Question

Salary information regarding employees of two retail chains s is shown below.

1.   What is the null and alternative hypothesis if we want to determine whether the mean salary of employees of the two retail chains is different? (2 Points)

2.   Calculate the t statistic (2 Points)

3.   Using a level of significance of 0.05, what is the rejection rule for this test using the critical value approach? The degrees of freedom (df) for this test has been calculated and is equal to 66. (2 Points)

4.   Based on the above, what is the conclusion of this statistical test? (2 Points)

Store 1	Store 2
Sample Size	35	38
Sample Mean Salary (in 1,000)	45.6	40.1
Sample Standard Deviation	12.5	10.5

Answer 1

For Store 1 :     

x̅1 = 45.6, s1 = 12.5, n1 = 35    

For Store 2 :     

x̅2 = 40.1, s2 = 10.5, n2 = 38    

α = 0.05    

1). Null and Alternative hypothesis:

Ho : µ1 = µ2     

H1 : µ1 ≠ µ2     

2). Test statistic:     

t = (x̅1 - x̅2)/[√(s1²/n1 + s2²/n2 )] = 2.0266    

3). df = ((s1²/n1 + s2²/n2)²)/[(s1²/n1)²/(n1-1) + (s2²/n2)²/(n2-1) ] = 66.6753 = 66

Critical value :     

Two tailed critical value, t crit = T.INV.2T(0.05, 66 ) = ± 1.997

Reject Ho if t > 1.997 or if t < -1.997

4. Conclusion:

t = 2.0266 >1,997, Reject the null hypothesis.

There is enough evidence to conclude that the mean salary of employees of the two retail chains is different at 0.05 significance level.