You are a college student, and you have a friend at a rival university. The two of you compete in almost everything! One day, your friend boasted that students at her university are taller than the students at yours. You each gather a random sample of heights of people from your respective campuses. Your data are displayed below (units are inches).
Your friend's data: (checksum: 1111.9)
| 78 | 68 | 64.6 | 65.3 | 73.8 | 66.4 | 67.4 | 67.4 | 71.5 | 67.1 |
| 76.6 | 72.9 | 74 | 62.8 | 70.1 | 66 |
Your data: (checksum: 1214.3)
| 61.6 | 73.9 | 70.1 | 68.7 | 70.5 | 69.7 | 64.8 | 66.7 | 65.5 | 66.1 |
| 70.8 | 66.9 | 66 | 68.6 | 67.7 | 65.7 | 62.9 | 68.1 |
Construct a 95% confidence interval for the difference in mean height between the two college populations.
a) State the parameter of interest, and verify that the necessary conditions are present in order to carry out the inference procedure.
b) Find the critical value and standard error. It is assumed that you are using the more accurate estimate for the degree of freedom. It is recommended that you use technology to find the degree of freedom!
Degree of freedom: Critical Value:
Standard Error: Margin of error:
c) Find the confidence interval: (,)
d) Interpret your 95% confidence interval in context.
e) Based on the confidence interval, is there evidence that the mean height at your friend's university is higher? Explain.