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 50 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 51. The standard deviation of the sample is 1 calls. Using the 0.05 significance level, can we conclude that the mean number of calls per salesperson per week is more than 50

Answer 1

Answer)

Null hypothesis Ho : u = 50

Alternate hypothesis Ha : u > 50

Claimed mean = 50

Sample mean = 51

S.d = 1

As the population s.d is unknown here we will use t distribution to conduct the test

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

N = sample size = 28

t = (51-50)/(1/√28)

t = 5.292

Degrees of freedom is = n-1, 27

For df 27 and test statistics of 5.292

P-Value from t distribution is = < 0.00001

P-value is 0

As the obtained P-value is less than 0.05(given significance level)

We reject the null hypothesis

So, yes we have enough evidence to conclude that the mean number of calls per salesperson per week is more than 50