Question

In a​ study, 272 moderately obese subjects were randomly assigned to one of three​ diets: low-fat,​ restricted-calorie; Mediterranean,​ restricted-calorie; or​ low-carbohydrate, nonrestricted-calorie. The prediction was that subjects on a​ low-carbohydrate diet would lose​ weight, on the average. After two​ years, the mean weight loss was 5.5 kg for the 109 subjects in the​ low-carbohydrate group with a standard deviation of 7.0 kg. The technology output below shows results of a significance test for testing

Upper H 0 : mu equals 0H0: μ=0

against

Upper H Subscript a Baseline : mu not equals 0Ha: μ≠0​,

where

muμ

is the population mean weight change. Note that weight change is determined by calculating after

weightminus−before

weight. Complete parts a through c below.

N	Mean	StDev	SE Mean	​95% CI	T	P
109	minus−5.500	7.000	0.670	​(minus−​6.829,minus−​4.171)	minus−8.20	0.000

a. Identify the​ P-value for this test.

The​ P-value is ​(Type an integer or a decimal. Do not​ round.)

b. How is the​ P-value interpreted?

A. The​ P-value is the probability of observing a sample mean weight change​ (loss or​ gain) of 5.5 kg or more if the null hypothesis is true.

B. The​ P-value is the probability of observing a sample mean weight loss of exactly 5.5 kg if the null hypothesis is true.

C. The​ P-value is the probability of observing a sample mean weight change​ (loss or​ gain) of exactly 5.5 kg if the null hypothesis is true.

c. Would the​ P-value and​ 95% confidence interval lead to the same conclusion about H0​? Explain.

The​ 95% confidence interval is (fill in) which (fill in) the hypothesized value for the​ mean, so (fill in) H0. The​ P-value is (fill in) than a significance level of​ 0.05, so (fill in) H0.

​So, the​ P-value and​ 95% confidence interval (fill in) to the same conclusion about H0.

Answer 1