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 28 sales representatives reveals that the mean number of calls made last week was 42. The standard deviation of the sample is 2.1 calls. Using the 0.05 significance level, can we conclude that the mean number of calls per salesperson per week is more than 40?

Question

Mathematics

Jonathan

19 March, 03:52

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 28 sales representatives reveals that the mean number of calls made last week was 42. The standard deviation of the sample is 2.1 calls. Using the 0.05 significance level, can we conclude that the mean number of calls per salesperson per week is more than 40?

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Cortez Spears · Answer 1

Yes, the mean number is more than 40

Step-by-step explanation:

The null hypothesis

H0 = mean is 40

Let's make the t test

t = (x - mean) / standard deviation / √sample size

t = (42 - 40) / 2.1 / √28

t = 5.039

now we find t value for one tail, using a T-distribution table

df = n - 1 = 27

α = 0.05

so, t = 1.703

since our calculated t value is greater than the t for the table, the null hypothesis can be rejected. So the mean number of calls per salesperson per week is more than 40.