The Rocky Mountain district sales manager of Rath Publishing Inc., a college tex

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 40 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 32 sales representatives reveals that the mean number of calls made last week was 41. The standard deviation of the sample is 2.9 calls. Using the 0.010 significance level, can we conclude that the mean number of calls per salesperson per week is more than 40? H0 : 40 H1 : > 40 1. Compute the value of the test statistic. (Round your answer to 3 decimal places.) Value of the test statistic 2. What is your decision regarding H0? H0. The mean number of calls is than 40 per week.

Explanation / Answer

Soluton:

Null hypothesis: H0 =40

Alternate Hypothesis: Ha :>40

sample size=n=32

as the sample size is more than 30 use Z test one tail.

Formula:

sample mean= x bar=41

sample std dev=denominator =sigma/sqrt(n)=2.9/sqrt(32)=0.5127

population mean = =40

z (calc)=41-40/0.5127

=1/0.5127

z(calc) =1.9506

given level of significance=0.010=1%

confidencelevel=100-1=99%

confidence level 90% 95% 99%

z/2 1.645 1.96 2.575

from the above table cofidence level =99%

Z(table value)=2.575

Acceptance Region:

since Z calcvalue=1.9506 is less than Z table value of 2.575 at 1% level of significance.

Accept null hypothesis.

We statistically conclude that

the mean number of calls is
less than equal to 40.

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