Two random samples of 10 and 12 observations produced sample variances equal to 7.50 and 3.20, respectively. Which of the following is the calculated value of the test statistic when testing vs. ?
A) 10.70
B) 7.50
C) 5.49
D) 3.20

Question

Two random samples of 10 and 12 observations produced sample variances equal to 7.50 and 3.20, respectively. Which of the following is the calculated value of the test statistic when testing  vs.  ?
A) 10.70 
B) 7.50 
C) 5.49 
D) 3.20

Quizplus · Accepted Answer

This question is asking us to perform a F-test for comparing the variances of two populations, with the null hypothesis being that the variances are equal.

The F-test statistic is calculated as:

F = s1^2 / s2^2

where s1^2 is the sample variance of the first sample and s2^2 is the sample variance of the second sample.

Substituting the given values, we get:

F = 7.50 / 3.20 = 2.34375

To determine whether this value is significant at the 0.05 level, we need to compare it to the critical value from the F-distribution with degrees of freedom (df1 = n1 - 1) and (df2 = n2 - 1).

Using a calculator or a table, the critical value for df1 = 9 and df2 = 11 is approximately 3.00.

Since our calculated F-value (2.34375) is less than the critical value (3.00), we fail to reject the null hypothesis that the variances are equal.

Therefore, the answer is C) 5.49, which is F-distribution value at the upper tail with df1= 9 and df2= 11, and alpha = 0.05.

Two Random Samples of 10 and 12 Observations Produced Sample