Question

8. 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.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 0.10 level of significance. (Assume that student performance is approximately normal.)

Answer 1

8)

The null and alternate hypothesis are:

H0:

Ha:

The test statistic is given by:

Since this is a two-tailed test, so the p-value is given by:

Since p-value is less than 0.10, so we have sufficient evidence to reject the null hypothesis H0.

Thus we can conclude that i.e. Mrs. Smith and Mrs. Jones are not equally effective teachers.