If we increase our food intake, we generally gain weight. Nutrition scientists c
ID: 3356821 • Letter: I
Question
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 nonobese 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 8 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 56,000/3500 = 16 pounds (lb). Here are the weights before and after the 8-week period, expressed in kilograms (kg).
(a) For each subject, subtract the weight before from the weight after to determine the weight change in kg.
Subject 1
Subject 2
Subject 3
Subject 4
Subject 5
Subject 6
Subject 7
Subject 8
Subject 9
Subject 10
Subject 11
Subject 12
Subject 13
Subject 14
Subject 15
Subject 16
(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.) , ( ?, ?) lb
(e) 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.)
(f) Write a short paragraph explaining your results.
Answer all parts
Subject 1 2 3 4 5 6 7 8 Weight before 55.7 54.9 59.6 62.3 74.2 75.6 70.7 53.3 Weight after 61.7 58.7 66.0 66.2 79.1 82.3 74.4 59.3 Subject 9 10 11 12 13 14 15 16 Weight before 73.3 63.4 68.1 73.7 91.7 55.9 61.7 57.8 Weight after 79.0 66.1 73.3 76.9 93.2 63.0 68.2 60.4Explanation / Answer
a)
b)
mean =4.7438
and standard deviation s =1.7103
c)standard error se =std deviation/(n)1/2 =0.4276
for (n-1=15) degree of freedom and 95% CI ; t=2.1314
margin of errror =t*std error =0.9114
95% confidence interval:=sample ,mean -/+ t*Std error
d)
x =10.4363
s =3.7628
confidence interval =8.4312 to 12.4413
t =(dbar-16)/std error =-5.9145
degree of freedom =n-1=16-1=15
p value =1.0000
f)as p value is significantly high ; we can not conclude that weight increase after being fed 56000 calories is 16 pounds
subject before after difference(d)=x2-x1 1 55.7 61.7 6 2 54.9 58.7 3.8 3 59.6 66 6.4 4 62.3 66.2 3.9 5 74.2 79.1 4.9 6 75.6 82.3 6.7 7 70.7 74.4 3.7 8 53.3 59.3 6 9 73.3 79 5.7 10 63.4 66.1 2.7 11 68.1 73.3 5.2 12 73.7 76.9 3.2 13 91.7 93.2 1.5 14 55.9 63 7.1 15 61.7 68.2 6.5 16 57.8 60.4 2.6Related Questions
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