People gain weight when they take in more energy from food than they expend. Researchers wanted to investigate the link between obesity and energy spent on daily activity. Choose 20 healthy volunteers who don't exercise. Deliberately choose 10 who are lean and 10 who are mildly obese but still healthy. Attach sensors that monitor the subjects' every move for 10 days. The table below presents data on the time (in minutes per day) that the subjects spent standing or walking, sitting, and lying down. Is there a significant difference between the mean times the two groups spend lying down? Let ?1 be the mean time spent lying down by the lean group, and ?2 be the mean time for the obese group. Time (minutes per day) spent in three different postures by lean and obese subjects Group Subject Stand/Walk Sit Lie Lean 1 509.100 366.300 554.500 Lean 2 603.925 374.512 452.650 Lean 3 322.212 580.138 533.362 Lean 4 581.644 362.144 489.269 Lean 5 580.869 343.994 511.081 Lean 6 548.388 382.312 509.500 Lean 7 677.188 271.188 472.700 Lean 8 552.656 317.219 572.006 Lean 9 378.831 538.031 527.431 Lean 10 505.700 526.838 397.962 Obese 11 258.244 642.281 519.044 Obese 12 467.756 461.644 516.931 Obese 13 365.138 574.662 562.300 Obese 14 410.667 581.662 531.208 Obese 15 346.375 581.662 503.931 Obese 16 418.531 563.556 443.856 Obese 17 356.650 617.262 465.550 Obese 18 271.344 641.181 504.981 Obese 19 407.631 575.769 443.706 Obese 20 425.356 592.369 414.919 1) Find the size, mean and standard deviation of each group. n x s Lean Obese 2) Calculate the test statistic. t= 3) What is the practical question that requires a statistical test? Does the average time spent sitting differ from the average time spent lying down for lean and obese people? Do lean and obese people differ in the average time they spend lying down? Does the average time spent sitting or standing differ from the average time spent lying down for lean and obese people? Do lean and obese people differ in the average time they spend sitting

People gain weight when they take in more energy from food than they expend. Researchers wanted to investigate the link between obesity and energy spent on daily activity. Choose 20 healthy volunteers who don't exercise. Deliberately choose 10 who are lean and 10 who are mildly obese but still healthy. Attach sensors that monitor the subjects' every move for 10 days. The table below presents data on the time (in minutes per day) that the subjects spent standing or walking, sitting, and lying down. Is there a significant difference between the mean times the two groups spend lying down? Let ?1 be the mean time spent lying down by the lean group, and ?2 be the mean time for the obese group. Time (minutes per day) spent in three different postures by lean and obese subjects Group Subject Stand/Walk Sit Lie Lean 1 509.100 366.300 554.500 Lean 2 603.925 374.512 452.650 Lean 3 322.212 580.138 533.362 Lean 4 581.644 362.144 489.269 Lean 5 580.869 343.994 511.081 Lean 6 548.388 382.312 509.500 Lean 7 677.188 271.188 472.700 Lean 8 552.656 317.219 572.006 Lean 9 378.831 538.031 527.431 Lean 10 505.700 526.838 397.962 Obese 11 258.244 642.281 519.044 Obese 12 467.756 461.644 516.931 Obese 13 365.138 574.662 562.300 Obese 14 410.667 581.662 531.208 Obese 15 346.375 581.662 503.931 Obese 16 418.531 563.556 443.856 Obese 17 356.650 617.262 465.550 Obese 18 271.344 641.181 504.981 Obese 19 407.631 575.769 443.706 Obese 20 425.356 592.369 414.919 1) Find the size, mean and standard deviation of each group. n x s Lean Obese 2) Calculate the test statistic. t= 3) What is the practical question that requires a statistical test? Does the average time spent sitting differ from the average time spent lying down for lean and obese people? Do lean and obese people differ in the average time they spend lying down? Does the average time spent sitting or standing differ from the average time spent lying down for lean and obese people? Do lean and obese people differ in the average time they spend sitting

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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Question

Time (minutes per day) spent in three different postures by lean and obese subjects
Group	Subject	Stand/Walk	Sit	Lie
Lean	1	509.100	366.300	554.500
Lean	2	603.925	374.512	452.650
Lean	3	322.212	580.138	533.362
Lean	4	581.644	362.144	489.269
Lean	5	580.869	343.994	511.081
Lean	6	548.388	382.312	509.500
Lean	7	677.188	271.188	472.700
Lean	8	552.656	317.219	572.006
Lean	9	378.831	538.031	527.431
Lean	10	505.700	526.838	397.962
Obese	11	258.244	642.281	519.044
Obese	12	467.756	461.644	516.931
Obese	13	365.138	574.662	562.300
Obese	14	410.667	581.662	531.208
Obese	15	346.375	581.662	503.931
Obese	16	418.531	563.556	443.856
Obese	17	356.650	617.262	465.550
Obese	18	271.344	641.181	504.981
Obese	19	407.631	575.769	443.706
Obese	20	425.356	592.369	414.919

1) Find the size, mean and standard deviation of each group.

	n	x	s
Lean
Obese

2) Calculate the test statistic. t=

3) What is the practical question that requires a statistical test?

Does the average time spent sitting differ from the average time spent lying down for lean and obese people?

Do lean and obese people differ in the average time they spend lying down?

Does the average time spent sitting or standing differ from the average time spent lying down for lean and obese people?

Do lean and obese people differ in the average time they spend sitting?

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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