Confidence Intervals and Sample Size-

1. A study of 40 bowlers showed that their average score was 186. The standard deviation of the population is 6.

(a) Construct a 95% confidence interval for the mean score of all bowlers.

(b) Construct a 95% confidence interval for the mean score of all bowlers if a sample of size 100 is used instead of 40.

(c) Explain why one confidence interval is larger than the other.

2. A health care professional wishes to estimate the birth weights of infants. How large a sample must she select if she desires to be 90% confident that the true mean is within 6 ounces of the sample mean? The standard deviation is estimated to be 8 ounces.

3. A random sample of 78 students were interviewed and 59 said they would vote for Jennifer McNamara as student body president. Let p represent the proportion of all students who will vote for Jennifer. Find a 90% confidence interval for p.

4. As part of an Environmental Studies class project students measured the circumference of a random sample of 45 Blue Spruce trees near Brainard Lake, Colorado. The sample mean circumference was 29.8 inches. Assume that σ is known to be 7.2 inches. Find a 95% confidence interval for the population mean circumference of all Blue Spruce trees near this lake.

5. A random sample of 56 credit card holders showed that 41 regularly paid their credit card bills on time. Find a 95% confidence interval for the proportion of all people who regularly paid their credit card bill on time.

6. A researcher wants to know what percentage of males athletes wear contact lenses during performances. Let p represent the proportion of males athletes who wear contact lenses. If there is no preliminary estimate for p, how many male athletes should be included in a random sample to be 90% sure that a point estimate for p will be within a distance of 0.05 from p.

7. A sample of 25 novels has a standard deviation of 9 pages. Find the 95% confidence interval of the population standard deviation.