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)

Note: if you need to use symbols , please use

• "u" for population mean "μ",

• Ho and Ha for  for the null and alternate hypothesis,

• "Y-hat" for "ŷ", "alpha" for α

Answer 1

a] NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS HA:

b]

c] P value= 0.000

d] Since P value SMALLER THAN 0.05 THEREFORE SIGNIFICANT.

DECISION: REJECT NULL HYPOTHESIS H0.

CONCLUSION: WE HAVE SUFFICIENT EVIDENCE TO CONCLUDE THAT THE mean number of calls per salesperson per week is more than 40.