A new method of teaching mathematics is being tested on sixth grade students. A group of sixth grade students is taught using the new curriculum. A control group of sixth grade students is taught using the old curriculum. The mathematics test scores for the two groups are shown in the back-to-back stem-and-leaf plot.

At α = 0.05, is there enough evidence to support the claim that the new method of teaching mathematics produces higher mathematics test scores than the old method does? Assume the population variances are equal.

(a) Identify the claim and state H₀ and H_a, 

(b) Find the critical value(s) and identify the rejection region(s), 

(c) Find the standardized test statistic t, 

(d) Decide whether to reject or fail to reject the null hypothesis, and

(e) Interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed.

Transcribed Image Text:

Old Curriculum New Curriculum 4 5 8 0 11 57 1 6 0 12 8 2 4 577 3 4 7 2 5 6 7 0 26 9 4 1 3 4 9 1 57 2 3 5 6 6 7 3 3 3 4 4 6 8 700 2 5 5 6 2 3 6 6 9 0 1 4 6 8 19 8 4 4 4 9. Key: 6|22 = 26 for old curriculum and 22 for new curriculum