Question

1. A sample size of n = 70 is drawn from a population with proportion p = 0.32. Let p̂ be the sample proportion.

1. Find p̂m and p̂s . Round the standard deviation to four decimal places.
2. Find )28.0p̂P ( > .
3. Find )40.0p̂P ( <

2.  On a certain television channel, 20% of the commercials are local advertisers. A sample of 150 commercials is selected. Would it be unusual for more than 26% of the commercials to be local advertisers? Be sure to support your answer.

3.   In a sample of 78 young adults, the average time per day spent sleeping was 7.09 hours. Assume the population standard deviation is 1.15 hours.

1. Construct a 90% confidence interval for the mean time spent sleeping. Round your result to three decimal digits.
2. Some health experts recommend that people get 8 hours or more of sleep per night. Based on your confidence interval, is it reasonable to believe that the mean number of hours of sleep for young people is 8 or more hours?
3. How large would the sample have to be so that a 95% confidence interval would have a margin of error of 0.2?

4.  According to a national report, a sample of 95 men aged 20-29 years had a mean waist size of 36.7 inches with a standard deviation of 8.9 inches.

1. Construct a 98% confidence interval for the mean waist size. Round your results to two decimal digits.
2. The results of a different study suggested the mean waist size is 38.7 inches. Based on your confidence interval, is it reasonable to believe that the mean waist size may be 38.7 inches?

5.  If we increase the confidence level and keep the sample size the same, we (circlene) increase / decrease the margin of error.

Answer 1