Question

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.

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Answer 1

(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