Random samples that are drawn independently from two normally distributed popula

Question

Random samples that are drawn independently from two normally distributed populations yielded the following statistics.

=n112

=n218

=x1254

=x2238.9

=s21789.61

=s22306.25

(The first row gives the sample sizes, the second row gives the sample means, and the third row gives the sample variances.)

Can we conclude, at the 0.05 significance level, that the two population variances, 21 and 22, differ?

Perform a two-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a  list of formulas.)

The null hypothesis:

H0:

The alternative hypothesis:

H1:

The type of test statistic:

(Choose one)Z,t,Chi square,F

The value of the test statistic:
(Round to at least three decimal places.)

0.05

and

Can we conclude that the two population variances differ?

Yes

No

p

x

s

p

=n112

=n218

=x1254

=x2238.9

=s21789.61

=s22306.25

Explanation / Answer

Here

H0 : 12 = 22

Ha : 12 22

s12 = 789.61 ; s22 = 306.25

Type of test statistic we use is F statistic

F = s22 /s12 = 306.25/789.61 = 0.3878

Here dF1 = 12 - 1= 11 and dF2 = 18 -1 = 17

so Critical value of F's are

Fcritical -1 = FINV(0.025, 17, 11) = 3.2816

Fcritical -2 = FINV(0.975, 11, 17) = 0.3475

we will reject the null if F < Fcritical -2 and F > Fcritical -1

so here as we see that

F > Fcritical -2 so we failed to reject the null hypothesis and can conclude that the two population doesn't differ. Answer is no.

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