7.38 (d-f)(d) Convert the mean weight gain in kilograms to mean weight gain in pounds. Because there are 2.2 kg per pound, multiply the value in kilograms by 2.2 to obtain pounds. Do the same for the standard deviation and the confidence interval.(e) Test the null hypothesis that the mean weight gain is 16 lb. Be sure to specify the null and alternative hypotheses, the test statistic with degrees of freedom, and the P-value. What do you conclude?(f) Write a short paragraph explaining your results. 7.38 Food intake and weight gain. If we increase our food intake, we generallygain weight. Nutrition scientists can calculate the amount of weight gain that would beassociated 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. Thesubjects maintained this diet for eight weeks, so they consumed a total of 56,000 extra calories. 18According to theory, 3500 extra calories will translate into a weight gain of 1 pound. Therefore, weexpect each of these subjects to gain 56,000/3500 = 16 pounds (lb). Here are the weights before andafter the eight-week period, expressed in kilograms (kg): Im WTGAINSubject1 2 34 5 6 7 8Weight before55.754.959.662.374.275.670.753.3Weight after61.758.866.066.279.082.374.359.3Subject910111213141516Weight beforeWeight after73.363.468.173.791.755.961.757.879.166.073.476.993.163.068.260.3

Name: 7.38 (d-f)(d) Convert the mean weight gain in kilograms to mean weight
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Description: 7.38 (d-f)(d) Convert the mean weight gain in kilograms to mean weight gain in pounds. Because there are 2.2 kg per pound, multiply the value in kilograms by 2.2 to obtain pounds. Do the same for the standard deviation and the confidence interval.(e)

Given information: The data showing the n = 16 matched pairs of the weights before and after the…

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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7.38 (d-f)

(d) Convert the mean weight gain in kilograms to mean weight gain in pounds. Because there are 2.2 kg per pound, multiply the value in kilograms by 2.2 to obtain pounds. Do the same for the standard deviation and the confidence interval.

(e) Test the null hypothesis that the mean weight gain is 16 lb. Be sure to specify the null and alternative hypotheses, the test statistic with degrees of freedom, and the P-value. What do you conclude?

(f) Write a short paragraph explaining your results.

7.38 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 eight weeks, so they consumed a total of 56,000 extra calories. 18
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 eight-week period, expressed in kilograms (kg): Im WTGAIN
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
58.8
66.0
66.2
79.0
82.3
74.3
59.3
Subject
9
10
11
12
13
14
15
16
Weight before
Weight after
73.3
63.4
68.1
73.7
91.7
55.9
61.7
57.8
79.1
66.0
73.4
76.9
93.1
63.0
68.2
60.3

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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