The accompanying data on food intake (in Kcal) for 15 men on the day following two nights of only 4 hours of sleep each night and for 15 men on the day following two nights of 8 hours of sleep each night is consistent with summary quantities in the paper "Short-Term Sleep Loss Decreases Physical Activity under Free-Living Conditions But Does Not Increase Food Intake under Time Deprived Laboratory Conditions in Healthy Men" (American Journal of Clinical Nutrition [2009]: 1476–1482). The men participating in this experiment were randomly assigned to one of the two sleep conditions. 4-hour sleep group: 3585 4470 3068 5338 2221 4791 4435 3099 3187 3901 3868 3869 4878 3632 4518 8-hour sleep group: 4965 3918 1987 4993 5220 3653 3510 3338 4100 5792 4547 3319 3336 4304 4057 Verify the assumption of approximate normality for each of the populations. Carry out a two-sample t test with ? = 0.05 to determine if there is a significant difference in mean food intake for the two different sleep conditions. (Use ?4-hour − ?8-hour.) Find the test statistic. (Round your answer to two decimal places.) t = Find the df. (Round your answer down to the nearest whole number.) df = Use technology to find the P-value. (Round your answer to four decimal places.) P-value =

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The accompanying data on food intake (in Kcal) for 15 men on the day following two nights of only 4 hours of sleep each night and for 15 men on the day following two nights of 8 hours of sleep each night is consistent with summary quantities in the paper "Short-Term Sleep Loss Decreases Physical Activity under Free-Living Conditions But Does Not Increase Food Intake under Time Deprived Laboratory Conditions in Healthy Men" (American Journal of Clinical Nutrition [2009]: 1476–1482). The men participating in this experiment were randomly assigned to one of the two sleep conditions.

4-hour sleep group:	3585	4470	3068	5338	2221
4791	4435	3099	3187	3901
3868	3869	4878	3632	4518
8-hour sleep group:	4965	3918	1987	4993	5220
3653	3510	3338	4100	5792
4547	3319	3336	4304	4057

Verify the assumption of approximate normality for each of the populations. Carry out a two-sample t test with ? = 0.05 to determine if there is a significant difference in mean food intake for the two different sleep conditions. (Use ?_4-hour − ?_8-hour.)

Find the test statistic. (Round your answer to two decimal places.)

t =

Find the df. (Round your answer down to the nearest whole number.)

df =

Use technology to find the P-value. (Round your answer to four decimal places.)

P-value =

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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