Question

Eleven employees were put under the care of the company nurse because of high cholesterol readings. The nurse lectured them on the dangers of this condition and put them on a new diet. Shown are the cholesterol readings in millimoles per litre (mmol/L) of the 11 employees both before the new diet and one month after use of the diet began. Construct a 98% confidence interval to estimate the population mean difference of cholesterol readings for people who are involved in this program. Assume differences in cholesterol readings are normally distributed in the population. Employee Before After 1 6.59 5.09 2 5.95 5.82 3 7.50 5.56 4 6.26 5.56 5 7.76 6.21 6 6.46 6.08 7 5.56 4.91 8 5.95 6.21 9 5.82 5.17 10 5.66 5.25 11 6.10 5.77

          Eleven employees were put under the care of the company nurse because of high cholesterol readings. The nurse lectured them on the dangers of this condition and put them on a new diet. Shown are the cholesterol readings in millimoles per litre (mmol/L) of the 11 employees both before the new diet and one month after use of the diet began. Construct a 98% confidence interval to estimate the population mean difference of cholesterol readings for people who are involved in this program. Assume differences in cholesterol readings are normally distributed in the population.

Employee Before After
1 6.59 5.09
2 5.95 5.82
3 7.50 5.56
4 6.26 5.56
5 7.76 6.21
6 6.46 6.08
7 5.56 4.91
8 5.95 6.21
9 5.82 5.17
10 5.66 5.25
11 6.10 5.77

Show more…

Eleven employees were put under the care of the company nurse because of high cholesterol readings. The nurse lectured them on the dangers of this condition and put them on a new diet. Shown are the cholesterol readings in millimoles per litre (mmol/L) of the 11 employees both before the new diet and one month after use of the diet began. Construct a 98% confidence interval to estimate the population mean difference of cholesterol readings for people who are involved in this program. Assume differences in cholesterol readings are normally distributed in the population.

Employee Before After
1 6.59 5.09
2 5.95 5.82
3 7.50 5.56
4 6.26 5.56
5 7.76 6.21
6 6.46 6.08
7 5.56 4.91
8 5.95 6.21
9 5.82 5.17
10 5.66 5.25
11 6.10 5.77

Added by Heidi M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Paul A.

02/06/2023

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00:02 Once again, welcome to a new problem.

00:04 This time we're dealing with confidence intervals.

00:09 We're dealing with confidence intervals.

00:11 And of course, when it comes to confidence intervals, we have confidence intervals for means.

00:19 And when we're looking at the confidence intervals for means, we have x bar plus minus margin of error.

00:29 Or we could also have the confidence interval for mean difference, so the difference between the difference between subjects, the same subject, same subject before, or rather not before, but after minus before.

00:57 So after minus before.

01:00 So we have d bar plus minus margin of error where margin of error is t alpha over 2, s subd over radical n, s subd of a radical n, plus minus t alpha over 2, s subd over radical n.

01:34 So that's the confidence interval you're looking for.

01:38 So we have a new problem and this problem involves 11 employees.

01:46 The problem involves 11 employees with the high cholesterol.

01:51 So there's a new diet that comes in to help them with their cholesterol problems.

01:58 And this is measured in millimoles per later.

02:01 So the cholesterol is measured in millimoles per litter.

02:04 And we have the before and after readings.

02:10 So these are the before the diet and then after the diet.

02:16 And these are the readings that we have 11 subjects before and after.

02:22 We want to get a 98 % confidence interval for the population mean difference.

02:29 So we want to get the 98 % confidence interval for the population main difference...

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