Question

Instructions: This question contains four (4) parts. Answer all parts. Label your response to each part clearly, using bold text (e.g. Part a: Your response...).

Jerry has created two versions of assignments for his class. He has randomly selected 40 students and asked each of them to attempt one of the two versions of the assignments. The table below shows the amount of time (in minutes) each student has spent completing the assigned assignment.

Project A 88 83 70 81 126 55 41 114 90 109 71 37 60 45 67 48 91 70 47 84 54 105 82 75

Project B 55 5767 47 46 60 39 56 35 49 56 45 52 60 49 67        

(a) The standard deviation of the amount of time needed to complete Project A is __________ minutes. (Round to two decimal places.)

(b) The F statistic that allows to test the equality of the two population variances of the amount of time needed is ____________. (Round to two decimal places.)

(c) To test the hypotheses:

H₀: Variance (A) = Variance (B)

H_A: Variance (A) ≠ Variance (B)

The critical values of the F statistics for the rejection region are __________ and __________ if α = 10%. (Round to two decimal places.)

Answer 1

using excel>addin>phstat>two sample test

we have

F Test for Differences in Two Variances
Data
Level of Significance	0.10
Larger-Variance Sample
Sample Size	24
Sample Variance	576.7373188
Smaller-Variance Sample
Sample Size	16
Sample Variance	81.73333333
Intermediate Calculations
F Test Statistic	7.0563
Population 1 Sample Degrees of Freedom	23
Population 2 Sample Degrees of Freedom	15
Two-Tail Test
Upper Critical Value	2.30
p-Value	0.0003
Reject the null hypothesis

a) The standard deviation of the amount of time needed to complete Project A is 24.02minutes.

(b) The F statistic that allows to test the equality of the two population variances of the amount of time needed is 7.06.

(c) To test the hypotheses:

H0: Variance (A) = Variance (B)

HA: Variance (A) ≠ Variance (B)

The critical values of the F statistics for the rejection region are 0.47 and 2.30 if α = 10%.