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 25 doors is made, and it is found that they have a mean of 2043.0 millimeters with a standard deviation of 6.0 Is there evidence at the 0.1 level that the doors are either too long or too short? 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

(A) Null hypothesis

Alternate hypothesis

(B)

test statistics t =

= -15/1.2

= -12.500

(C) Test is two tailed as want to test the doors are either too long or too short.

(D) degree of freedom = n- 1 = 25- 1 = 24

using t distribution table with df = 24 and alpha level 0.01, t critical = -2.797 and +2.797

We will reject the null hypothesis if t calculated is below -2.797 or above +2.797

(E) Since the t calculated is below -2.797, we will reject the null hypothesis and conclude that the mean is not equal to 2058, i.e. the doors are either too long or too short