Question

Managers at a local phone service wireless retail center have a goal that 75​% of the​ center's customers will have to wait less than five minutes for service. The data below shows the wait times of a random sample of 25 customers in minutes. Does this sample provide evidence that​ management's goal is being​ achieved? LOADING... Click the icon to view the random sample of wait times. Does this sample provide evidence that​ management's goal is being​ achieved? ​(Round to four decimal places as​ needed.) A. No​, because the probability of observing a sample proportion as low as the one in this sample given a population proportion of 0.75 is nothing​, which is less than 0.05. B. No​, because the probability of observing a sample proportion as low as the one in this sample given a population proportion of 0.75 is nothing​, which is more than 0.05. C. Yes​, because the probability of observing a sample proportion as low as the one in this sample given a population proportion of 0.75 is nothing​, which is less than 0.05. D. Yes​, because the probability of observing a sample proportion as low as the one in this sample given a population proportion of 0.75 is nothing​, which is more than 0.05.

4.2
5.1
2.9
9.6
3.3
3.6
0.3
7.6
4.1
3.2
4.3
2.8
3.1
9.7
6.1
5.4
4.4
0.3
2.3
5.2
4.4
3.3
2.4
2.7
4.3

Answer 1

Here

sample proportion of customers will have to wait less than five minutes for service

To test against

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 0.05 level of significance if P-value< 0.05

Now,

The value of the test statistic

Now,

The probability of observing a sample proportion as low as the one in this sample given a population proportion of 0.75 is

D. Yes​, because the probability of observing a sample proportion as low as the one in this sample given a population proportion of 0.75 is 0.364517 which is more than 0.05.