Which statement completes this proof

Mathematics

1 answer:

Gennadij [26K]2 years ago

8 0

The answer to this question is A

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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

marysya [2.9K]

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.

<h3>How to decide whether the null hypothesis is rejected or accepted?</h3>

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.

<h3>Calculation:</h3>

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.