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 17 doors is taken, and it is found that they have a mean of 2069 millimeters with a standard deviation of 24. Assume the population is normally distributed. Is there evidence at the 0.02 level that the doors are either too long or too short

Answer 1

There is not enough evidence at the 0.02 level that the doors are either too long or too short. So, the null hypothesis is accepted.

How to decide whether the null hypothesis is rejected or accepted?

Using the p-value approach for the hypothesis test, whether the null hypothesis is rejected or accepted.

• If the p-value is greater than the significance level then the null hypothesis is accepted.
• If the p-value is less than the significance level then the null hypothesis is rejected.

Calculation:

It is given that,

Sample size n = 17

Sample mean X = 2069

Standard deviation σ = 24

Population mean  μ = 2058

Significance level α = 0.02

Hypothesis:

The null hypothesis: H0: μ = 2058

The alternative hypothesis: Ha: μ ≠ 2058

So, the z-test score for the given distribution is,

z-score = (X - μ)/(σ/√n)

On substituting,

z-score = (2069 - 2058)/(24/√17)

            = 11/5.82

            = 1.89

Thus, the p-value for the z-score of 1.89 is 0.0587 ≅ 0.06.

Since 0.06 > 0.02(significance level), the null hypothesis is accepted. So, there is no sufficient evidence that the doors are either too long or too short.

Learn more about p-value approaches for hypothesis testing here:

https://brainly.com/question/14805123

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