atistician wants to test for the equality of me rawn from normal populations of people enroll will not perform the equal-variance t-test of the means if the condition necessary for its use is n ost at the completion of the program data follor

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22. A statistician wants to test for the equality of means in two independent samples
drawn from normal populations of people enrolled in a diet program. However, he
will not perform the equal-variance t-test of the difference between the population
means if the condition necessary for its use is not satisfied. The number of pound
lost at the completion of the program data follow:
Sample 1
Sample 2
7
2
9
25
6
9
15
15
7
10
10
18
8
5
12
22 27
3
Can the statistician conclude at the 5% significance level that the required condition is
not satisfied (i.e. the population variances differ)?
Transcribed Image Text:22. A statistician wants to test for the equality of means in two independent samples drawn from normal populations of people enrolled in a diet program. However, he will not perform the equal-variance t-test of the difference between the population means if the condition necessary for its use is not satisfied. The number of pound lost at the completion of the program data follow: Sample 1 Sample 2 7 2 9 25 6 9 15 15 7 10 10 18 8 5 12 22 27 3 Can the statistician conclude at the 5% significance level that the required condition is not satisfied (i.e. the population variances differ)?
Expert Solution
Step 1

Calculation of variances for each sample:

For sample 1:

Statistics homework question answer, step 1, image 1

sample size (n1) = 8

sample mean (x̄1) = Σx1 /n1 = 74/8=9.25

sample variance  (s1)2 = Σ(x1-x̄1)2 /(n1-1) = 63.5000/(8-1) = 9.0714

 

For sample 2:

Statistics homework question answer, step 1, image 2

sample size (n2) = 10

sample mean (x̄2) = Σx2/n2 = 136/10 = 13.6

sample variance  (s2)2 = Σ(x2-x̄2)2 /(n2-1) = 756.400/(10-1) = 84.0444

 

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