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 42 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 37 sales representatives reveals that the mean number of calls made last week was 44. The standard deviation of the sample is 2.9 calls. Using the 0.100 significance level, can we conclude that the mean number of calls per salesperson per week is more than 42?

Answer 1

Answer:

Sample size = n = 37

$x= 44$

$\sigma = 2.9$

Now we are supposed to find  that the mean number of calls per salesperson per week is more than 42?

Since n > 30 so we will use z test

$H_0:\mu\leq 42\\H_a:\mu > 42$

Formula : $z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

Substitute the values

$z=\frac{44-42}{\frac{2.9}{\sqrt{37}}}$

$z=4.195$

Z value at 0.100 is 1.64

Since the calculated z value is greater than the defined z value

So, we accept the null hypothesis

Hence we conclude that the mean number of calls per salesperson per week is not more than 42