Question

In: Statistics and Probability

In a​ study, 272 moderately obese subjects were randomly assigned to one of three​ diets: low-fat,​...

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.

Solutions

Expert Solution


Related Solutions

In a​ study, 272 moderately obese subjects were randomly assigned to one of three​ diets: low-fat,​...
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...
Are low-fat diets or low-carb diets more effective for weight loss? A sample of 70 subjects...
Are low-fat diets or low-carb diets more effective for weight loss? A sample of 70 subjects went on a low-carb At the end of that time, the sample mean weight loss was 10.5 pounds with a sample standard deviation of 7.09 pounds. A second sample of 76 went on a low-fat diet. Their sample mean weight loss was 18.0 with a standard deviation of 7.26. Can you conclude that their was no difference in the mean weight loss between the...
Low-fat or low-carb? Are low-fat diets more effective for weight loss? A sample of 58 subjects...
Low-fat or low-carb? Are low-fat diets more effective for weight loss? A sample of 58 subjects went on a low-carbohydrate diet for six months. At the end of that time, the sample mean weight loss was 3.2 kilograms with a sample standard deviation of 5.42 kilograms. A second sample of 60 subjects went on a low-fat diet. Their sample mean weight loss was 2.4 kilograms with a standard deviation of 4.48 kilograms. Can you conclude that the mean weight loss...
) In a study of the effects of caffeine on alertness, 32 subjects were randomly assigned...
) In a study of the effects of caffeine on alertness, 32 subjects were randomly assigned to four groups. These groups were C1: wait-list control (no treatment), C2: placebo control, E1: experimental group 1 (mild caffeine treatment) and E2: experimental groups 2 (high caffeine treatment). Several subjects were not able to complete the study, reducing the group n’s to 7, 5, 6, and 3, respectively. The dependent variable scores were performance scores on a visual-motor task requiring alertness. The results...
12 subjects in a study were randomly assigned into two equally sized groups. One group was...
12 subjects in a study were randomly assigned into two equally sized groups. One group was shown a short video on how to fold paper cranes. The other group was given an instruction booklet on how to do so. They were then asked to make paper cranes for the next hour. The number of paper cranes each subject made was recorded and is listed in the table below. The researchers are interested in whether there was a difference in the...
Low-fat or low-carb? Are low-fat diets or low-carb diets more effective for weight loss? A sample...
Low-fat or low-carb? 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 4.7 kilograms with a sample standard deviation of 7.16 kilograms. A second sample of 79 subjects went on a low-fat diet. Their sample mean weight loss was 2.6 kilograms with a standard deviation of 5.90 kilograms. Can you conclude that the...
1) In a study of the effects of caffeine on alertness, 32 subjects were randomly assigned...
1) In a study of the effects of caffeine on alertness, 32 subjects were randomly assigned to four groups. These groups were C1: wait-list control (no treatment), C2: placebo control, E1: experimental group 1 (mild caffeine treatment) and E2: experimental groups 2 (high caffeine treatment). Several subjects were not able to complete the study, reducing the group n’s to 7, 5, 6, and 3, respectively. The dependent variable scores were performance scores on a visual-motor task requiring alertness. The results...
Question 6 options: In a study of n=76 subjects that were placed on a low-fat diet,...
Question 6 options: In a study of n=76 subjects that were placed on a low-fat diet, their sample mean weight loss was 2.2 kg. with a sample standard deviation of 6.1 kg. What is the test statistic for testing the mean weight loss is GREATER than 0? Note: Enter X.XX AT LEAST ONE DIGIT BEFORE THE DECIMAL, TWO AFTER and round up. Thus, 27 is entered as 27.00, 3.5 is entered as 3.50, 0.3750 is entered as 0.38 | |...
Question 6 options: In a study of n=76 subjects that were placed on a low-fat diet,...
Question 6 options: In a study of n=76 subjects that were placed on a low-fat diet, their sample mean weight loss was 2.2 kg. with a sample standard deviation of 6.1 kg. What is the test statistic for testing the mean weight loss is GREATER than 0? Note: Enter X.XX AT LEAST ONE DIGIT BEFORE THE DECIMAL, TWO AFTER and round up. Thus, 27 is entered as 27.00, 3.5 is entered as 3.50, 0.3750 is entered as 0.38 | |...
An experiment on memory was performed, in which 16 subjects were randomly assigned to one of...
An experiment on memory was performed, in which 16 subjects were randomly assigned to one of two groups, called "Sentences" or "Intentional". Each subject was given a list of 50 words. Subjects in the "Sentences" group were told to form multiple sentences, each using at least two words from the list, and to keep forming sentences until all the words were used at least once. Subjects in the "Intentional" group were told to spend five minutes memorizing as many of...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT