Question

Is the mean salary of accountants who have reached partnership status higher than that for accoun... 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 $62,000 with a standard deviation of $5,500. A sample of 12 accountants who were not partners showed a mean of $58,000 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. Find the critical value: c. Compute the value of the test statistic. d. What is your decision regarding the null hypothesis?

Answer 1

Claim: Accountants at the partnership level earn larger salaries.

a) The null and alternative hypothesis is

b) Level of significance = 0.05

Degrees of freedom = n1 + n2 - 2 = 15 + 12 - 2 = 25

Critical value = 1.708 ( Using t table)

c) For doing this test first we have to check the two groups have population variances are equal or not.

The null and alternative hypothesis is

Test statistic is

F = largest sample variance / Smallest sample variances

n1 = 15

= 62000

= 5500^2 = 30250000

n2 = 12

= 58000

= 6500^2 = 42250000

F = 42250000 / 30250000 = 1.40

Degrees of freedom = n1 - 1 , n2 - 1 = > 15 - 1 , 12 - 1 = > 14 , 11

Critical value = 2.739 ( Using f table)

F < critical value we fail to reject null hypothesis.

Conclusion: Population variances are equal, so we have to use pooled variance.

Test statistic is

d) Test statistic > critical value we reject null hypothesis.

Conclusion:

Accountants at the partnership level earn larger salaries.