The Rocky Mountain district sales manager of Rath Publishing Inc., a college tex
ID: 3200335 • Letter: T
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 40 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 38 sales representatives reveals that the mean number of calls made last week was 41. The standard deviation of the sample is 2.6 calls. Using the 0.025 significance level, can we conclude that the mean number of calls per salesperson per week is more than 40? H0 : 40 H1 : > 40 1.
Compute the value of the test statistic.?
Explanation / Answer
Solution:
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: < 40
Alternative hypothesis: > 40
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.025. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 0.42178
DF = n - 1 = 38 - 1 = 37
t = (x - ) / SE
t = 2.371
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of 2.371. We use the t Distribution Calculator to find P(t > 2.371) = 0.01153.
Thus the P-value in this analysis is 0.01153
Interpret results. Since the P-value (0.01153) is less than the significance level (0.025), we have to reject the null hypothesis.
From this we can conclude that we have strong evidence in the favor of the claim that the mean number of calls per salesperson per week is more than 40.
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