这个作业是使用计量统计模型来统计痤疮医疗效果、澳洲幸福报告等
MATH 1065 – Quantitative Methods in Health

问题1(15分)
哪种治疗更好?一家制药公司为痤疮创造了一种新疗法。决定
新疗法是否比旧疗法更好,该公司进行了一项研究,其中
90例患者接受了旧的治疗,110例患者接受了新的治疗。结果,四个星期后
的治疗方法,总结如下:
治疗
健康)状况
改进未改进
旧版42 48
新42 68
表1.两种治疗的总体效果。表格值代表患者人数。
使用MINITAB构造此问题中要求的所有图表。
对于完整的标记,请确保包含适当的轴标签,有意义的标题和图例
与所有图形显示有关此问题。
(a)(6个标记)使用表1中的汇总数据构建100%堆叠的柱形图,以说明
治疗类型与结果之间的关系。可以得出什么结论
您的图表?做两个观察,引用从图表中估计的相关百分比。
(b)(6分)在研究开始时,对每个患者的痤疮严重程度进行了评估和分类
表示为“轻微”或“严重”。数据存储在一个名为Acne.xlsx的Excel文件中,该文件可以是
从课程网站的“数据”标签下载。使用此数据构建100%堆叠
柱状图说明了治疗类型与结果之间的关系
病情严重。您可以从图表中得出什么结论?做三
观察,并引用从图表中估算出的相关百分比。
MINITAB的其他说明:图形>条形图
单击确定,然后根据需要编辑图表。
(c)(3分)检查您从(a)和(b)部分获得的结果。是否可以确切地说出哪种治疗方法
更好?为什么?为什么不?简要说明。
3
问题2(25分)
澳大利亚如何比较?世界幸福报告(https://worldhappiness.report/)是一项调查
全球幸福感的排名依据其公民对自己的幸福感进行排名的156个国家
成为。该报告分析了国家的幸福分数以及认为会影响其幸福感的六个因素
市民对生活质量的看法:人均GDP,社会支持,健康的预期寿命,自由
做出生活选择,慷慨大方和对腐败的看法。我们对整体幸福感很感兴趣
分数和社会支持分数。该问题的数据存储在一个名为
Happiness.xlsx,可以从课程网站的“数据”选项卡下载。该文件中的变量
如下面所述:
名称说明
国家/地区名称
CountryCode三字母的国家代码
HappinessScore国家幸福分数来自对盖洛普世界民意测验的主要反应
评估问题,要求被访者按比例对他们目前的生活进行排名
从0 =“最糟糕的生活”到10 =“最佳可能的生活”。
社会支持对盖洛普世界民意调查的二进制响应的全国平均值(0 =否,1 =是)
(GWP)问题‘如果遇到麻烦,您有亲戚或朋友吗?
指望在需要时帮助您吗?’
表2. Happiness.xlsx中存储的数据的变量描述
要获得满分,请确保您所有的产品都包含适当的轴标签和有意义的标题
此问题的图形显示。
(a)(3分)使用MINITAB生成变量的直方图,箱形图和描述性统计量
“幸福分数”。
(b)(8分)使用(a)的输出,对幸福分数在整个社区中的分布进行评论
世界。特别是,简要讨论:
•分布的形状(主峰,对称);
•是否有异常值(按国家/地区名称标识);
•集中趋势和分散的适当措施。要获得满分,请确保您有理由
您选择的度量并解释相应的值。
(c)(3分)现在使用MINITAB生成直方图,箱形图和描述性统计
变量“ SocialSupport”。
(d)(8分)使用(c)的输出,对周围的社会支持分数分布进行评论
世界。特别是,简要讨论:
•分布的形状(主峰,对称);
•是否有异常值(按国家/地区名称标识);
•集中趋势和分散的适当措施。要获得满分,请确保您有理由
您选择的度量并解释相应的值。
(e)(3分)查找澳大利亚的总体幸福感分数和社会支持分数。多么不寻常
这些价值相对于其他国家而言吗?哪个值更不寻常,幸福
分数还是社会支持分数?简要说明。提示:使用z分数,但不要尝试计算
任何概率。
Question 3 (22 marks)
Are we getting enough iron? Iron is an important mineral that is involved in various bodily functions,
including the transport of oxygen in the blood, essential for providing energy for daily life. The average
person needs to absorb just a small amount of iron each day to stay healthy, but to achieve this we need
to consume several times that amount as our bodies absorb only a fraction of the iron contained in the
food we eat. The amount of dietary iron required as well as actual daily intake is different for different age
groups and life stages. In a 2003 report1 based on the data from the National Health and Nutrition
Examination Survey (NHANES) conducted annually in the US, investigators included the following summary
values (in mg) of daily iron intake for the 20-39 age group:
Mean Median Standard deviation
Female 13.7 11.7 8.9
Male 17.9 15.7 10.9
Table 3. Dietary daily intake of iron (mg) in the 20-39 age group by gender
For the following questions, use MINITAB and show your MINITAB output unless instructed
otherwise. Using standard Normal tables is not required.
For full marks, make sure you use correct statistical notation when expressing probabilities,
show all relevant steps and round off each result with a comment.
Not sure how to present your work? The template posted under Week 3 might help.
(a) (2 marks) Based on these summary measures, does it make sense to assume that daily iron intake
levels for males and females in the 20-39 age group are Normally distributed? Explain briefly.
(b) (4 marks) Suppose that we plan to observe the mean daily iron intake for 50 randomly selected
females aged between 20 and 39 years. State the distribution of this mean (given reason). Ensure you
include a justification as well as the values of the mean and standard deviation for this distribution.
(c) (6 marks) Using your answer to part (b), find the probability that a sample of 50 randomly selected
women in the 20-39 age group will have the mean daily iron intake of at least 18 mg, the
recommended daily intake (RDI) for that age group.
(d) (8 marks) Suppose that we plan to observe the mean daily iron intake for 50 randomly selected men
aged between 20 and 39 years. Use MINITAB to find the probability that their mean daily iron intake
is below the RDI for men in that age group of 8 mg. If you are using Normal distribution for this
calculation, clearly state what quantity is assumed to be Normal and why. Also include values of the
mean and standard deviation for this distribution.
(e) (2 marks) Based on your results from parts (c) and (d), what can you conclude about daily iron intake
in the US population? Do Americans in the 20 to 39 age group get enough iron? Explain briefly.
1 Wright, JD, Wang,CY, Kennedy-Stephenson, J, Ervin, RB, Dietary Intake of Ten Key Nutrients for Public Health,
United States: 1999-2000, Advance Data 334, 17 April 2003, 1-4.


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