Question

Independent random samples taken at two companies provided the following information regarding annual salaries of the employees. The population standard deviations are also given below.

	Company A	Company B
Sample Size	72	50
Sample Mean (in $1000)	48	43
Population Standard Deviation (in $1000)	12	10

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a.	We want to determine whether or not there is a significant difference between the average salaries of the employees at the two companies. Compute the test statistic.
b.	Compute the p-value; and at α = .05, test the hypotheses.

Answer 1

we have given

Company A	Company B
Sample Size (n)	72	50
Sample Mean )	48	43
Population Standard Deviation ()	12	10

H0:u₁=u₂

H1 : u₁u₂

Based on the information provided, the significance level is α=0.05, and the critical value for a two-tailed test is z_c​=1.96

z-statistic =

z-statistic = =

z-statistic = 2.5

Since it is observed that ∣z∣=2.5>zc​=1.96, it is then concluded that the null hypothesis is rejected.and concluded that there is a not significant difference between the average salaries of the employees at the two companies.\

b )The p-value isp=0.0124, and since p=0.0124<0.05, it is concluded that the null hypothesis is rejected.and concluded that there is a not significant difference between the average salaries of the employees at the two companies.\