Question 1 (35 pts) - A recent study of cardiovascular risk factors reported that 30% of adults meet criteria for hypertension. If 35 adults are assessed for hypertension, answer the following questions. Assume that the data follows a binomial distribution. a) Find the mean and SD of the distribution. (10 pts) b) Manually, find the probability that exactly 10 of them meet the criteria for hypertension? (10 pts) c) Using SPSS/stat trek/etc. determine the probability that no more than 25 meet the criteria for hypertension? Provide documentation such as a screenshot of stat trek of what you input and your final solution. (5 pts) d) Using SPSS/stat trek/etc., determine the probability that at least 20 meet the criteria for hypertension? Provide documentation such as a screenshot of stat trek of what you input and your final solution. Would you expect to see 20 or more people have hypertension of the 30? Explain. (10 pts)

Question 2 (25 pts) - A study from 2020 among 2,340 patients showed that diastolic blood pressures in this population are normally distributed with a mean of 77.8 and a standard deviation of 4.5. a) Manually find the probability a randomly selected person in this population has diastolic blood pressure above 86.6. (10 pts) b) What is the probability a randomly selected person in this population has diastolic blood pressure less than 71? (10 pts) c) Using stat trek/SPSS/etc., find the probability a randomly selected person in this population has diastolic blood pressure between 73 and 85? Provide documentation (i.e. screenshot) of results. (5 pts)

Question 3 (40 pts) - The following data is collected on a hypothetical set of 20 students. Students were asked to indicate: 1) How many total hours they spent on social media during an average week 2) Do you feel like time on social media leads to body dissatisfaction (yes/no). ID Hours on social media per week Social media leads to body dissatisfaction (Yes/No) ID Hours on social media per week Social media leads to body dissatisfaction (Yes/No) ID01 6 Yes ID11 4 Yes ID02 9 No ID12 3 No ID03 11 Yes ID13 8 No ID04 14 No ID14 14 Yes ID05 12 Yes ID15 12 Yes ID06 9 No ID16 8 Yes ID07 12 Yes ID17 7 No ID08 7 No ID18 10 No ID09 5 Yes ID19 11 No ID10 10 Yes ID20 1 No a) Use SPSS to make a histogram of the 'hours on social media per week' variable. (5 pts) b) Use SPSS to compute the sample mean and standard deviation of the data. (5 pts) c) Based on the mean and standard deviation calculated in part b, manually calculate the 95% confidence interval for the true mean hours spent on social media in a given week. (10 pts) d) Now use SPSS to calculate a 99% confidence interval for the true mean hours spent on social media in a given week. (10 pts) e) Interpret the 99% CI from part (d). (10 pts)

BONUS (5 pts) - You can use SPSS to assist you here. If you do provide evidence (i.e. screenshot, etc.) of output. a)Calculate the average hours spent on social media for those who responded 1) "Yes" to the social media and body dissatisfaction variable and 2) those who responded "No" to the social media and body dissatisfaction variable. (Hint: there should be 2 means reported.) b) Construct a 95% confidence interval for the true mean hours spent on social media for those who responded 1) "Yes" to the social media and body dissatisfaction variable and 2) those who responded "No" to the social media and body dissatisfaction variable. (Hint: there should be 2 confidence intervals reported.) c) Comment on the difference between the two means and the two confidence intervals. Looking at these results, does there seem to be a difference in the mean hours of time spent on social media for those who responded "Yes" to the social media and body dissatisfaction as compared to those who responded "No". Explain