Question

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

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.

Thus null and alternative hypothesis are:

Part b) Calculate the test statistic value

Part c) Determine the probability value

That is we have to find P-value:

First find df = degrees of freedom:

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 we get P-value = 0.0000

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

Smaller the P-value, more or stronger evidence against the null hypothesis.

That is we reject null hypothesis if P-value is very small or less than specified level of significance .

We have: P-value = 0.0000 < 0.05 level of significance, thus we reject null hypothesis.

Conclusion:

At 0.05 level of significance, we have sufficient evidence to conclude that the mean number of calls per salesperson per week is more than 40.