Question

Winnipeg district sales manager of Far End Inc. a university textbook publishing company, claims that the sales representatives makes an average of 20 calls per week on professors. Several representatives say that the estimate is too low. To investigate, a random sample of 28 sales representatives reveals that the mean number of calls made last week was 44 and variance is 2.41.

Conduct an appropriate hypothesis test, at the 5% level of significance to determine if the mean number of calls per salesperson per week is more than 40.

(a)     Provide the hypothesis statement

(b)     Calculate the test statistic value

(c)     Determine the probability value

(d) Provide an interpretation of the P-value (1 Mark)

Answer 1

Solution:

Given:

Sample size = n = 28

Sample mean =

Sample Variance = s² = 2.41

Sample Standard Deviation = s = 1.552417

Level of significance = 0.05

We have to test  if the mean number of calls per salesperson per week is more than 40.

Part a)     Provide the hypothesis statement

Hypothesis statement : the mean number of calls per salesperson per week is more than 40.

Vs

Part b) Calculate the test statistic value

Part c) Determine the probability value

That is find P-value:

df = n - 1 = 28 - 1 = 27

Use following Excel command to get exact P-value:

=T.DIST.RT(t , df)

=T.DIST.RT(13.634, 27)

=6.34E-14

=0.0000

Thus P-value = 0.0000

Part d) Provide an interpretation of the P-value:

P-value is the probability of obtaining test results at least as extreme as results actually observed under the assumption that the null hypothesis is true.

Smaller the P-value, more or strong evidence against the null hypothesis. That is we reject null hypothesis when P-value is very small or less than level of significance.

Since P-value = 0.0000 < 0.05 level of significance, we reject null hypothesis and thus at 0.05 level of significance, we conclude that the mean number of calls per salesperson per week is more than 40.