Question

4) Educators introduce a new math curriculum and measure 45 students' scores before and at the end of the academic year using an exam widely believed to accurately measure students' understanding. The average score at the start the year was 65%, and after was 75%.

a) In words, what are the null and alternative hypothesis tests that the educators would most likely be interested in testing?
b) What does a hypothesis test tell us that we can't learn from simply noting that students improved 10 percentage points?
c) Suppose the p-value from this hypothesis test was 0.54. Explain how to interpret this value in this context.

Answer 1

a) The hypothesis to be tested is as follows:

The null hypothesis is that there is no change in student's score before and after introducing the new math curriculum.

The alternative hypothesis is that there is an increase in student's score after introducing the new math curriculum.

b)Hence, evenif we think that there is a 10 % increase in the score, the test says us that there is no evidence to reject the hypothesis that the scores before and after introducing the new math curriculum are different. Hence we accept that there is no effect in the new curriculum.

C) p-value is the probability that reject H0, based on an observed value assuming that H0 is true. If the p-value is greater than the allowed significance level, then it is evident that there is no evidence to reject H0. H0 is rejected when p-value is less than the maximum limit(significance level). Hence, p-value is 0.54 implies that as the p-value is higher, there is no evidence against the null hypothesis.