Note, this is revisiting a problem in Homework 4 (the sorority GPA problem). Gro

Question

Note, this is revisiting a problem in Homework 4 (the sorority GPA problem). Group means and sample sizes are found below:
Sorority A B C D

¯yi 3.22 3.57 2.87 2.98
ni 10 10. 10 10
The value of MS(within) is 0.1278. Let A = group 1, B = group 2, C = group 3, and D = group 4.

(a) Calculate the lower bound for the family-wise (si-multaneous, Bonferroni) 99% condence intervals for (µ2 µ1), assuming you will make k = 3 total con-dence intervals.

(b) Calculate the upper bound for the family-wise (si-multaneous, Bonferroni) 99% condence intervals for (µ2 µ1), assuming you will make k = 3 total con-dence intervals.

(c) Calculate the lower bound for the family-wise (si-multaneous, Bonferroni) 99% condence intervals for (µ2 µ3), assuming you will make k = 3 total con-dence intervals.

(d) Calculate the upper bound for the family-wise (si-multaneous, Bonferroni) 99% condence intervals for (µ2 µ3), assuming you will make k = 3 total con-dence intervals.

(e) Calculate the lower bound for the family-wise (si-multaneous, Bonferroni) 99% condence intervals for (µ2 µ4), assuming you will make k = 3 total con-dence intervals.

(f) Calculate the upper bound for the family-wise (si-multaneous, Bonferroni) 99% condence intervals for (µ2 µ4), assuming you will make k = 3 total con-dence intervals.

(g) Which condence intervals suggest a signicant dif-ference in the means?

(h) Which condence interval suggests the largest dier-ence between two means?

(i) Interpret the family-wise condence interval for (µ2
µ3) in terms of the problem.

Explanation / Answer

Result:

Note, this is revisiting a problem in Homework 4 (the sorority GPA problem). Group means and sample sizes are found below:
Sorority A B C D

¯yi 3.22 3.57 2.87 2.98
ni 10 10. 10 10
The value of MS(within) is 0.1278. Let A = group 1, B = group 2, C = group 3, and D = group 4.

Standard error = sqrt(MSE/n) = sqrt(0.1278/10) =0.1130

Df for error = 36

For 3 comparisons, Bonferroni level of significance = 0.01/3 =0.0033

Table value =3.136

(a) Calculate the lower bound for the family-wise (si-multaneous, Bonferroni) 99% condence intervals for (µ2 µ1), assuming you will make k = 3 total con-dence intervals.

lower bound = (3.57-3.22)-3.136*0.1130 = -0.00437

(b) Calculate the upper bound for the family-wise (si-multaneous, Bonferroni) 99% condence intervals for (µ2 µ1), assuming you will make k = 3 total con-dence intervals.

Upper bound = (3.57-3.22)+3.136*0.1130 =0.704368

0.704368

(c) Calculate the lower bound for the family-wise (si-multaneous, Bonferroni) 99% condence intervals for (µ2 µ3), assuming you will make k = 3 total con-dence intervals.

lower bound = (3.57-2.87)-3.136*0.1130 =0.345632

(d) Calculate the upper bound for the family-wise (si-multaneous, Bonferroni) 99% condence intervals for (µ2 µ3), assuming you will make k = 3 total con-dence intervals.

upper bound = (3.57-2.87)+3.136*0.1130=1.054368

(e) Calculate the lower bound for the family-wise (si-multaneous, Bonferroni) 99% condence intervals for (µ2 µ4), assuming you will make k = 3 total con-dence intervals.

lower bound = (3.57-2.98)-3.136*0.1130 =0.235632

(f) Calculate the upper bound for the family-wise (si-multaneous, Bonferroni) 99% condence intervals for (µ2 µ4), assuming you will make k = 3 total con-dence intervals.

Upper bound = (3.57-2.98)+3.136*0.1130 =0.944368

(g) Which condence intervals suggest a signicant dif-ference in the means?

(µ2 µ3) and (µ2 µ4) are significant.

(h) Which condence interval suggests the largest dier-ence between two means?

(µ2 µ3) has largest difference.

(i) Interpret the family-wise condence interval for (µ2-µ3) in terms of the problem.

There is significant mean difference in GPA between Group 2 (B) and Group 3 (C) .

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.