A core mathematics project is testing an innovative approach to teaching Mathematics that emphasizes group investigations and mathematics modeling. Researchers compared 20 students who were exposed to...

A core mathematics project is testing an innovative approach to teaching Mathematics that emphasizes group investigations and mathematics modeling. Researchers compared 20
students who were exposed to this new approach to 22 students who learned through a traditional
curriculum. Student learning was assessed through a test at the end of the academic year to see
if this new approach led to higher learning gains as compared to the traditional approach.
New Approach Traditional
n1 = 20 n2 = 22
x¯1 = 79.4 x¯2 = 74.6
s
2
1 = 12.5 s
2
2 = 14.2
We are interested in finding out if there is a difference between the approaches. Use a 96%
confidence interval. Assume approximately normal populations with equal variances. To do this,
answer the following questions:
(a) Should the data be paired or not?
(b) Should you use the pooled variance or not?
(c) State α.
(d) State whether you should use z or t.
2
(e) Find / provide the appropriate value (z or t) from the table (or your calculator).
(f) Find the confidence interval. It is fine to round intermediate calculations to 3 decimals.
Round your final values to 3 decimals. Use your z or t value from the previous part (not
the exact value). Show all by-hand work.
(g) What is the parameter your confidence interval is for? (Examples: µ, p, etc.)
(h) Write an interpretation of your confidence interval in the context of the problem. (For
example: We are xx% confident...)
(i) Does it appear that one approach is more effective than the other, or is there approximately
the same effectiveness? Explain your reasoning by using the confidence interval you found.
(j) If you were to use R to find a 96% confidence interval for µ1 − µ2, what would be the
appropriate code (assuming that you were able to obtain the full dataset)? Assume you
have imported the data as new_scores and traditional_scores.