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Assume that the heights of adult males in a certain region are normally distributed. The heights (in inches) of 20 randomly selected adult males from this region are listed below:

70, 72, 71, 70, 69, 73, 69, 68, 70, 71, 67, 71, 70, 74, 69, 68, 71, 71, 71, 72

Use this sample data and a 0.05 significance level to test the claim that the variance of all heights in this region is less than 6.25.

Answer :

Using the null hypothesis test we calculate that variance is less than 6.25 .

Data sample is 0.05.

20 people make up the sample.

And ,

The theories are:

H₀ : μ² = 6.25

H₁ : μ² < 6.25

The critical value = 10.117.

If the test statistic is less than this number, the null hypothesis will be rejected. When the p-value is less than or equal to your significance level, we reject the null hypothesis. The alternative theory, which contends that the effect is widespread, is supported by your sample data. The null must be removed when the p-value is low, as a mnemonic device.

This is the test statistic:

2.976 × 19 / 6.25 = 9.047.

Therefore, we disregard the null hypothesis. The difference is less than 6.25 since it is not 6.25.

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