Question

A manager is trying to figure out which of her top 2 salespeople is the best, as measured by average number of sales made per week. Thus, she’s set up the following hypothesis test that they are equally as good, & if she can reject that hypothesis, she will conclude that the salesperson with the highest average weekly sales (Salesperson #2) is the best. She’s looked back at all the weeks worked for both employees to calculate the statistics below.

sales person 1 n1 = 80 , x¯1 = 104 ,σ1 = 8.4

Sales person 2 n2 = 70 ¯x2 = 106 σ2=7.6

a) Estimate the difference between the two population means. = -2

(b) Provide a 90% confidence interval for this mean difference.

(c) Provide a 95% confidence interval for this mean difference.

(d) Provide a 99% confidence interval for this mean difference.

(e) What is the value of the test statistic (the z -value)?

(f) What is the p-value?

(g) With α = 0.10, do you Reject H0 or Fail to reject H0?

(h) With α = 0.05, do you Reject H0 or Fail to reject H0?

Answer 1

Part a)

Confidence interval :-

Lower Limit =
Lower Limit = -4.1491
Upper Limit =
Upper Limit = 0.1491
90% Confidence interval is ( -4.1491 , 0.1491 )

Part b)

Confidence interval :-



Lower Limit =
Lower Limit = -4.5608
Upper Limit =
Upper Limit = 0.5608
95% Confidence interval is ( -4.5608 , 0.5608 )

Part c)

Confidence interval :-



Lower Limit =
Lower Limit = -5.3655
Upper Limit =
Upper Limit = 1.3655
99% Confidence interval is ( -5.3655 , 1.3655 )

Part e)

To Test :-

H0 :-  

H1 :-

Test Statistic :-


Z = -1.5307

Part f)

P value = 2 * P ( Z > -1.5307 ) = 0.1258

Part g)  (g) With α = 0.10, do you Reject H0 or Fail to reject H0?

Decision based on P value
P - value = P ( Z > -1.5307 ) = 0.1258
Reject null hypothesis if P value < α = 0.10 level of significance
P - value = 0.1258 > 0.10 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

Part h)  With α = 0.05, do you Reject H0 or Fail to reject H0?

Decision based on P value
P - value = P ( Z > -1.5307 ) = 0.1258
Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.1258 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis