People gain weight when they take in more energy from food than they expend. Som
ID: 3358517 • Letter: P
Question
People gain weight when they take in more energy from food than they expend. Some 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. It can be concluded that mildly obese people spend less time standing and walking (on the average) than lean people. Is there a significant difference between the mean times the two groups spend lying down? Use the four-step process to answer this question from the data. (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
373.300
550.500
Lean
2
609.925
369.512
449.650
Lean
3
317.212
582.138
533.362
Lean
4
583.644
352.144
485.269
Lean
5
576.869
347.994
511.081
Lean
6
541.388
380.312
507.500
Lean
7
677.188
271.188
471.700
Lean
8
552.656
324.219
568.006
Lean
9
375.831
537.031
533.431
Lean
10
502.700
525.838
396.962
Obese
11
255.244
642.281
519.044
Obese
12
463.756
459.644
511.931
Obese
13
364.138
582.662
559.300
Obese
14
411.667
574.662
530.208
Obese
15
352.375
580.662
509.931
Obese
16
413.531
563.556
446.856
Obese
17
355.650
617.262
460.550
Obese
18
262.344
641.181
509.981
Obese
19
411.631
570.769
452.706
Obese
20
427.356
594.369
410.919
STATE:
What is the practical question that requires a statistical test?
Do lean and obese people differ in the average time they spend sitting?
Does the average time spent sitting or standing differ from the average time spent lying down for lean and obese people?
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?
PLAN:
State the null and alternative hypotheses.
H0: 1 > 2
Ha: 1 2
H0: 1 = 2
Ha: 1 2
H0: 1 2
Ha: 1 = 2
H0: 1 = 2
Ha: 1 > 2
SOLVE:
Find the size, mean and standard deviation of time spent lying of each group. (Round your means and standard deviations to four decimal places.)
n
x-bar
s
Lean
_____ _______ _____
Obese
_______ _________ _______
Calculate the test statistic. (Round your answer to three decimal places.)
t =
Use Table C to give two values between which P lies.
0.50 < P 1.00
0.40 < P 0.50
0.30 < P 0.40
0.20 < P 0.30
0.10 < P 0.20
0.05 < P 0.10
0.04 < P 0.05
CONCLUDE:
Describe your results in this setting.
There is not enough evidence to reject the hypothesis that lean and moderately obese people spend (on the average) the same amount of time lying down.
There is enough evidence at the 5% significance level to reject the hypothesis that lean and moderately obese people spend (on the average) the same amount of time lying down.
Time (minutes per day) spent in three different postures by lean
and obese subjects
Group
Subject
Stand/Walk
Sit
Lie
Lean
1
509.100
373.300
550.500
Lean
2
609.925
369.512
449.650
Lean
3
317.212
582.138
533.362
Lean
4
583.644
352.144
485.269
Lean
5
576.869
347.994
511.081
Lean
6
541.388
380.312
507.500
Lean
7
677.188
271.188
471.700
Lean
8
552.656
324.219
568.006
Lean
9
375.831
537.031
533.431
Lean
10
502.700
525.838
396.962
Obese
11
255.244
642.281
519.044
Obese
12
463.756
459.644
511.931
Obese
13
364.138
582.662
559.300
Obese
14
411.667
574.662
530.208
Obese
15
352.375
580.662
509.931
Obese
16
413.531
563.556
446.856
Obese
17
355.650
617.262
460.550
Obese
18
262.344
641.181
509.981
Obese
19
411.631
570.769
452.706
Obese
20
427.356
594.369
410.919
Explanation / Answer
State :Do lean and obese people differ in the average time they spend lying down
Plan:H0: 1 = 2
Ha: 1 2
Find the size, mean and standard deviation of time spent lying of each group. (Round your means and standard deviations to four decimal places.)
n
x-bar
s
Lean
10 500.75 51.37
Obese
10 491.14 45.82
Calculate the test statistic. (Round your answer to three decimal places.)
t =0.441
t=(mean1-mean2)/((sp*(1/n1 +1/n2)1/2) and sp2=((n1-1)s12+(n2-1)s22)/n and with df is n=n1+n2-2
Use Table C to give two values between which P lies.
0.50 < P 1.00
There is not enough evidence to reject the hypothesis that lean and moderately obese people spend (on the average) the same amount of time lying down.
since p-value is more than alpha=0.05
n
x-bar
s
Lean
10 500.75 51.37
Obese
10 491.14 45.82
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