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.
Learn more about p-value approaches for hypothesis testing here:
brainly.com/question/14805123
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