Question

1. A mathematics professor believes that the performance of students taking an elementary calculus course has declined in recent years. The professor decides to reuse a final exam that was first administered 10 years ago. At that time the mean score was 81 with s=10, for the 50 students in the section taught by that professor When given to the current class of 53 students, who observed essentially the same set of lectures, the mean is 75 with s=15. If we treat these students as random samples of the populations of all such students taking calculus at this college during these two years, do the results indicate a decline in performance on the average? Conduct the appropriate test at the alpha =.05 level.

a. Is there one or two populations in this problem?

b. Is this a problem about quantitative or qualitative data?

c. Will you use the t stats or proportion stats option in StatCrunch to complete this problem?

d. State the null and alternative hypothesis using the correct statistical symbols.

e. State the test statistic

f. State the P-value

g. In a complete sentence, indicate the strength of this P-value and five a conclusion using the context of the problem that you are testing. I should be a able to read your conclusion and tell that you were testing about student performance in a calculus class.

h. Construct a 95% confidence interval to estimate the difference in the mean score for the two classes.

Answer 1

Solution:

iven ニフ5 253 Test stakush whene S12.95 24S x0 197 p-val ve 0.01030 Hert_ P-value く 1) (20 ) O.S Henct wr may rgeut the null hypaheu we can Conclude that op the avera4 there is decline in dhe persfosmante