# MATHEMATICS

randomsample of 40 hours was used to determine the average. Find the 99% confidence interval of the population mean

2. A health care professional wishes to estimate the birth weights of infants. How large a samplemust be obtained if she desires to be 90% confident that the true mean is

1

is within 2 ounces of the sample mean? Assume σ = 8 ounces

3.A random sample of 10 children found that their average growth for the first year was

9.8 inches. Assume the variable is normally distributed and the standard deviation is

0.96 inch. Find the 95% confidence interval of the population mean for growth during the first year.

4. What is the margin of error E for problem #1?

5. For n = 80 and X = 40, calculate p and q.

6. Calculate a 95% confidence interval for *p *in problem #5.

7. A recent study indicated that 29% of 100 women over age 55 in the study were widows. How large of a sample must you take to be 90% confident that the estimate is within 0.05 of the true proportion of women over age 55 who are widows?

8. Find the 90% confidence interval for the variance and standard deviation for the number of named storms per year in the Atlantic Basin. A random sample of 10 years has been used, with a variance of 16.9 years.

9. Given the following claim: The average age of community college students is 24.6 years.

(a) State the null and the alternative hypothesis for this claim

(b) Is this a right tailed, left tailed, or two-tailed test?

10. For a specific year, the average score on the SAT Math test was 515. The variable is normally distributed with a population standard deviation of 100. The super-

intendent wishes to see ifher students scored significantly below the national average on the test. She randomly selects 36 students and finds that the mean is 509 and the

standard deviation is 100.At α = 0.10, is there enough evidence to support the claim?

11. A researcher wishes to test the claim that the average cost of tuition and fees at a four-year public college is greater than $5700. She selects a random sample of 36 four-year public colleges and finds the mean to be $5950. The population standard deviation is $659. Is there evidence to support the claim at α = 0.05 ? Use the p-value method.

12. A physician claims that joggers’ maximal volume oxygen uptake is greater than the average of all adults. A random sample of 15 joggers has a mean of 40.6 millimeters per kilogram and a standard deviation of 6 millimeters per kilogram. If the average of all adults is 36.7 millimeters per kilogram, is there enough evidence to support the physician’s claim at α = 0.05 ? Assume the variable is normally distributed.

13.Each month, an American household generates an average of 28 pounds of newspaper for garbage or recycling. Assume the variable is normally distributed and the standard deviation is 2 pounds.

(a) Find the probability that it will generate between 27 and 31 pounds.

(b) Find the probability that it will generate more than 30 pounds.