Question

Winnipeg district sales manager of Far End Inc. a university textbook publishing company, claims that the sales representatives makes an average of 40 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 42 and variance is 4.41.

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 (1 Marks)
(b)     Calculate the test statistic value (2 Marks)
(c)     Determine the probability value (1 Marks)
(d) Provide an interpretation of the P-value (1 Mark)

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 40
Alternative Hypothesis, Ha: μ > 40

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (42 - 40)/(2.1/sqrt(28))
t = 5.04

P-value Approach
Probability = P-value = 0
p-value is the probability of getting a sample mean of 42 or greater if the true mean of population is 40.
As P-value < 0.05, reject the null hypothesis.