Question

In a sample of 45 adults, the mean assembly time for a child's swing set was 1.76 hours with a standard deviation of 0.79 hours. The makers of the swing set claim the average assembly time is less than 2 hours. Test their claim at the 0.01 significance level.

(a) What type of test is this?

This is a right-tailed test.

This is a two-tailed test.    

This is a left-tailed test.

(b) What is the test statistic? Round your answer to 2 decimal places.
t_x =  

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value =  

(d) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀    

(e) Choose the appropriate concluding statement.

The data supports the claim that the mean assembly time is less than 2 hours.

There is not enough data to support the claim that the mean assembly time is less than 2 hours.     

We reject the claim that the mean assembly time is less than 2 hours.

We have proven that the mean assembly time is less than 2 hours.

Answer 1

Solution:

(a) What type of test is this?

Answer: This is a left-tailed test. because the claim is the average assembly time is less than 2 hours.

(b) What is the test statistic?

Answer:

The test statistic is:

  

  

  

(c) Use software to get the P-value of the test statistic.

Answer: Using the excel, we have:

Where:

2.04 is the absolute value of the test statistic

44 is the degrees of freedom

1 represents the one-tailed test.

(d) What is the conclusion regarding the null hypothesis?

Answer: fail to reject H0 because the p-value is greater than the significance level 0.01

(e) Choose the appropriate concluding statement.

Answer: We reject the claim that the mean assembly time is less than 2 hours.