Respuesta :
Answer:
No, we cannot conclude that the mean number of calls per salesperson per week is more than 41.
Step-by-step explanation:
We are given that a college textbook publishing company, claims that the sales representatives make an average of 41 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 42. The standard deviation of the sample is 3.9 calls.
Let [tex]\mu[/tex] = mean number of calls per salesperson per week
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 41 sales calls per week {means that the mean number of calls per salesperson per week is less than or equal to 41}
Alternate Hypothesis, [tex]H_a[/tex] : [tex]\mu[/tex] > 41 sales calls per week {means that the mean number of calls per salesperson per week is more than 41}
The test statistics that will be used here is One-sample t test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X -\mu}{{\frac{s}{\sqrt{n} } } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\mu[/tex] = sample mean number of calls made last week = 42 calls
s = sample standard deviation = 3.9 calls
n = sample of sales representatives = 38
So, test statistics = [tex]\frac{42-41}{{\frac{3.9}{\sqrt{38} } } }[/tex] ~ [tex]t_3_7[/tex]
= 1.581
Now at 0.025 significance level, the t table gives critical value of 2.026 at 37 degree of freedom for right-tailed test. Since our test statistics is less than the critical value of t so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the mean number of calls per salesperson per week is less than or equal to 41.
