# Testing of hypothesis

These are word problems concerning hypothesis theory.

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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. What is the level of significance?

c. State the Critical Value.

d. State the decision rule.

e. Compute the value of the test statistic.

f. Formulate the decision rule.

g. Compute the p-value.

h. What is your decision regarding the null hypothesis?

13. 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. What is the level of significance?

c. State the Critical Value.

d. State the decision rule.

e. Compute the value of the test statistic.

f. Formulate the decision rule.

g. Compute the p-value.

h. What is your decision regarding the null hypothesis?

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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. What is the level of significance?

c. State the Critical Value.

d. State the decision rule.

e. Compute the value of the test statistic.

f. Formulate the decision rule.

g. Compute the p-value.

h. What is your decision regarding the null hypothesis?

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Two boats, the Parada (Italy) and the Oracle (USA), area competing for a spot in the upcoming America's Cup race. They race over a part of the course several times. Below are the sample times in minutes. At the .05 significance level, can we conclude that there is a difference in their mean times? (textbook problem 11-38).

Parada Oracle

12.9 14.1

12.5 14.1

11.0 14.2

13.3 17.4

11.2 15.8

11.4 16.7

11.6 16.1

12.3 13.3

14.2 13.4

11.3 13.6

10.8

19.0

a. State the null and alternate hypotheses.

H0: H1:

b. What is the level of significance?

c. State the Critical Value.

d. State the decision rule.

e. Compute the value of the test statistic.

f. Formulate the decision rule.

g. Compute the p-value.

h. What is your decision regarding the null hypothesis?

The President and CEO of Cliff Hanger International Airlines is concerned about high cholesterol levels of the pilots. In an attempt to improve the situation a sample of seven pilots is selected to take part in a special program, in which each pilot is given a special diet by the company physician. After six months each pilot's cholesterol level is checked again. At the 0.01 significance level can we conclude that the program was effective in reducing cholesterol levels?

Pilot Before After d

1 255 210

2 230 225

3 290 215

4 242 215

5 300 240

6 250 235

7 215 190

a. State the null and alternate hypotheses.

H0: H1:

b. What is the level of significance?

c. State the Critical Value.

d. State the decision rule.

e. Compute the value of the test statistic.

f. Formulate the decision rule.

g. Compute the p-value.

h. What is your decision regarding the null hypothesis?

#### Solution Summary

To test if there is significant difference in mean funds.