5. A teacher wishes to compare two different groups of students with respect to their mean time to complete a standardized test. The time required is determined for each group. The data summary is given below. Test the claim at = 0.10, that there is no difference in variance. Give the critical region, test statistic value, and conclusion for the F test.
n1 = 60 s1 = 11
n2 = 120 s2 = 17
= 0.10
· State the null and alternate hypotheses
· Determine which test statistic applies, and calculate it
· Determine the critical region
· State your decision: Should the null hypothesis be rejected?
Your data:
Sample 1
Sample size = 60
Variance = 121 (variance is standard deviation squared)
df = n - 1 = 59 (df = degrees of freedom)
Sample 2
Sample size = 120
Variance = 289
df = n - 1 = 119
Determine your test statistic from the appropriate formula using variance.
Critical value using an F-distribution at 0.10 level of significance with the above information is... (check an F-distribution table for this value).
If the test statistic exceeds the critical value from the table, the null will be rejected in favor of the alternative hypothesis. (The null would state that the ratio of the two variances is less than or equal to 1, and the alternative hypothesis would state that the ratio of the two variances is greater than 1.) If the test statistic does not exceed the critical value from the table, the null will not be rejected.
I hope this helps.
To test the claim that there is no difference in variance between the two groups of students, we can use an F-test. The null and alternate hypotheses for the F-test are as follows:
Null hypothesis (H0): The variances of the two groups are equal.
Alternate hypothesis (H1): The variances of the two groups are not equal.
To conduct the F-test, we need to calculate the F-test statistic using the formula:
F = (s1^2 / s2^2)
where s1^2 and s2^2 are the sample variances of the two groups.
In this case, we have the following data:
n1 = 60 (sample size of group 1)
s1 = 11 (sample standard deviation of group 1)
n2 = 120 (sample size of group 2)
s2 = 17 (sample standard deviation of group 2)
α = 0.10 (significance level)
Now, we can calculate the F-test statistic:
F = (11^2 / 17^2) ≈ 0.4341
To determine the critical region, we need to consult the F-distribution table or use a statistical software to find the critical value for α = 0.10, with degrees of freedom df1 = n1 - 1 = 60 - 1 = 59 and df2 = n2 - 1 = 120 - 1 = 119. The critical value is F_critical = F(0.10, 59, 119).
Once we have the critical value, we compare it to our calculated F-test statistic. If the calculated F-test statistic falls within the critical region (i.e., it is greater than the critical value), we reject the null hypothesis. If it does not fall within the critical region, we fail to reject the null hypothesis.
Without the specific critical value, we cannot determine the critical region or reach a conclusion. Please provide the critical value, and I can help you with the final step.