Math 221 Week 6 Lab Name: Change the color of your answers to red or highlight your answers. Write complete sentences for answers when applicable. 1. Age Discrimination? The accompanying data below depict ages of applicants who were unsuccessful in winning promotion and ages of applicants who were successful in winning promotion (based on data from \"Debating the Use of Statistical Evidence in Allegations of Age Discrimination\" by Barry and Boland, American Statistican, Vol. 58, No. 2) Assume that the samples are simple random samples. Ages of Unsuccessful Applicants: 34 41 44 46 53 56 37 42 45 48 54 57 37 43 45 49 54 60 38 44 45 53 55 36 39 43 45 46 48 51 37 42 44 45 46 48 51 38 42 44 45 47 49 52 Ages of Successful Applicants: 33 38 43 44 45 47 49 54 a. Use Statcrunch to find the summary statistics for each group necessary to construct confidence interval for the mean age of applicants. For your convenience you can copy the date from Excel file \"Promotion\" under Doc Sharing Lab folder. Round statistics to 4 decimal places. Mean Unsuccessful Successful Standard Deviation b. Construct a 95% confidence interval for the mean of unsuccessful applicants and interpret it in words. c. Construct a 95% confidence interval for the mean of successful applicants and interpret it in words. d. Compare the two confidence intervals. What do you conclude about the issue of age discrimination? 2. Mean Grade Point Average: As part of a study of grade inflation, you want to estimate the mean grade point average of all current college students in the U.S. All grade point averages are to be standardized for a scale between 0 and 4. How many grade point averages must be obtained so that the sample mean is within 0.2 of the population mean? Assume that a 99 confidence level is desired. Also assume that a pilot study showed that the population standard deviation is estimated to be 0.79. a. Find the desired sample size for this study. b. Does it make sense to collect the entire sample at your college? Why or why not? 3. A medical researcher conjectures that smoking can result in wrinkled skin around the eyes. The researcher recruited 150 smokers and 250 nonsmokers to take part in an observational study and found that 95 of the smokers and 105 of the nonsmokers were seen to have prominent wrinkles around the eyes (based on a standardized wrinkle score administered by a person who did not know if the subject smoked or not). Results from the study are found in the table below: Smokers Nonsmokers Sample Size 150 250 Number with Prominent Wrinkles 95 105 a. Use the data to construct a 95% confidence interval estimate for the population proportion of smokers with prominent wrinkles around the eyes. b. Use the data to construct a 95% confidence interval estimate for the population proportion of non-smokers with prominent wrinkles around the eyes. c. Compare the confidence intervals from parts a and b. What can you conclude about the difference in proportion between smokers and non-smokers who have prominent wrinkles? Explain. 4. You plan to develop a new software system that you believe will surpass the success of Google and Facebook combined. In planning for the operating system that you will use, you need to estimate the percentage of computers that use Windows. How many computers must be surveyed in order to be 99% confident that your estimate is in error by no more than one percentage point? a. Assume that nothing is known about the percentage of computers with Windows operating systems. b. Assume that a recent survey suggest that about 90% of computers use Windows operating systems (based on data from Net Applications). c. Does the additional survey information from part (b) have much of an effect on the sample size that is required