Please provide solutions stepwise to these stats questions, thank you. QUESTION

Question

Please provide solutions stepwise to these stats questions, thank you.

QUESTION 13 In an upper-tailed F test of two population variances, the test statistic is F 3.65. The rejection region is F? 3.22 for the 5% level of significance, F24.07 for the 2.5% level, and F? 5.39 for the 1% level. For this test, what is the p-value? Greater than 0.05. Between 0.025 and 0.05. Between 0.01 and 0.025. O Less than 0.01 QUESTION 14 Which of the following distributions is used when testing Ho: 01 02 versus H1: 01 02? Chi-square distribution O Normal distribution F distribution Tdistribution

Explanation / Answer

Solution

Q13

The test statistic for testing equality of two population variances, i.e., H0: 12 = 22, is

F = s12/s22 where s12 and s22 are the respective sample variances [the larger sample variance is taken as s12 and the smaller one as s22].

Under the null hypothesis of equal variances, the above F has F-distribution with degrees of freedom (n1 - 1) and (n2 - 1), where n1 and n2 are the respective sample sizes.

Using the notation, Fn, m, for the upper % point of F-distribution with degrees of freedom n and m, we are given

Fn, m, 0.05 = 3.22;    Fn, m, 0.025 = 4.07    and    Fn, m, 0.01 = 5.39

Comparing these values with Standard F-Table, we find

F6, 10, 0.05 = 3.22;    F6,10, 0.025 = 4.07    and    F6, 10, 0.01 = 5.39.

So, the test statistic follows F6, 10

Now, p-value for 3.65 is given by P(F6, 10 > 3.65) = 0.0498 [obtained using Excel Function]

Thus, the correct answer is second option i.e., between 0.025 and 0.05

Q14

The test statistic for testing equality of two population variances, i.e., H0: 12 = 22, is

F = s12/s22 where s12 and s22 are the respective sample variances [the larger sample variance is taken as s12 and the smaller one as s22].

Under the null hypothesis of equal variances, the above F has F-distribution with degrees of freedom (n1 - 1) and (n2 - 1), where n1 and n2 are the respective sample sizes.

So, the correct answer is third option i.e., F-distribution

Q15

If 100(1 – ) % Confidence Interval for (1 - 2) includes zero, then the null hypothesis

H0: 1 = 2 is accepted at % level of significance.

Since (-5.73, 4.13) includes zero, 1 = 2.

Thus, the correct answer is first option.

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