Within a school district, students were randomly assigned to one of two Math tea

Question

Within a school district, students were randomly assigned to one of two Math teachers - Mrs. Smith and Mrs. Jones. After the assignment, Mrs. Smith had 30 students, and Mrs. Jones had 25 students. (Hint: Here scores are coming from two different samples. We can compute variance from SD). At the end of the year, each class took the same standardized test. Mrs. Smith's students had an average test score of 78, with a standard deviation of 10; and Mrs. Jones' students had an average test score of 85, with a standard deviation of 15. Test the hypothesis that Mrs. Smith and Mrs. Jones are equally effective teachers. Use a 0.05 level of significance.

Explanation / Answer

1 -Mrs Smith ,n1 = 30 , x1bar =78 , s1 = 10

2 -Mrs Jones , n2 = 25 , Xbar= 85 ,s2 = 15

df = n1+n2- 2 = 53

t0.025 = 2.005746

Sp = sqrt((s1^2 *(n1 -1)+s2^2)*(n2-1)/(n1+n2 - 2))

=sqrt((100*29 +225*24)/53) = 12.51414

X1bar -X2bar = 78-85 = -7

sp*sqrt(1/n1 +1/n2) = 12.51414*sqrt(1/30+1/25)) =  3.388845

Ts = (X1bar -X2bar)/sp*sqrt(1/n1 +1/n2) = -7/ 3.388845

= -2.0656

since |TS| > t-critical (2.0656 > 2.0057)

we reject the null hypothesis to conclude that  Mrs. Smith and Mrs. Jones are not equally effective teachers

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

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