all questions A-F 7.36 Food intake and weight gain. If we increase our food inta

Question

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7.36 Food intake and weight gain. 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 l 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 perlod expressed in kilograms subject weight before 55. T 54.9 59.6 62.3 74.2 15.6 7o 7 533 Weight after Di 58.8 66.0 66.2 79.0 82.3 74.3 59.3 9 10 11 12 13 14 15 16 Weight before 73.3 634 68 l 73.7 91.7 55.9 61.7 57.8 Weight after 79. 660 73.4 T6.9 93 63 0 682 603 (a) For each subject, subtract the weight before from the weight after to determine the weight change. (b) Find the mean and the standard deviation for the weight change.

Explanation / Answer

Table (in KGs)

Subject

Before

After

Weight Change (D)

1

55.7

61.7

6

2

54.9

58.8

3.9

3

59.6

66

6.4

4

62.3

66.2

3.9

5

74.2

79

4.8

6

75.6

82.3

6.7

7

70.7

74.3

3.6

8

53.3

59.3

6

9

73.3

79.1

5.8

10

63.4

66

2.6

11

68.1

73.4

5.3

12

73.7

76.9

3.2

13

91.7

93.1

1.4

14

55.9

63

7.1

15

61.7

68.2

6.5

16

57.8

60.3

2.5

Mean

4.73125

SD

1.745744827

Table (in LBs)

Subject

Before

After

Weight Change (D)

1

122.54

135.74

13.2

2

120.78

129.36

8.58

3

131.12

145.2

14.08

4

137.06

145.64

8.58

5

163.24

173.8

10.56

6

166.32

181.06

14.74

7

155.54

163.46

7.92

8

117.26

130.46

13.2

9

161.26

174.02

12.76

10

139.48

145.2

5.72

11

149.82

161.48

11.66

12

162.14

169.18

7.04

13

201.74

204.82

3.08

14

122.98

138.6

15.62

15

135.74

150.04

14.3

16

127.16

132.66

5.5

Mean

10.40875

SD

3.840638619

c)

SE=SD/n=1.745745/16=1.745745/4=0.43643

The t critical value for 15 degrees of freedom is 2.1314. Hence, confidence interval is

D+-ta/2*SE

4.73+-2.1314*0.43643

LCL=4.73-0.93=3.80

UCL=4.73+0.93=5.66

d)

SE=SD/n=3.84/16=3.84/4=0.96

D+-ta/2*SE

10.40875+-2.1314*0.96

LCL=10.40875-2.046=8.36275

UCL=10.40875+2.046=12.45475

e)

H0: D = 16

H1: D ¹ 16

10.40875-0/0.96=10.84

The t critical value for 15 degrees of freedom is 2.1314. Since 10.84>2.1314, it lies in the rejection region and hence reject the null hypothesis.      

The p-value is <.00001

f)

Here, since we needed to test the hypothesis for subjects before and after some treatment, we applied the paired difference test and we concluded to reject the null hypothesis. Generally, if the value is less than -tCRIT and greater than +tCRIT, then we reject the null hypothesis which was the case over here and hence we rejected.

Subject

Before

After

Weight Change (D)

1

55.7

61.7

6

2

54.9

58.8

3.9

3

59.6

66

6.4

4

62.3

66.2

3.9

5

74.2

79

4.8

6

75.6

82.3

6.7

7

70.7

74.3

3.6

8

53.3

59.3

6

9

73.3

79.1

5.8

10

63.4

66

2.6

11

68.1

73.4

5.3

12

73.7

76.9

3.2

13

91.7

93.1

1.4

14

55.9

63

7.1

15

61.7

68.2

6.5

16

57.8

60.3

2.5

Mean

4.73125

SD

1.745744827

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