Question 2 pertains to two-mean inference based on independent samples. In practice, there are two possible...

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Question 2 pertains to two-mean inference based on independent samples. In practice, there are two possible versions of this test: in one case, the "pooled" approach is used (if the sample variances are "close" in value, we assume equal population variances); in the other case the "unpooled" approach is used (if sample variances are not "close" in value, we do not assume equal population variances). Some instructors teach the pooled approach as the assumption of equal variances is necessary in other tests that look at comparing the means of several populations and, when the test is valid, the pooled approach is slightly more powerful. However, other instructors choose to not teach the pooled approach since the increase in statistical power is generally quite small, and it requires an additional assumption that should only be made that if we are very familiar with the background population. Your lecture instructor will let you know what approach you should use in the lecture. In the lab, we will solve all two independent sample problems using the non-pooled approach (i.e. without the assumption of equal variances). R allows for either approach; the default is "unpooled". Note: For two mean problems, R specifies the differences in means in alphabetical order. 2. Use R to perform the requested inference. (a) The dataset Insurance.xlxs contains information from random sample of 1338 policy holders of an insurance company. The variables of interest are "bmi" (the body mass index of policy holders) and "sex" (the reported gender of policy holders). You may assume the males and females are independent samples. Use the proper analytical tools in R to determine if there is significant evidence that the average BMI of females differs from that of males. Use the 10% significance level. Include all steps of your hypothesis test, and make sure to justify your assumptions. (7 marks) (b) Use the proper analytical tools in R with the dataset Insurance.xlsx to obtain a 90% confidence interval for the difference in average BMI of female and male policyholders. Does the interval provide evidence to indicate that the average BMI differs between females and males? (6 marks) (c) Interpret the confidence interval obtained in part (b). Does this interval support the conclusion of the hypothesis test in part (a)? Justify your answer. (4 marks: 2+2) (d) The dataset SummerStudents.xlsx contains information from a random sample of 44 students who took Statistics at MacEwan in the summer term. Your columns (variable) of interest are MUSICSTUDY (a column that records whether students listen to music while studying for an exam (no, yes)) and YAGE (a column that records student age). For education purposes assume that the two groups are two independent samples from a much larger normal population of statistics students and that the two populations have unequal variances. Use R to determine if, for a significance level of 5%, there is significant evidence that the mean age of students in the yes group is lower than the mean age of students in the no group. Choose the most correct (closest) answer. HINT. Be careful here. Recall that when doing a 2 independent samples t problem, R will calculate the numerator of the test statistic by subtracting the sample mean of the yeses from the sample mean of the nos. (7 marks) Question 2 pertains to two-mean inference based on independent samples. In practice, there are two possible versions of this test: in one case, the "pooled" approach is used (if the sample variances are "close" in value, we assume equal population variances); in the other case the "unpooled" approach is used (if sample variances are not "close" in value, we do not assume equal population variances). Some instructors teach the pooled approach as the assumption of equal variances is necessary in other tests that look at comparing the means of several populations and, when the test is valid, the pooled approach is slightly more powerful. However, other instructors choose to not teach the pooled approach since the increase in statistical power is generally quite small, and it requires an additional assumption that should only be made that if we are very familiar with the background population. Your lecture instructor will let you know what approach you should use in the lecture. In the lab, we will solve all two independent sample problems using the non-pooled approach (i.e. without the assumption of equal variances). R allows for either approach; the default is "unpooled". Note: For two mean problems, R specifies the differences in means in alphabetical order. 2. Use R to perform the requested inference. (a) The dataset Insurance.xlxs contains information from random sample of 1338 policy holders of an insurance company. The variables of interest are "bmi" (the body mass index of policy holders) and "sex" (the reported gender of policy holders). You may assume the males and females are independent samples. Use the proper analytical tools in R to determine if there is significant evidence that the average BMI of females differs from that of males. Use the 10% significance level. Include all steps of your hypothesis test, and make sure to justify your assumptions. (7 marks) (b) Use the proper analytical tools in R with the dataset Insurance.xlsx to obtain a 90% confidence interval for the difference in average BMI of female and male policyholders. Does the interval provide evidence to indicate that the average BMI differs between females and males? (6 marks) (c) Interpret the confidence interval obtained in part (b). Does this interval support the conclusion of the hypothesis test in part (a)? Justify your answer. (4 marks: 2+2) (d) The dataset SummerStudents.xlsx contains information from a random sample of 44 students who took Statistics at MacEwan in the summer term. Your columns (variable) of interest are MUSICSTUDY (a column that records whether students listen to music while studying for an exam (no, yes)) and YAGE (a column that records student age). For education purposes assume that the two groups are two independent samples from a much larger normal population of statistics students and that the two populations have unequal variances. Use R to determine if, for a significance level of 5%, there is significant evidence that the mean age of students in the yes group is lower than the mean age of students in the no group. Choose the most correct (closest) answer. HINT. Be careful here. Recall that when doing a 2 independent samples t problem, R will calculate the numerator of the test statistic by subtracting the sample mean of the yeses from the sample mean of the nos. (7 marks)