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Question: To test the efficacy of a new cholesterol-lowering medication, 10 people are selected at random. ...

To test the efficacy of a new cholesterol-lowering medication, 10 people are selected at random. Each has their LDL levels measured (shown below as Before), then take the medicine for 10 weeks, and then has their LDL levels measured again (After).

Subject Before After

1    196    181

2 142 124

3 133 177

4    119    85

5 175 169

6    191 203

7    200    161

8    153 151

9 165    171

10 120 95

Give a 90% confidence interval for the difference between LDL levels before and after taking the medication.

Confidence Interval =

Answer 1

= (15 + 18 + (-44) + 34 + 6 + (-12) + 39 + 2 + (-6) + 25)/10 = 7.7

s_d = sqrt(((15 - 7.7)^2 + (18 - 7.7)^2 + (-44 - 7.7)^2 + (34 - 7.7)^2 + (6 - 7.7)^2 + (-12 - 7.7)^2 + (39 - 7.7)^2 + (2 - 7.7)^2 + (-6 - 7.7)^2 + (25 - 7.7)^2)/9) = 24.53

At 90% confidence interval the critical value is t_0.05,9 = 1.833

The 90% confidence interval is

+/- t_0.05,9 * s_d/

= 7.7 +/- 1.833 * 24.53/

= 7.7 +/- 14.22

= -6.52, 21.92