Based on data from the National Health Survey, men aged from 25 to 34 have heigh

Question

Based on data from the National Health Survey, men aged from 25 to 34 have heights with a standard deviation of 2.9 inches. Test the claim that men in a higher age bracket -45 through 54 - have heights with a different variability. The heights of 25 randomly selected men in the 45 to 54 age bracket are listed below. If you reject the null hypothesis, you want a risk of no more than five percent of being incorrect. 66.80 71.22 65.80 66.24 69.62 70.49 70.00 71.46 65.72 68.10 72.14 71.58 66.85 69.88 68.69 72.77 67.34 68.40 68.96 68.70 72.69 68.67 67.79 63.97 67.19

Explanation / Answer

Solution:

Here, we have to use Chi square test for variance or standard deviation.

H0: ? = 2.9

H0: ? ? 2.9

From the given data, we have

Level of significance = alpha = 0.05

Sample size = n = 25

Sample standard deviation = 2.34012

Degrees of freedom = n – 1 = 25 – 1 = 24

Lower critical value = 12.4012

Upper critical value = 39.3641

Test statistic formula is given as below:

Chi square = (n – 1)*S^2/?^2

Chi square = (25 – 1)* 2.34012*2.34012/2.9*2.9

Chi square = 24*2.34012*2.34012/2.9*2.9

Chi square = 15.62757

Lower critical value < Chi square test statistic < upper critical value

P-value = 0.0990

P-value > alpha = 0.05

So, we do not reject the null hypothesis that the given sample has same standard deviation as 2.9.

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