Question

The heights were recorded for a Simple Random Sample of 270 junior.  The mean of this sample was 66.5 inches.  The heights are known to be Normally Distributed with a population standard deviation of 5.1 inches. (You do not need a data set for this). Test the claim that the mean height of Juniors has increased from 65.7 at a 0.01 significance level. (Use MINITAB to do the hypothesis test and copy and paste the output of the hypothesis test here (0.5pts). Then answer a-h based on that output.):

1. (2) State the null and alternative hypothesis using the correct symbols and values.

(examples: H₀: m = m₀ vs. H_a: m < m₀  or H₀: p = p₀ vs. H_a: p ≠ p₀ )

2. (0.5)State the significance level.
3. (0.5)State the test statistic.
4. (0.5)State the p-value.
5. (1) State whether you reject or do not reject the null hypothesis.
6. (1)State the critical value(s).
7. (3)Give your conclusion in the context of the problem.  (If you say something like I reject the null or do not reject the null you will receive no credit)
8. (0.5)If the mean height of Juniors has not changed, did you make an error, and if so, which one?

Answer 1

H0 : Mu = 65.7

H1 : Mu > 65.7

Significance level = 0.01

Test statistics = 2.58

P value = 0.005

As p value < 0.01

We reject the null hypothesis.

Critical Value = 2.33

As we reject the null hypothesis at 1% level of significance, we conclude that the claim is true that the mean height of Juniors has increased from 65.7.

Here, correct error is type I error.

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