Associate of the Society of Actuaries (ASA)
PhD, Statistics, Yale University, anticipated 2014
BA, Applied Mathematics, UC Berkeley, 2006
9. The Department of Economic and Community Development (DECD) reported that in 2005 the average number of new jobs created per county was 450. The department also provided the following information regarding a sample of 5 counties in 2006.
County New Jobs Created In 2006 Bradley 410 Rhea 480 Marion 407 Grundy 428 Sequatchie 400
Ho: mu >= 450 Ha: mu < 450
95% confidence level a. Compute the test statistic b. Compute the p-value c. Compute the critical value d. Reject or do not reject
10. The Bureau of Labor Statistics reported that the average yearly income of dentists in the year 2005 was $110,000. A sample of 81 dentists, which was taken in 2006, showed an average yearly income of $120,000. Assume the standard deviation of the population of dentists in 2006 is $36,000. Ho: mu <= $110,000 Ha: mu > $110,000 95% confidence level a. Compute the test statistic b. Compute the p-value c. Compute the critical value d. Reject or do not reject
11. A tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. Now the company is advertising that its new tires' life expectancy has increased. In order to test the legitimacy of the advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data.
Life Expectancy (In Thousands of Miles) 28 27 25 28 29 25
12. A new soft drink is being market tested. A sample of 400 individuals participated in the taste test and 100 indicated that they like the taste. We are interested in determining if more than 21% of the population will like the new soft drink.
H0: p <= 0.21 Ha: p > 0.21
13. In the past, the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older individuals. In order to determine whether there has been an increase in the average age of all the employees, a sample of 64 employees was selected. The average age in the sample was 45 years with a standard deviation of 16 years. Let = .05. H0: mu <= 40 Ha: mu > 40 95% confidence level a. Compute the test statistic b. Compute the p-value c. Compute the critical value d. Reject or do not reject
14. The average gasoline price of one of the major oil companies has been $2.20 per gallon. Because of cost reduction measures, it is believed that there has been a significant reduction in the average price. In order to test this belief, we randomly selected a sample of 36 of the company's gas stations and determined that the average price for the stations in the sample was $2.14. Assume that the standard deviation of the population () is $0.12.
H0: mu >= 2.20 Ha: mu < 2.20 95% confidence level a. Compute the test statistic b. Compute the p-value c. Compute the critical value d. Reject or do not reject
15. A lathe is set to cut bars of steel into lengths of 6 centimeters. The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 6 centimeters. A sample of 121 bars is selected randomly and measured. It is determined that the average length of the bars in the sample is 6.08 centimeters with a standard deviation of 0.44 centimeters.
H0: mu = 6 Ha: mu not equal to 6
16. An official of a large national union claims that the fraction of women in the union is not significantly different from one-half. Using the critical value approach and the sample information reported below, carry out a test of this statement. Let alpha = 0.05.
sample size 400 women 168 men 232
H0: P = 0.5 Ha: P not equal to 0.5
17. Consider the following hypothesis test:
Ho: mu >= 40 Ha: mu < 40
A sample of 49 provides a sample mean of 38 and a sample standard deviation of 7. 95% confidence level a. Compute the test statistic b. Compute the p-value c. Compute the critical value d. Reject or do not reject
18. A sample of 64 account balances from a credit company showed an average daily balance of $1,040. The standard deviation of the population is known to be $200. We are interested in determining if the mean of all account balances (i.e., population mean) is significantly different from $1,000.
Ho: mu = 1000 Ha: mu not equal to 1000
19. Automobiles manufactured by the Efficiency Company have been averaging 42 miles per gallon of gasoline in highway driving. It is believed that its new automobiles average more than 42 miles per gallon. An independent testing service road-tested 36 of the automobiles. The sample showed an average of 42.8 miles per gallon with a standard deviation of 1.2 miles per gallon.
Ho: mu <= 42 Ha: mu > 42 95% confidence level a. Compute the test statistic b. Compute the p-value c. Compute the critical value d. Reject or do not reject
