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 40?

Answer 1

GIVEN:

Sample size of sales representatives

Sample mean number of calls made last week

Sample standard deviation

The given problem is to test whether the mean number of calls per salesperson per week is more than 40, thus we use "One sample t test" to test this claim.

HYPOTHESIS:

The hypothesis is given by,

(That is, the mean number of calls per salesperson per week is not significantly different from 40.)

(That is, the mean number of calls per salesperson per week is more than 40.)

LEVEL OF SIGNIFICANCE:

TEST STATISTIC:

which follows t distribution with degrees of freedom.

CALCULATION:

CRITICAL VALUE:

The right tailed t critical value with degrees of freedom at significance level is .

DECISION RULE:

CONCLUSION:

Since the calculated t statistic (58.2) is greater than the t critical value (1.7033), we reject null hypothesis and conclude that the mean number of calls per salesperson per week is more than 40.