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Answer:
We conclude that the mean number of calls per salesperson per week is more than 37.
Step-by-step explanation:
We are given that the Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 37 sales calls per week on professors.
To investigate, a random sample of 41 sales representatives reveals that the mean number of calls made last week was 40. The standard deviation of the sample is 5.6 calls.
<em><u>Let </u></em><em><u> = true mean number of calls per salesperson per week.</u></em>
SO, <u>Null Hypothesis</u>, :
37 {means that the mean number of calls per salesperson per week is less than or equal to 37}
<u>Alternate Hypothesis,</u> :
> 37 {means that the mean number of calls per salesperson per week is more than 37}
The test statistics that will be used here is <u>One-sample t test statistics</u> as we don't know about the population standard deviation;
T.S. = ~
where, = sample mean number of calls made last week = 40
s = sample standard deviation = 5.6 calls
n = sample of sale representatives = 41
So, <em><u>test statistics</u></em> = ~
= 3.43
Hence, the value of test statistics is 3.43.
<em>Now at 0.025 significance level, the t table gives critical value of 2.021 at 40 degree of freedom for right-tailed test. Since our test statistics is more than the critical value of t as 3.43 > 2.021, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.</em>
Therefore, we conclude that the mean number of calls per salesperson per week is more than 37.