Question

The waiting time to check out of a supermarket has had a population mean of 10.99 minutes.​ Recently, in an effort to reduce the waiting​ time, the supermarket has experimented with a system in which there is a single waiting line with multiple checkout servers. A sample of 50 customers was​ selected, and their mean waiting time to check out was 9.78 minutes with a sample standard deviation of 5.8 minutes. Complete parts​ (a) through​ (d).

A. At the 0.10 level of​ significance, using the critical value approach to hypothesis​ testing, is there evidence that the population mean waiting time to check out is less than 10.99 ​minutes?

Reject or Do Not reject H0? There is sufficient or insufficient evidence to conclude that the population mean waiting time to check out is less than 10.99 minutes?

B) At the .010 level of significance, using the p-value approach to hypothesis testing, is there evidence that the population mean waiting time to check out is less than 10.99 minutes?

Reject or Do not reject H0? There is sufficient or insufficient evidence to conclude the population mean waiting time to check out is less than 10.99?

C) Interpret the meaning of the​ p-value in this problem. Choose the correct answer below

1) The​ p-value is the probability of obtaining a sample whose mean is 9.78

minutes or​ less, assuming the population mean is less than 10.99 minutes.

2) The​ p-value is the probability of obtaining a sample whose mean is 9.78 minutes or​ less, assuming the population mean is greater than or equal to 10.99 minutes.

3) The​ p-value is the probability of obtaining a sample whose mean is 9.78 minutes or​ greater, assuming the population mean is greater than or equal to 10.99 minutes.

D) Compare your conclusions in​ (a) and​ (b). Which of the following statements best describes the relationship between the conclusions in​ (a) and​ (b)?

1. The conclusions are different because the critical value approach and the​ p-value approach are two fundamentally different statistical methods.

         2) The conclusions are unrelated.

3). The conclusions are the​ same, by sheer coincidence.

4). The conclusions are the same because the critical value approach and the​ p-value approach are mathematically identical

Answer 1

It is given that

Population mean waiting time of supermarket is 10.99 min

Population mean is given as

Total number of customers =50

Mean waiting time is 9.78 minute

Sample standard deviation=5.8 minute

a)

We have to check weather there is any evidence that population mean waiting time to checkout is less than 10.99 minutes

at 0.10 level of significance using the critical value

let us suppose the hypothessi

(Left tailed test)

using level of significance

because sample size is large

and sample standard deviation is known

use Z test

Substitute the values & find value of Z

Critical value of Z at 0.10 level of significance will be -1.645

So calculate value of Z is more than Z critical

we do not reject null hypothesis

So there is insufficient evidence that population waiting time is less than 10.99 minutes

b)

At the .010 level of significance, using the p-value approach to hypothesis testing,we have to check weather  there evidence that the population mean waiting time to check out is less than 10.99 minutes

Level of significance is 0.10

As we know that P value =probability (Z<=-1.475)

The  P-Value is .070106. which is greater than >0.05

The result is significant at p < .10.

We will accept null hypothesis

So there is insufficient evidence that population waiting time is less than 10.99 minutes

c)

Interpret the meaning of the​ p-value in this problem. Choose the correct answer below

p value is probabibility that supermarket has mean waiting time to check out is 10.99

The​ p-value is the probability of obtaining a sample whose mean is 9.78

minutes or​ less, assuming the population mean is less than 10.99 minutes

d)

The conclusions are the same because the critical value approach and the​ p-value approach are mathematically identical