Question

A carpenter is making doors that are 2058.0 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 23 doors is made, and it is found that they have a mean of 2070.0 millimeters with a variance of 441.00. Is there evidence at the 0.05 level that the doors are too long and need to be trimmed? Assume the population distribution is approximately normal.

Step 1 of 5:

State the null and alternative hypotheses.

Step 2 of 5:

Find the value of the test statistic. Round your answer to three decimal places.

Step 3 of 5:

Specify if the test is one-tailed or two-tailed.

Step 4 of 5:

Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Step 5 of 5:

Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Solution :

Given that,

Population mean = = 2058

Sample mean = = 2070

Sample standard deviation = s = 21

Sample size = n = 23

Level of significance = = 0.05

1)

The null and alternative hypothesis is,  

Ho: 2058

Ha: 2058

2)

The test statistics,

t = ( - )/ (s/)

= ( 2070 - 2058 ) / ( 21 / 23 )

= 2.740

3)

This a right (One) tailed test.

4)

Critical value of  the significance level is α = 0.05, and the critical value for a right-tailed test is

= 1.717

t > 1.717

5)

Since it is observed that t = 2.740 > = 1.717, it is then concluded that the null hypothesis is rejected.