Question

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 μ1 be the mean time spent lying down by the lean group, and μ2 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 1 516.100 373.300 558.500

Lean 2 603.925 375.512 448.650

Lean 3 324.212 583.138 541.362

Lean 4 580.644 357.144 488.269

Lean 5 576.869 343.994 513.081

Lean 6 548.388 381.312 501.500

Lean 7 678.188 265.188 462.700

Lean 8 560.656 318.219 563.006

Lean 9 369.831 538.031 531.431

Lean 10 504.700 530.838 397.962

Obese 11 264.244 641.281 517.044

Obese 12 465.756 453.644 517.931

Obese 13 364.138 581.662 560.300

Obese 14 411.667 575.662 533.208

Obese 15 344.375 580.662 506.931

Obese 16 420.531 570.556 445.856

Obese 17 359.650 624.262 460.550

Obese 18 269.344 644.181 506.981

Obese 19 408.631 570.769 446.706

Obese 20 425.356 588.369 412.919

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

-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?

-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 sitting?

(b) State the null and alternative hypotheses.

-H0: μ1 ≠ μ2 Ha: μ1 = μ2

-H0: μ1 > μ2 Ha: μ1 ≠ μ2

-H0: μ1 = μ2 Ha: μ1 ≠ μ2

-H0: μ1 = μ2 Ha: μ1 > μ2

(c) Find the size, mean and standard deviation of each group. n x s

Lean _____

Obese _____

(d) Calculate the test statistic. t =

(e) Describe your results in this setting.

-There is enough evidence at the 5% significance level to reject the hypothesis that lean and moderately obese people spend (on average) the same amount of time lying down.

-There is not enough evidence at the 5% significance level to reject the hypothesis that lean and moderately obese people spend (on average) the same amount of time lying down.

Answer 1

a)

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

b)

this si two-tailed test

option C)

H0: μ1 = μ2 Ha: μ1 ≠ μ2

c)

d)

using minitab

stat -> basic statistics -> 2-sampel t

t = 0.44

e)

since p-value = 0.664 > alpha

we fail to reject the null hypothesis

we conclude that there is not significant difference

option B)

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