Question 1

A research firm conducted a survey to determine the mean amount steady smokers spend oncigarettes per week in Kingston, Jamaica. A sample of 100 steady smokers revealed that the mean amount spent on cigarettes per week is JA $3500 with a standard deviation of $500.

a. What is the point estimate for the mean amount spent on cigarettes per week for steady smokers in Kingston, Jamaica? If the researcher randomly selects another sample of 100 steady smokers in Kingston, do you expect the point estimate to change? Explain.

b. Using the 99% level of confidence, determine the confidence interval for . Explain what it indicates.

c. Suppose the researcher instead constructs a 95% confidence interval using the same sample size. Construct this new interval estimate for the population mean and compare it to the confidence interval that was calculated in part b.

d. Suppose the researcher constructs a 99% confidence interval for the mean amount spent on cigarettes per week for steady smokers in Kingston, Jamaica but instead of using a sample of 100, she now uses a sample of 150. Calculate this new interval estimate and compare it to the confidence interval that was calculated in part b.

e. What can you conclude based on the confidence intervals that you calculated in parts b, c, and d?

Question 2

The Academic Planning and Delivery Department (APAD) is concerned about the impact of full-time college students working while they are enrolled in classes, and they would like to know if students work too much and therefore are spending less time on their classes than they should be. First, they need to find out, on average, how many hours per week students are working. They know from previous studies that the standard deviation of this variable is about 10 hours. A survey of 50 full-time Open Campus students provides a sample mean of 20 hours worked per week.

a. APAD wants to construct a 99% confidence interval for the mean number of hours worked by college students. Explain to the APAD why a larger sample may give a better interval estimate than a sample of 50.

b. To prove your point to APAD, calculate the margin of error for a 99% confidence level using a sample of 50 students and a larger sample of your choice.

c. Suppose one day, a member of APAD finds a full-time student who works more than the number of hours per week estimated by the 99% confidence interval calculated from the information in part a. Explain to the APAD how this is possible.

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