Question

Things to note

The mean time it takes a man to run a mile is known to be 25 minutes.

A running company has developed a shoe that claim provides faster times time. Scientists tested the new shoe on a sample of 25 individuals.

For this sample, the mean mile time was 20 mins.

The population standard deviation for the mile is known to be 7 minutes.

A level of significance of .01 is to be used to test if the new shoe provides faster mile times

Mean = 25 min

Sample size 25

Sample average time taken 20 minutes

Standard deviation 7 minutes.

A level of significance of .01

1.            State the null and alternative hypotheses

2.            Determine the critical value (cut-off point) for the test.

3.            a. Draw a diagram of the sampling distribution used to perform the test.

b. Label the horizontal axis of your diagram.   

c. Locate the critical value on your diagram.    

Answer 1

A running company has developed a shoe that claim provides faster times i.e Time taken < 25 minutes;

1. Null hypothesis : Ho : = 25

Alternative hypothesis : H1 : <25

2.

Level of significance : =0.01

For right left tailed test, Critical value for the test : -Z : -Z0.01 = - 2.3263

3.

Test Statistic :

Sample mean : = 20

Population standard deviation: = 7

Sample size : n= 25

Hypothesized mean : = 25

Test Statistic = -3.5714

As Value of the test statistic : z is less than Critical Value:Z0.01 i.e. ( -3.5714<-2.3263 ); Reject Null Hypothesis.

There is sufficient evidence to support the claim that new shoe provides faster times.