A financial planner wants to compare the yield of income- and growth-oriented mutual funds. Fifty thousand dollars is invested in each of a sample of 35 income-oriented and 40 growth-oriented funds. The mean increase for a two-year period for the income funds is $1100 with a standard deviation of $45. For the growth‑oriented funds the mean increase is $1090 with a standard deviation of $55. At the 0.01 significance level is there a difference in the mean yield of the two funds?
a. State the null and alternate hypotheses.
H0: _______________________
H1: _______________________
b. State the decision rule.
c. Compute the value of the test statistic.
d. Compute the p-value.
e. What is your decision regarding the null hypothesis?
2. Is the mean salary of accountants who have reached partnership status higher than that for accountants who are not partners? A sample of 15 accountants who have the partnership status showed a mean salary of $82,000 with a standard deviation of $5,500. A sample of 12 accountants who were not partners showed a mean of $78,000 with a standard deviation of $6,500. At the 0.05 significance level can we conclude that accountants at the partnership level earn larger salaries?
a. State the null and alternate hypotheses.
H0: _______________________
H1: _______________________
b. State the decision rule.
c. Compute the value of the test statistic.
d. Compute the p-value.
e. What is your decision regarding the null hypothesis?
3. The Human Resources Director for a large company is studying absenteeism among hourly workers. A sample of 120 day shift employees showed 15 were absent more than five days last year. A sample of 80 afternoon employees showed 18 to be absent five or more times. At the 0.01 significance level can we conclude that there is a higher proportion of absenteeism among afternoon employees?
a. State the null and alternate hypotheses.
H0: _______________________
H1: _______________________
b. State the decision rule.
c. Compute the value of the test statistic.
d. Compute the p-value.
e. What is your decision regarding the null hypothesis?
Youngsville: 2.2, 1.2, 1.9, 3.1, 1.8, 1.5
Northeast: 2.3, 1.5, 1.2, 1.4, 2.2
Corry: .9, .8, 1.1, 1.2, .7
4. The County Executive for Monroe County is concerned about the response time for the three fire companies in the county. Samples of the response times (in minutes) for each company follow. At the 0.05 significance level is there a difference in the mean response time?
a. State the null and alternate hypotheses.
H0:________________
H1:________________
b. State the decision rule.
c. Compute the value of the test statistic.
d. What is your decision regarding the null hypothesis? Interpret the result.