Question

 

Independent random samples taken at two companies provided the following information regarding annual salaries of the employees.

	Whitney Co.	Max Co.
Sample Size	72	50
Sample Mean (in $1,000)	48	43
Sample Standard Deviation (in $1,000)	12	10

?

a.	Use Excel. We want to determine whether there is a significant difference between the average salaries of the employees at the two companies. Compute the test statistic.
b.	Use Excel. State the null and alternative hypotheses. Compute the p-value; and at 95% confidence, test the hypotheses and interpret the results.

Answer 1

 

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁ = u ₂
Alternative hypothesis: u₁ u ₂

Note that these hypotheses constitute a two-tailed test.  

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 2.00
DF = 120
t = [ (x₁ - x₂) - d ] / SE

t = 2.50

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is the size of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.

Since we have a two-tailed test, the P-value is the probability that a t statistic having 120 degrees of freedom is more extreme than -2.50; that is, less than -2.50 or greater than 2.50.

Thus, the P-value = 0.014.

Interpret results. Since the P-value (0.014) is less than the significance level (0.05), we cannot accept the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that there is a significant difference between the average salaries of the employees at the two companies.