Use for the following for the next 6 questions: People gain weight when they tak
ID: 3353670 • Letter: U
Question
Use for the following for the next 6 questions:
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 (State, Plan, Solve, Conclude) to answer this question from the data. (Let 1 be the mean time spent lying down by the lean group, and 2be the mean time for the obese group.)
STATE:
From the above information, what is practical question of interest that requires a statistical test?
Does the average time spent sitting differ from the average time spent lying down for lean and obese people?
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 lying down?
Do lean and obese people differ in the average time they spend sitting?
PLAN:
What are the appropriate null and alternative hypotheses?
SOLVE: Match the means, standard deviations and degrees of freedom (conservative) to their appropriate numerical values.
Mean Time Lying Down for Obese
9
Mean Time Lying Down for Lean
45.603
Standard Deviation of Time Lying Down for Obese
556.156
Standard Deviation of Time Lying Down for Lean
18
Conservative Degrees of Freedom
52.313
SOLVE:
95%CI(40.32, 60.67)
95%CI(-39.94, 59.35)
95%CI(-33.31, 52.72)
95%CI(-46.87, 64.34)
Question 14
2 / 2 pts
SOLVE:
Calculate the appropriate test statistic.
CONCLUDE: Based on the p-value and your previous findings what can you conclude from this problem?
There is convincing evidence that the average time spent lying down is different between people who are lean and those who are mildly obese.
There is moderately suggestive evidence that the average time spent lying down is different between people who are lean and those who are mildly obese.
There is slightly suggestive evidence that the average time spent lying down is different between people who are lean and those who are mildly obese.
There is no evidence that the average time spent lying down is different between people who are lean and those who are mildly obese.
Time (minutes per day) spent in three different postures by Lean and Obese subjects Group Subject Stand/Walk Sit Lie Lean 1 507.1 367.3 559.5 Lean 2 609.925 369.512 453.65 Lean 3 319.212 586.138 532.362 Lean 4 580.644 355.144 494.269 Lean 5 582.869 346.994 509.081 Lean 6 539.388 385.312 503.5 Lean 7 680.188 267.188 464.7 Lean 8 557.656 327.219 570.006 Lean 9 371.831 533.031 528.431 Lean 10 503.7 531.838 395.962 Obese 11 256.244 650.281 516.044 Obese 12 461.756 453.644 513.931 Obese 13 364.138 583.662 568.3 Obese 14 410.667 581.662 527.208 Obese 15 348.375 576.662 500.931 Obese 16 419.531 572.556 450.856 Obese 17 356.65 626.262 461.55 Obese 18 268.344 650.181 510.981 Obese 19 407.631 570.769 446.706 Obese 20 427.356 596.369 417.919Explanation / Answer
Is there a significant difference between the mean times the two groups spend lying down?
1)
State:
Do lean and obese people differ in the average time they spend lying down?
2)
PLAN:
Ho: u1 – u2 = 0 v/s h1: u1 – u2 =/= 0
3)
SOLVE:
Mean Time Lying Down for Obese = 491.44
Mean Time Lying Down for Lean = 501.15
Standard Deviation of Time Lying Down for Obese = 45.60
Standard Deviation of Time Lying Down for Lean = 52.31
Conservative Degrees of Freedom = Min(n1-1, n2-1) = 9
4)
SOLVE:
95%CI(-39.94, 59.35)
t(A/2,n1+N2-2) =T.INV.2T(0.05,9)=2.262157163
CI = (mean1-mean2) - t(a/2,df)*Sqrt(s1^2/n1 + s2^2/n2)
lower =(501.15-491.44)-2.262157*SQRT(52.31^2/10+45.6^2/10) = -39.93234393
upper = (501.15-491.44)+2.262157*SQRT(52.31^2/10+45.6^2/10) = 59.35234393
5)
t=
(mean1-mean2)/sqrt(s1^1/n1+s2^2/n2)
=(501.15-491.44)/SQRT(52.31^2/10+45.6^2/10)
0.442475974
6)
CONCLUDE:
p-value
2*(1-P(T<0.442476))
=T.DIST.2T(0.442476,9)
0.668587511
There is convincing evidence that the average time spent lying down is different between people who are lean and those who are mildly obese.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.