Question: Are low carbohydrate diets effective? A random sample of six individuals who wanted to try a low carbohydrate diet was obtained. Each individual was placed on a low carbohydrate diet for eight weeks. The weight in pounds was determined for each individual both before and after the diet, as shown in Table.
a. The two samples are which of the following: two independent or matched pairs? Explain.
b. What type of study is found-observational or randomized experiment? Explain.
c. What is the experimental (or observational) unit?
d. What is the response variable?
e. What is the explanatory variable?
f. What sample(s) are used to calculate the appropriate confidence interval?
g. The following information was obtained from the table found below.
sample mean difference = 13.2 pounds
S.D. = 13 pounds
standard error (S.E) = 5.2 pounds
sample size (n) = 6 people
Set up the calculation for a 95% confidence interval to estimate the population mean difference.
h. Suppose the 95% confidence for the population mean difference in weight is (2.8 to 23.6) pounds. What conclusion can be made in this instance about the effectiveness of the diet? Explain in statistical terms.
i. What is the advantage of using the differences rather than the original data in the calculation of the confidence intervals?
Table: Weight Before and After Diet
|
Person
|
Weight Before Diet
(pounds)
|
Weight After Diet
(pounds)
|
Difference in pounds =
(Before-After)
|
|
1
|
125
|
117
|
8
|
|
2
|
165
|
151
|
14
|
|
3
|
205
|
169
|
36
|
|
4
|
115
|
117
|
-2
|
|
5
|
138
|
132
|
6
|
|
6
|
152
|
135
|
17
|