Question

Are low-fat diets or low-carb diets more effective for weight loss? A sample of 77 subjects went on a low-carbohydrate diet for six months. At the end of that time, the sample mean weight loss was 4.6 kg with a sample standard deviation of 7.2 kg. A second sample of 79 subjects went on a low-fat diet. Their sample mean weight loss was 2.6 kg with a standard deviation of 5.8 kg. Can you conclude that the mean weight loss is greater for those on the low-carbohydrate diet? Find the P-value and state a conclusion. Round the answer to four decimal places. The P-value is 0.0233. We can conclude that the mean weight loss is greater for those on the low-carbohydrate diet.

          Are low-fat diets or low-carb diets more effective for weight loss? A sample of 77 subjects went on a low-carbohydrate diet for six months. At the end of that time, the sample mean weight loss was 4.6 kg with a sample standard deviation of 7.2 kg. A second sample of 79 subjects went on a low-fat diet. Their sample mean weight loss was 2.6 kg with a standard deviation of 5.8 kg.
Can you conclude that the mean weight loss is greater for those on the low-carbohydrate diet? Find the P-value and state a conclusion. Round the answer to four decimal places.
The P-value is 0.0233. 
We can conclude that the mean weight loss is greater for those on the low-carbohydrate diet.

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Added by Victor R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Lucas Finney

06/13/2022

Step 1

6 - 2.6}}{{\sqrt{\frac{{7.2^2}}{{77}} + \frac{{5.8^2}}{{79}}}} \] \[ T = \frac{2}{\sqrt{\frac{51.84}{77} + \frac{33.64}{79}}} \] \[ T = \frac{2}{\sqrt{0.672 + 0.426}} \] \[ T = \frac{2}{\sqrt{1.098}} \] \[ T = \frac{2}{1.047} \] \[ T \approx 1.91 \] ** Show more…

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Are low-fat diets or low-carb diets more effective for weight loss? A sample of 77 subjects went on a low-carbohydrate diet for six months. At the end of that time, the sample mean weight loss was 4.6 kg with a sample standard deviation of 7.2 kg. A second sample of 79 subjects went on a low-fat diet. Their sample mean weight loss was 2.6 kg with a standard deviation of 5.8 kg. Can you conclude that the mean weight loss is greater for those on the low-carbohydrate diet? Find the P-value and state a conclusion. Round the answer to four decimal places. The P-value is 0.0233. We can conclude that the mean weight loss is greater for those on the low-carbohydrate diet.

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00:01 For this problem, we are told that we have an experiment where one group is put on a low -carb diet.

00:07 The other group is on a low -fat diet.

00:10 We have the size of the first group is 77, with a sample mean of 4 .6 kilograms lost and a standard deviation of 7 .2 kilograms.

00:19 Then for the second group, the low -fat group, you have 79 participants, sample mean of 2 .6 kilograms lost, and standard deviation of 5 .8 kilograms.

00:28 And we are essentially being asked to do the hypothesis test where the null hypothesis is that the mean amount of weight loss between the two groups would be equal to zero.

00:38 And the alternate hypothesis is that mu 1 minus mu 2 is greater than 0, or in other words, mu 1 minus mu 2.

00:45 Or, pardon me.

00:47 In other words, mu 1 is greater than mu 2.

00:50 So for doing a means comparison test like this, we would want to use the t statistic, particularly, because we don't know what the population standard deviations are for the two groups.

01:06 So we would have t equals x bar 1 minus x bar 2.

01:12 So that's going to be 4 .6 minus 2 .6 minus 2 .6 minus the difference between the null hypothesized mean values, which would just be 0, so i'll exclude that.

01:24 Then we're dividing that by s1 squared.

01:27 So that's 7 .2 squared.

01:29 Over n1, so over 77, plus s2 squared over n2, so plus 5 .8 squared over 79...

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