In: Statistics and Probability
Individuals who consume large amounts of alcohol do not use the calories from this source as efficiently as calories from other sources. One study examined the effects of moderate alcohol consumption on body composition and the intake of other foods. Fifteen subjects participated in a crossover design where they either drank wine for the first 6 weeks and then abstained for the next 6 weeks or vice versa. During the period when they drank wine, the subjects, on average, lost 0.31 kilograms (kg) of body weight; when they did not drink wine, they lost an average of 1.13 kg. The standard deviation of the difference between the weight lost under these two conditions is 8.4 kg. During the wine period, they consumed an average of 2572 calories; with no wine, the mean consumption was 2557. The standard deviation of the difference was 206.
(a) Compute the differences in means and the standard errors for comparing body weight and caloric intake under the two experimental conditions. (To find the differences, subtract the relevant scores when the participants did not drink wine from the relevant scores when they did drink wine. Round your standard errors to three decimal places.)
xD | SE | |
weight | ||
caloric intake |
(b) A report of the study indicated that there were no significant
differences in these two outcome measures. Verify this result for
each measure, giving the test statistic, degrees of freedom, and
the P-value. (Use
α = 0.10.
Round your answers for t to three decimal places, and round your P-values to four decimal places.)
df | t | P-value | |
weight | |||
caloric intake |
State your conclusion for body weight.
a) Reject the null hypothesis. There is significant evidence of a difference in body weight.
b) Fail to reject the null hypothesis. There is not significant evidence of a difference in body weight.
c) Reject the null hypothesis. There is not significant evidence of a difference in body weight.
d) Fail to reject the null hypothesis. There is significant evidence of a difference in body weight.
State your conclusion for caloric intake.
a) Fail to reject the null hypothesis. There is not significant evidence of a difference in caloric intake.
b)Reject the null hypothesis. There is significant evidence of a difference in caloric intake.
c) Reject the null hypothesis. There is not significant evidence of a difference in caloric intake.
d) Fail to reject the null hypothesis. There is significant evidence of a difference in caloric intake.
(c) One concern with studies such as this, with a small number of
subjects, is that there may not be sufficient power to detect
differences that are potentially important. Address this question
by computing 95% confidence intervals for the two measures and
discuss the information provided by the intervals. (Round your
answers to three decimal places.)
weight ( kg, kg)
caloric intake ( calories, calories)
Discussion:
(d) Here are some other characteristics of the study. The study
periods lasted for 6 weeks. All subjects were males between the
ages of 21 and 50 years who weighed between 68 and 91 kg. They were
all from the same city. During the wine period, subjects were told
to consume two 135-milliliter (ml) servings of red wine per day and
no other alcohol. The entire 6-week supply was given to each
subject at the beginning of the period. During the other period,
subjects were instructed to refrain from any use of alcohol. All
subjects reported that they complied with these instructions except
for three subjects, who said that they drank no more than three to
four 12-ounce bottles of beer during the no-alcohol period. Discuss
how these factors could influence the interpretation of the
results.
(a)
For weight:
The standard error is
For caloric intake:
The standard error is
(b)
For weight :
For caloric intake
State your conclusion for body weight.
Fail to reject the null hypothesis. There is not significant evidence of a difference in body weight.
State your conclusion for caloric intake.
Fail to reject the null hypothesis. There is not significant evidence of a difference in caloric intake.
(c)
For weight :
For caloric intake:
(D)
Since subject are only 15 and out of these 3 did not follow instruction. So it may be possible that study is not very good. That is it not give true picture of population.