If we increase our food intake, we generally gain weight. Nutrition scientists can calculate the amount of weight gain that would be associated with a given increase in calories. In one study, 16 non-obese adults, aged 25 to 36 years, were fed 1000 calories per day in excess of the calories needed to maintain a stable body weight. The subjects maintained this diet for eight weeks, so they consumed a total of 56,000 extra calories. According to theory, 3500 extra calories will translate into a weight gain of 1 pound. Therefore, we expect each of these subjects to gain 56000/3500 = 16 pounds (lb). Here are the weights before and after the 8-week period, expressed in kilograms (kg). Subject12345678
Weight before55.754.959.662.374.275.670.75 3.3
Weight after61.758.866.066.178.982.374.459 .3
Subject910111213141516
Weight before73.363.468.173.791.755.961.75 7.8
Weight after79.166.173.477.093.163.068.160 .2
(a) For each subject, subtract the weight before from the weight after to determine the weight change in kg.
Subject 1 kg
Subject 2 kg
Subject 3 kg
Subject 4 kg
Subject 5 kg
Subject 6 kg
Subject 7 kg
Subject 8 kg
Subject 9 kg
Subject 10 kg
Subject 11 kg
Subject 12 kg
Subject 13 kg
Subject 14 kg
Subject 15 kg
Subject 16 kg
(b) Find the mean and the standard deviation for the weight change. (Round your answers to four decimal places.)
xkg=kg
skg=kg
(c) Calculate the standard error se and the margin of error me for 95% confidence. (Round your answers to four decimal places.)
se=
me=
Report the 95% confidence interval for weight change in a sentence that explains the meaning of the 95%. (Round your answers to four decimal places.)
Based on a method that gives correct results 95% of the time, the mean weight change is kg to kg.
(d) Convert the mean weight gain and standard deviation in kilograms to pounds. Because there are 2.2 kg per pound, multiply the value in kilograms by 2.2 to obtain pounds. (Round your answer to four decimal places.)
xlb=lb
slb=lb
Do the same for the confidence interval. (Round your answers to four decimal places.)
leftparen1.gif
,
rightparen1.gif
lb
(e) Test the null hypothesis that the mean weight gain is 16 lb. (Let
? = 0.05.)
Specify the null hypothesis.
H0: ? > 16
H0: ? ? 16
H0: ? = 16
H0: ? ? 16
H0: ? ? 16
Specify the alternate hypothesis.
Ha: ? = 16
Ha: ? < 16
Ha: ? ? 16
Ha: ? > 16
Ha: ? ? 16
Carry out the test. (Round your answer for t to three decimal places.)
t =
Give the degrees of freedom.
Give the P-value. (Round your answer to four decimal places.)
What do you conclude?
We have sufficient evidence to conclude that the mean weight change is not 16 pounds. We do not have sufficient evidence to conclude that the mean weight change is not 16 pounds.
(f) Write a short paragraph explaining your results.