Question

Suppose you take two random samples of dieters to show that
those on a Low-Carb Diet lose more weight than those on a Low-Fat
Diet. Use the following table to test the hypothesis H_{0}:
µ_{1} ≤ µ_{2} versus H_{1}: µ_{1}
> µ_{2} at 0.05 level of significance (Assume that the
population variances are equal but unknown). What is the
pooled-variance?

weight loss(in pounds) low carb diet group 1, low fat diet group 2

mean 9.70 8.30

variance 3.55 3.75

observations 25 40

pooled variance

Select one:

3.076

3.674

None of these are correct

3.157

3.233

Answer #1

Given data in problem

Sample 1 -

Sample 2-

Level of significance

Pooled-variance for given two sample variances is

So option 2nd is correct which is 3.674

Suppose you take two random samples of dieters to show that
those on a Low-Carb Diet lose more weight than those on a Low-Fat
Diet. Use the following table to test the hypothesis H0:
µ1 ≤ µ2 versus H1: µ1
> µ2 at 0.10 level of significance (Assume that the
population variances are equal but unknown). Which of the following
statements is true?
weight loss(in pounds)
, low carb diet group 1 , low fat diet
group 2...

Find the test statistic for the t test and state the
conclusion. Are low-fat diets or low-carb diets more
effective for weight loss? A sample of 78 subjects went on a
low-carbohydrate diet for six months. At the end of that time, the
sample mean weight loss was 15.0 pounds with a sample standard
deviation of 7.77 pounds. A second sample of 74 subjects went on a
low-fat diet. Their sample mean weight loss was 16.3 with a
standard deviation of...

According to a study published in the New England Journal of
Medicine, overweight people on low-carbohydrate and
Mediterranean diets lost more weight and got greater cardiovascular
benefits than people on a conventional low-fat diet (The Boston
Globe, July 17, 2008). A nutritionist wishes to verify these
results and documents the weight loss (in pounds) of 30 dieters on
the low-carbohydrate and Mediterranean diets and 30 dieters on the
low-fat diet. Let Low-carb or Mediterranean and Low-fat diets
represent populations 1...

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