The manager of an online shop wants to determine whether the mean length of calling time of its customers is significantly more than 3 minutes.A random sample of 100 customers was taken.The average length of calling time in the sample was 3.1 minutes with a standard deviation of 0.5 minutes.At a 0.05 level of significance,it can be concluded that the mean of the population is
A)significantly greater than 3.
B)not significantly greater than 3.
C)significantly less than 3.
D)significantly not different from 3.10.

Question

Quizplus · Accepted Answer

We need to conduct a one-sample t-test to determine if the sample mean length of calling time is significantly different from 3 minutes. The null and alternative hypotheses are:

H0: μ = 3
Ha: μ > 3

where μ is the population mean length of calling time.

Using a 0.05 level of significance, we can find the critical value for our t-distribution with 99 degrees of freedom (n-1):

tα,df= t0.05,99 = 1.660

The test statistic is calculated as:

t = (x̄ - μ) / (s / √n) = (3.1 - 3) / (0.5 / √100) = 2

where x̄ is the sample mean length of calling time, s is the sample standard deviation, and n is the sample size.

The calculated t-value (t = 2) is greater than the critical value (tα,df= 1.660), which means we reject the null hypothesis. We can conclude that the mean length of calling time of the population is significantly greater than 3 minutes. Therefore, the best choice is A.

The Manager of an Online Shop Wants to Determine Whether