{kg}$& 76 & 150 &$202.5$&$273.5$&$326.5$& 396 & 436 & 420 & 390 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n可以求得$y$与$x$的线性相关系数约为$0.9375, y$与$x$具有很强的线性相关关系. 不过, 从下面的散点图可以看出, 当施肥量超过$15 \\text{kg}$时, 小麦产量在下降, 这与经验判断一致 : 过量施肥会降低农作物产量.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw [->] (0,0) -- (5.5,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,5.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i/\\j in {1/100,2/200,3/300,4/400,5/500}\n{\\draw [dashed,gray] (5,\\i) -- (0,\\i) node [left] {$\\j$};};\n\\foreach \\i/\\j in {1/5,2/10,3/15,4/20,5/25}\n{\\draw [dashed,gray] (\\i,5) -- (\\i,0) node [below] {$\\j$};};\n\\foreach \\i/\\j in {0/0.76,0.5/1.5,1/2.025,1.5/2.735,2/3.265,2.5/3.96,3/4.36,3.5/4.2,4/3.9}\n{\\filldraw (\\i,\\j) circle (0.03);};\n\\end{tikzpicture}\n\\end{center}\n(1) 施肥量在怎样的范围内, 线性回归模型的拟合效果比较好?\\\\\n(2) 感兴趣的同学可以查阅相关资料, 尝试用二次函数模型进行拟合, 并与线性回归模型比较, 看哪种模型更加符合本题中的现实问题.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031184": { + "id": "031184", + "content": "某桑场为了解职工发生皮炎是否与采桑有关, 对其工作人员进行了一次调查, 结果如下表. 问: 发生皮炎是否与采桑有关?\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 采桑 & 不采桑 & 合计 \\\\\n\\hline 患皮炎 & 18 & 12 & 30 \\\\\n\\hline 末患皮炎 & 4 & 78 & 82 \\\\\n\\hline 合计 & 22 & 90 & 112 \\\\\n\\hline\n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031185": { + "id": "031185", + "content": "为了鉴定新疫苗的效力, 将$60$只豚鼠随机地分为两组, 在其中一组接种疫苗后, 两组都注射了病源菌, 其结果列于下表. 问: 能否有$90 \\%$的把握认为新疫苗有效?\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 发病 & 没发病 & 合计 \\\\\n\\hline 接种 & 3 & 27 & 30 \\\\\n\\hline 没接种 & 17 & 13 & 30 \\\\\n\\hline 合计 & 20 & 40 & 60 \\\\\n\\hline\n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031186": { + "id": "031186", + "content": "某医疗研究机构为了解打鼾与患心脏病的关系, 进行了一次抽样调查, 得到如下数据. 问: 打鼾与患心脏病是否有关?\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 患心脏病 & 未患心脏病 & 合计 \\\\\n\\hline 每一晚都打鼾 & 30 & 224 & 254 \\\\\n\\hline 不打鼾 & 24 & 1355 & 1379 \\\\\n\\hline 合计 & 54 & 1579 & 1633 \\\\\n\\hline\n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031187": { + "id": "031187", + "content": "为了解小麦种子是否灭菌与小麦发生黑穗病的关系, 经试验观察, 得到如下数据. 根据这组数据, 能否认为发生黑穗病与种子是否灭菌有关?\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 种子灭菌 & 种子末灭菌 & 合计 \\\\\n\\hline 有黑穗病 & 26 & 184 & 210 \\\\\n\\hline 无黑穗病 & 50 & 200 & 250 \\\\\n\\hline 合计 & 76 & 384 & 460 \\\\\n\\hline\n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031188": { + "id": "031188", + "content": "下表所示的是关于$11$岁儿童患花粉热与湿疹情况的调查数据. 若按$95 \\%$的可靠性的要求, 则对$11$岁儿童能否做出花粉热与湿疹有关的结论?\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 患花粉热 & 末患花粉热 & 合计 \\\\\n\\hline 患湿疹 & 141 & 420 & 561 \\\\\n\\hline 末患湿疹 & 928 & 13525 & 14453 \\\\\n\\hline 合计 & 1069 & 13945 & 15014 \\\\\n\\hline\n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031189": { + "id": "031189", + "content": "一个随机抽取的样本包括$110$位女士和$90$位男士, 女士中约有$9 \\%$是左利手, 男士中约有$11 \\%$是左利手. 基于这些数据, 你认为在样本所代表的总体中, 左利手与性别有关吗? 为什么?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031190": { + "id": "031190", + "content": "``使用动物做医学实验是正确的, 这样做能够挽救人的生命''. 某机构调查了 1152 位成年人对这种说法的态度, 以下是调查对象回答情况的列联表:\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline 回答情况 & 男性 & 女性 \\\\\n\\hline 同意 & 346 & 306 \\\\\n\\hline 不置可否 & 87 & 139 \\\\\n\\hline 不同意 & 83 & 191 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 用适当的方式描述男性与女性对该问题态度的差异 (比例、图或文字均可).\\\\\n(2) 你能用独立性检验的思想方法研究``男性与女性对该问题态度的差异''吗? 如果希望解决这个问题, 请在独立研究的基础上, 查阅相关资料, 给出你的结论.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031191": { + "id": "031191", + "content": "如果$x, y$之间的一组数据如下表所示, 那么回归直线必过的一个定点坐标是\\blank{50}.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline$x$& 0 & 1 & 2 & 3 \\\\\n\\hline$y$& 1 & 2 & 5 & 8 \\\\\n\\hline\n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031192": { + "id": "031192", + "content": "下表中的数据是关于青年观众的性别与是否喜欢戏剧的调查数据, 那么女性青年观众喜欢戏剧的频率与男性青年观众喜欢戏剧的频率的比值是\\blank{50}.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 不喜欢戏剧 & 喜欢戏剧 & 合计 \\\\\n\\hline 男性青年观众 & 40 & 10 & 50 \\\\\n\\hline 女性青年观众 & 40 & 60 & 100 \\\\\n\\hline 合计 & 80 & 70 & 150 \\\\\n\\hline\n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031193": { + "id": "031193", + "content": "某单位通过对数据的统计与分析得知, 日用电量$y$(单位:$\\text{kW} \\cdot \\text{h}$) 与当天平均气温$x$(单位:${ }^{\\circ} \\text{C}$) 之间线性相关, 且线性回归方程为$\\hat{y}=-2 x+60$. 据此可以预测, 当平均气温为$-4^{\\circ} \\text{C}$时, 日用电量的度数约为\\blank{50}.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031194": { + "id": "031194", + "content": "已知变量$y$与$x$线性相关, 若$\\overline {x}=5$, $\\overline {y}=50$, 且$y$与$x$的线性回归直线的斜率为$6.5$, 则线性回归方程是\\blank{50}.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031195": { + "id": "031195", + "content": "为了考察某种药物预防疾病的效果, 进行动物试验后得到如下数据. 经过计算得$\\chi^2 \\approx 6.979$, 根据$\\chi^2$临界值表, 可以认为该种药物对预防疾病有效果的把握为\\blank{50}.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 患病 & 末患病 & 合计 \\\\\n\\hline 服用药 & 10 & 46 & 56 \\\\\n\\hline 末服用药 & 22 & 32 & 54 \\\\\n\\hline 合计 & 32 & 78 & 110 \\\\\n\\hline\n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031196": { + "id": "031196", + "content": "已知$x$, $y$的取值如下表所示, 从散点图分析可知$y$与$x$线性相关, 如果线性回归方程为$\\hat{y}=0.95 x+2.6$, 那么表格中的数据$m$的值为\\blank{50}.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline$x$& 0 & 1 & 3 & 4 \\\\\n\\hline$y$&$2.2$&$4.3$&$4.8$&$m$\\\\\n\\hline\n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031197": { + "id": "031197", + "content": "某中学对$50$名学生的学习兴趣和主动预习情况进行了长期的调查, 得到的统计数据如下表所示. 试运用独立性检验的思想方法判断: 是否有$99 \\%$以上的把握认为, 学生的学习兴趣与主动预习有关.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline & 主动预习 & 不太主动预习 & 合计 \\\\\n\\hline 学习兴趣高 & 18 & 7 & 25 \\\\\n\\hline 学习兴趣一般 & 6 & 19 & 25 \\\\\n\\hline 合计 & 24 & 26 & 50 \\\\\n\\hline\n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031198": { + "id": "031198", + "content": "为了对某班考试成绩进行分析, 现从全班同学中随机抽取$8$位, 他们的数学、物理成绩如下表所示. 根据表中数据分析: 变量$x$与$y$是否具有线性相关关系.\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|c|c|}\n\\hline 学生编号 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\\\\n\\hline 数学分数$x$& 60 & 65 & 70 & 75 & 80 & 85 & 90 & 95 \\\\\n\\hline 物理分数$y$& 72 & 77 & 80 & 85 & 88 & 90 & 93 & 95 \\\\\n\\hline\n\\end{tabular}\n\\end{center}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031199": { + "id": "031199", + "content": "某兴趣小组欲研究昼夜温差大小与患感冒人数多少之间的关系, 他们分别到气象局与某医院抄录了$1-6$月份每月$10$日的昼夜温差情况与因患感冒而就诊的人数, 得到如下资料:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline 日期 & 1 月 10 日 & 2 月 10 日 & 3 月 10 日 & 4 月 10 日 & 5 月 10 日 & 6 月 10 日 \\\\\n\\hline 昼夜温差$x /{ }^{\\circ} \\text{C}$& 10 & 11 & 13 & 12 & 8 & 6 \\\\\n\\hline 就诊人数$y$& 22 & 25 & 29 & 26 & 16 & 12 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n该兴趣小组确定的研究方案是: 先从这$6$组数据中选取$2$组, 用剩下的$4$组数据求线性回归方程, 再用被选取的$2$组数据进行检验.\\\\\n(1) 若选取的是$1$月与$6$月的两组数据, 请根据$2-5$月份的数据, 求出$y$关于$x$的线性回归方程$\\hat{y}=\\hat{b} x+\\hat{a}$;\\\\\n(2) 若由线性回归方程得到的估计数据与所选出的检验数据的误差均不超过$2$人, 则认为得到的线性回归方程是理想的. 问: 该小组所得线性回归方程是否理想?", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031200": { + "id": "031200", + "content": "下表提供了某厂进行技术改造后生产产品过程中记录的产量$x$(单位:$\\text{t})$与相应的生产能耗$y$(单位:$\\text{t}$标准煤)的几组对应数据:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|}\n\\hline$x / \\text{t}$& 3 & 4 & 5 & 6 \\\\\n\\hline$y / \\text{t}$标准煤 &$2.5$& 3 & 4 &$4.5$\\\\\n\\hline\n\\end{tabular}\n\\end{center}\n(1) 请画出表中数据的散点图, 并求出$y$关于$x$的线性回归方程$\\hat{y}=\\hat{b} x+\\hat{a}$;\\\\\n(2) 已知该厂技术改造前$100 \\text{t}$产品的生产能耗为$90 \\text{t}$标准煤, 试根据(1)中求出的线性回归方程, 预测该厂技术改造后$100 \\text{t}$产品的生产能耗比技术改造前降低了多少$\\text{t}$标准煤.", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "苏教版教材习题", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031201": { + "id": "031201", + "content": "设$x_i$($i=1,2,3,\\cdots,100$)和$y_i$($i=1,2,\\cdots,100$)是两组两两不同的数据, 以$x_i$为解释变量, $y_i$为反应变量计算可得相关系数$r_1$, 拟合直线的斜率为$\\hat{a}_1$; 以$y_i$为解释变量, $x_i$为反应变量计算可得相关系数$r_2$, 拟合直线的斜率为$\\hat{a}_2$. 则关于$r_1,r_2,\\hat{a}_1,\\hat{a}_2$的以下两个结论: \\textcircled{1} $r_1$一定与$r_2$相等; \\textcircled {2} $\\hat{a}_1\\cdot \\hat{a}_2$一定等于$1$, 它们的真假情况为\\bracket{20}.\n\\fourch{\\textcircled{1}和\\textcircled{2}都为真}{\\textcircled{1}和\\textcircled{2}都为假}{\\textcircled{1}为真, \\textcircled{2}为假}{\\textcircled{1}为假, \\textcircled{2}为真}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031202": { + "id": "031202", + "content": "若一组成对数据$x_i$($i=1,2,\\cdots,n$)与$y_i$($i=1,2,\\cdots,n$)的相关系数为$0.4$, 则$x_i$($i=1,2,\\cdots,n$)与$-y_i+0.1$($i=1,2,\\cdots,n$)的相关系数为\\bracket{20}.\n\\fourch{$0.5$}{$0.4$}{$-0.3$}{$-0.4$}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "031203": { + "id": "031203", + "content": "为了判断甲、乙两种药物对某疾病的疗效是否有显著差异, 在两个地区分别进行了采样, 所得的列联表如下:\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline\nA地区 & 治愈 & 未治愈 & 合计 \\\\ \\hline\n药物甲 & $a$ & $b$ & $a+b$ \\\\ \\hline\n药物乙 & $c$ & $d$ & $c+d$ \\\\ \\hline\n合计 & $a+c$ & $b+d$ & $a+b+c+d$\\\\ \\hline\n\\end{tabular}\n\\begin{tabular}{|c|c|c|c|}\n\\hline\nB地区 & 治愈 & 未治愈 & 合计 \\\\ \\hline\n药物甲 & $3a$ & $3b$ & $3a+3b$ \\\\ \\hline\n药物乙 & $3c$ & $3d$ & $3c+3d$ \\\\ \\hline\n合计 & $3a+3c$ & $3b+3d$ & $3a+3b+3c+3d$\\\\ \\hline\n\\end{tabular}\n\\end{center}\n巧合的是, B地区每一类型的人数恰好是A地区的$3$倍. 规定显著性水平为$p=0.05$, 则以下两个论断:\\\\\n\\textcircled{1} 如果A地区的数据支持两种药物的疗效有显著差异, 那么B地区的数据一定支持两种药物的疗效有显著差异;\\\\\n\\textcircled{2} 如果A地区的数据支持两种药物的疗效无显著差异, 那么B地区的数据一定支持两种药物的疗效无显著差异. 正确与否的情况为\\bracket{20}.\n\\fourch{\\textcircled{1}和\\textcircled{2}都正确}{\\textcircled{1}和\\textcircled{2}都错误}{\\textcircled{1}正确, \\textcircled{2}错误}{\\textcircled{1}错误, \\textcircled{2}正确}", + "objs": [], + "tags": [ + "第九单元" + ], + "genre": "", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20230110\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" } } \ No newline at end of file