Question

The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 36 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 44 sales representatives reveals that the mean number of calls made last week was 40. The standard deviation of the sample is 4.5 calls. Using the 0.050 significance level, can we conclude that the mean number of calls per salesperson per week is more than 36? Hops 36 H: > 36 a. Compute the value of the test statistic. (Round your answer to 3 decimal places.) Value of the test statistic b. What is your decision regarding Ho? than 36 per week. HO. The mean number of calls is

Answer 1

Given : Sample size=n=44

Sample mean=

X = 40

Sample standard deviation=s=4.5

Population mean=

Mo = 36

Significance level=

g= 0,05

Here , the population standard deviation is unknown , but sample mean is greater than 30

Therefore , use Z test.

Hypothesis :
Ho :μ< 36
VS  
H, :μ> 36

a. The test statistic is ,

(1‘0)N+ 017 - x = 7

40-36 4. 5 元 =0.896

Critical value : ; From normal probability integral table

Za = 20,05 = 1.64

Rejection region is

(1.64 x)

centurion Rejection region Acceptance 2-0 Ya Critical region

Rejection Rule : If , then reject the null hypothesis , accept otherwise

ZSTAT > 2

b. Decision : Here ,

ZSTAT = 5.896 > Za = 1.64

Therefore , reject the null hypothesis.

Conclusion : Reject Ho. The mean number of calls is more than 36 per week.