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?
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.
