Question

Two samples were taken to see if the standard deviations two populations are the same or...

Two samples were taken to see if the standard deviations two populations are the same or not.

Sample1:
-size of sample is 21
-sample variance is 120

Sample 2:
-sizo of sample is 16
-Sample variance is 105

conduct the appropriate hypothesis test using a 10% level of significance.
Math   Statistics-And-Probability   
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Answer #1

Null Hypothesis

Alternative Hypothesis

Under H0, the test statsitic is

Since , considering as numerator.

Degrees of freedom = (n1-1), (n2-1) = (20,15)

Significance level is = 0.10

The critical value of F for (20,15) df, at 10% significance level is 1.924

The p-value is 0.4018

Since p value is greater than significance level. Fail to Reject H0.

Hence , the two populations have the same standrad deviation.

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