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 statistical hypothesis (show your work) to determine whether the null hypothesis that Mrs. Smith and Mrs. Jones are equally effective teachers is supported or rejected. Use a 0.05 level of significance. (Assume that student performance is approximately normal.)

(1) State the Null hypothesis of the above statement that Mrs. Smith and Mrs. Jones are equally effective teachers.

(2) State (a) one-tail and (b) two-tail alternative hypotheses.

(3) Is it a dependent or independent t-test, and why?

(4) Conduct the appropriate t-test (show your work or copy Excel calculation if used).

(5) Interpret results (take a decision whether and why to reject or not reject the null hypothesis)