Question

a) Approximately 500 students take a particular college statistics course each year. As an exercise, each of the 500 students in the class is given a different random sample of the previous year's 500 final grades (in percentages) and asked to construct a 95% interval estimate of the previous year's overall average. Which of the following statements is correct? About 475 of the confidence intervals will contain the actual overall average for the previous year. It is probable that 475 of the confidence intervals will be identical. About 25 of the sample means will not be found in these confidence intervals. About 475 of the sample means will not be included in the confidence intervals. b) Suppose that a random sample of 48 retail salespeople is asked to record the number of days that their commissions exceed $100. A 99% confidence interval for the mean number of days turns out to be (15.96, 27.86). If instead a 90% confidence interval had been calculated, how would it differ from the 99% confidence interval The 90% confidence interval would the same as the 99% confidence interval. The 90% confidence interval would be wider. The 90% confidence interval would be narrower. None of the above can be determined without seeing the raw data. c) Justin and Hayley are conducting a study of restaurant servers who 'underestimate their yearly tip totals on their tax returns. They took a random sample of 100 servers and calculated a 99% confidence interval for the proportion of those who admit to underestimating their tip totals. What does a 99% confidence interval tell us in this case? Select the best answer I am confident that most (99%) of all servers will have underestimated their tips by the mean amount contained within the interval I am 99% confident that the minimum and maximum proportion of servers who admit to underestimating their tip totals will be captured by this interval I am 99% confident that this interval includes the sample proportion. I am 99% confident that this interval includes the true proportion of servers who would admit to underestimating their tip totals. d) The Human Resources Department at an electronics store gives aptitude tests to potential employees. The test is scored out of 100. A 95% confidence interval for the mean score for the population of new employees is constructed from the most recent sample (n = 30). The limits of the interval are (64, 70). The margin of error of this interval is O 0.03 03 O 6 0.06

Answer 1

a)here np=500*0.95 =475

About 475 of the confidence intervals will contain the actual overall average for the previous year.

b)

The 90% confidence interval would be narrower.

(because of smaller confidence coefficient)

c)

I am 99% confident that this interval includes the true proportion of servers who would admit to underestimating their tip totals.

d)

margin of error =(70-64)/2 =3