1. One year Ron had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 3.11. Also, Betty had the lowest ERA of any female pitcher at the school with an ERA of 3.09. For the males, the mean ERA was 4.376 and the standard deviation was 0.663. For the females, the mean ERA was 4.829 and the standard deviation was 0.708. Find their respective z-scores. Which player had the better year relative to their peers, Ron or Betty? (Note: In general, the lower the ERA, the better the pitcher.)

Ron had an ERA with a z-score of ______

Betty had an ERA with a z-score of ______ (Round to two decimal places as needed.)

2. random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.55 hours, with a standard deviation of 2.35 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.26 hours, with a standard deviation of 1.81 hours. Construct and interpret a 90% confidence interval for the mean difference in leisure time between adults with no children and adults with children 12.

Let 1 represent the mean leisure hours of adults with no children under the age of 18 and 2 represent the mean leisure hours of adults with children under the age of 18.

The 90% confidence interval for 12 is the range from ____ hours to___ hours. (Round to two decimal places as needed.)

3. A television sports commentator wants to estimate the proportion of citizens who "follow professional football." Complete parts (a) through (c).

(a) What sample size should be obtained if he wants to be within 2 percentage points with 95% confidence if he uses an estimate of 54% obtained from a poll?

The sample size is_____

(Round up to the nearest integer.)

(b) What sample size should be obtained if he wants to be within 2 percentage points with 95% confidence if he does not use any prior estimates?

The sample size is______(Round up to the nearest integer.)

(c) Why are the results from parts (a) and (b) so close? A. The results are close because the confidence 95% is close to 100%.

B.The results are close because 0.54(10.54)=0.2484 is very close to 0.25. C. The results are close because the margin of error 2% is less than 5%

4. In a random sample of 81 audited estate tax returns, it was determined that the mean amount of additional tax owed was $3466 with a standard deviation of $2511.Construct and interpret a 90% confidence interval for the mean additional amount of tax owed for estate tax returns.

The lower bound is ____ (Round to the nearest dollar as needed.)

The upper bound is____(Round to the nearest dollar as needed.)

Interpret a 90% confidence interval for the mean additional amount of tax owed for estate tax returns. Choose the correct answer below.

A. One can be 90% confident that the mean additional tax owed is between the lower and upper bounds.

B. One can be 90% confident that the mean additional tax owed is greater than the upper bound.

C.One can be 90% confident that the mean additional tax owed is less than the lower bound.

5.A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 3 points with 99% confidence assuming s=11.5 based on earlier studies? Suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size required?

A 99% confidence level requires____ subjects. (Round up to the nearest subject.)

A 90% confidence level requires_______ subjects. (Round up to the nearest subject.)

How does the decrease in confidence affect the sample size required?

A. Decreasing the confidence level increases the sample size needed.

B. The sample size is the same for all levels of confidence.

C.Decreasing the confidence level decreases the sample size needed.

6. Construct a 95% confidence interval of the population proportion using the given information. x=120,n=200

The lower bound is ______

The upper bound is______ (Round to three decimal places as needed.)