In: Statistics and Probability
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: 1213.5)
75.5 | 72 | 76.4 | 69.7 | 76 | 74.7 | 80.5 | 71.5 | 73.2 | 67.3 |
66.8 | 65.2 | 66.7 | 72.5 | 75.7 | 68.5 | 61.3 |
Your data: (checksum: 1301.2)
66.9 | 66.2 | 67.6 | 74.1 | 72.3 | 69.4 | 69.3 | 66.7 | 69 | 64.3 |
65.9 | 63.1 | 68 | 64.8 | 73.6 | 71.2 | 72.8 | 59 | 77 |
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 estimate for the degree of freedom and the margin of error.
Degree of freedom:
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.
(a) The parameter of interest is students at university.
This test assumes -
The means are of measurement variables.
Sampling (or allocation) is random and observations are independent.
The samples are drawn from normally distributed populations.
Sample variances are homogenous (that is they represent the same population)
The model is additive
(b) The estimate for the degree of freedom and the margin of error is 34 and 3.1501 respectively.
(c) The 95% confidence interval is between -0.2520 and 6.0483.
(d) We are 95% confident that the true mean difference is between -0.2520 and 6.0483.
(e) Since the confidence interval contains 0, we cannot conclude that the mean height at your friend's university is higher.
Friend | Your data |
75.5 | 66.9 |
72 | 66.2 |
76.4 | 67.6 |
69.7 | 74.1 |
76 | 72.3 |
74.7 | 69.4 |
80.5 | 69.3 |
71.5 | 66.7 |
73.2 | 69 |
67.3 | 64.3 |
66.8 | 65.9 |
65.2 | 63.1 |
66.7 | 68 |
72.5 | 64.8 |
75.7 | 73.6 |
68.5 | 71.2 |
61.3 | 72.8 |
59 | |
77 |
Friend | Your data | |
71.382 | 68.484 | mean |
4.948 | 4.354 | std. dev. |
17 | 19 | n |
34 | df | |
2.8981 | difference (Friend - Your data) | |
21.5579 | pooled variance | |
4.6431 | pooled std. dev. | |
1.5501 | standard error of difference | |
-0.2520 | confidence interval 95.% lower | |
6.0483 | confidence interval 95.% upper | |
3.1501 | margin of error |