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# A sample of 120 observations revealed that p = 0.30. At the .05 significance level, can the null hypothesis be rejected?

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10. The following hypotheses are given.
H0: Pi equals 0.40
H1: Pi does not equal 0.40
A sample of 120 observations revealed that p = 0.30. At the .05 significance level, can the
null hypothesis be rejected?
a. State the decision rule.
b. Compute the value of the test statistic.
c. What is your decision regarding the null hypothesis?

Use the five-step hypothesis-testing procedure in solving the following problem:

19. A spark plug manufacturer claimed that its plugs have a mean life in excess of 22,100 miles. Assume the life of the spark plugs follows the normal distribution. A fleet owner purchased a large number of sets. A sample of 18 sets revealed that the mean life was 23,400 miles and the standard deviation was 1,500 miles. Is there enough evidence to substantiate the manufacturer's claim at the .05 significance level?

13. The null and alternate hypotheses are:
H0: u1 = u2
H1: u1 does not equal u2
A random sample of 10 observations from one population revealed a sample mean of 23
and a sample deviation of 4. A random sample of 8 observations from another population
revealed a sample mean of 26 and a sample standard deviation of 5. At the .05 significance level, is there a difference between the population means?

13. A senior accounting major at Midsouth State University has job offers from four CPA firms. To explore the offers further, she asked a sample of recent trainees how many months each worked for the firm before receiving a raise in salary. The sample information is submitted to MINITAB with the following results:
Analysis of Variance
Source D F SS MS F P
Factor 3 32.33 10.78 2.36 0.133
Error 10 45.67 4.57
Total 13 78.00
At the .05 level of significance, is there a difference in the mean number of months before a raise was granted among the four CPA firms?