Question

A carpenter is making doors that are 2058 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 6 doors is made, and it is found that they have a mean of 2072 millimeters with a standard deviation of 27. Is there evidence at the 0.01 level that the doors are too long and need to be trimmed? State the null and alternative hypotheses for the above scenario.

Answer 1

Answer:

There is no evidence that the doors are too long and need to be trimmed (H₀ is accepted)

Step-by-step explanation:

$\bar{X} = 2072\\\mu = 2058\\sample size, n = 6\\\alpha = 0.01\\Standard deviation, s = 27$

The null hypothesis, $H_o: \mu = 2058$

Alternative hypothesis, $H_{a}: \mu > 2058$

Test statistic is calculated as follows:

$Z_{test} = \frac{\bar{X} - \mu}{s/\sqrt{n} } \\Z_{test} = \frac{2072 - 2058}{27/\sqrt{6} } \\Z_{test} =1.27$

Find the P-value

P(z > 1.27) = 1 - P(z < 1.27)

P(z > 1.27) = 1 - 0.898

P(z > 1.27) = 0.102

Significance level, α = 0.01

Since P - value(0.102) is greater than α (0.01), the null hypothesis will be accepted.