Question

the Department of Mental Health and Addiction Services, and Tobacco Prevention and Enforcement Program teamed up to see if stores around the area are obeying the law when it comes to selling tobacco to minors. The sting used underage teens hired by the Department of Mental Health and Addiction Services, they went into the stores and tried to buy tobacco products. The sting focused on 44 stores, of those 10 were caught violating the law by selling to someone under 18.

1) Is it safe to assume normality (Normal distribution) for p (proportion) from the above article?

2) Explain why.

3) Construct a 95 percent confidence interval for the above.

4) Using the 95 percent confidence level, what sample size would be needed to estimate the true proportion of stores selling cigarettes to minors with an error of ± 3 percent? (pages 322-323)

5) Using the 90 percent confidence level, what sample size would be needed to estimate the true proportion of stores selling cigarettes to minors with an error of ± 1 percent?

Answer 1

1) Yes, it is safe to assume the normality here.

2) This is because both the number of success and number failures here are more than 10.

3) The margin of error 95% confidence interval for a sample size of n is given by:

, here p= 10/44. We want this margin of error to be 0.03. Thus we have:

. Thus the answer is 750

4) The margin of error 90% confidence interval for a sample size of n is given by:

, here p= 10/44. We want this margin of error to be 0.01. Thus we have:

. Thus the answer is 4752