1. The data set HEARTFAILUREPREDICTION contains randomly collected data that looks at several variables that play a role in heart failure prediction for 918 people in the United States. (For the curious, this set of open data can be found at https://www.kaggle.com/datasets/fedesoriano/heart-failure-prediction .)The variables of interest to us in this question are "cholesterol" (the serum cholesterol of study participants, in mm/dl)) and "sex" (the reported gender of study participants). 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 serum cholesterol of females differs from that of males. Use the 1% significance level.Include all steps of your hypothesis test, and make sure to justify your assumptions. (8 marks)
2. Use the proper analytical tools in R to obtain a 99% confidence interval for the difference in average serum cholesterol of female and male study participants. Are the assumptions met for this confidence interval? (3 marks)
3. Explain andinterpret the confidence interval obtained in part (b). Does the interval provide evidence to indicate that the average serum cholesterol differs between females and males? Does theinterval support the conclusion of the hypothesis test in part (a)? Justify your answer. (5 marks)
4. (Question is similar to lab quiz question). The dataset SUMMERSTUDENTS 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 1%, 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 (indicate) 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 "Yes" sample mean from the "No" sample mean. (8 marks)

Answers:

1. Your test statistic is 1.7883, your pvalue is 0.04073, and you reject your null hypothesis.
2. Your test statistic is 1.7883, your pvalue is 0.04073, and you fail to reject your null hypothesis.
3. Your test statistic is 1.7883, your pvalue is 0.08146, and you reject your null hypothesis.
4. Your test statistic is 1.7883, your pvalue is 0.08146, and you fail to reject your null hypothesis.

1. (Question is similar to lab quiz question). The dataset SUMMERSTUDENTS contains information from a random sample of 44 students who took Statistics at MacEwan in the summer term. Your columns (variable) of interest are YPOFF (a column that records student willingness to serve in political office (no, yes)) and YWKRPNEWS (a column that records weekly hours of student election news consumption). 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 there is significant evidence that the average weekly news hours of political consumption are less for a student in the no group than for a student in the yes group. Use a level of significance of 10%.

Choose the most correct (closest) answer. (8 marks)

Answers:

1. Your test statistic is -3.6411, your p-value is 0.001597 and you reject your null hypothesis.
2. Your test statistic is -3.6411, your p-value is 0.003197 and you reject your null hypothesis.
3. Your p-value is -3.6411, your p-value is 0.001597, and you fail to reject your null hypothesis.
4. Your test statistic is -3.6411, your p-value is 0.003197 and you fail to reject your null hypothesis.