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	374.300	552.500
Lean	2	611.925	371.512	453.650
Lean	3	314.212	580.138	540.362
Lean	4	580.644	354.144	492.269
Lean	5	575.869	349.994	509.081
Lean	6	539.388	387.312	508.500
Lean	7	679.188	269.188	465.700
Lean	8	553.656	320.219	572.006
Lean	9	369.831	538.031	530.431
Lean	10	499.700	528.838	396.962
Obese	11	264.244	648.281	519.044
Obese	12	464.756	453.644	510.931
Obese	13	369.138	579.662	559.300
Obese	14	417.667	573.662	532.208
Obese	15	345.375	582.662	499.931
Obese	16	417.531	563.556	449.856
Obese	17	356.650	617.262	457.550
Obese	18	264.344	645.181	504.981
Obese	19	413.631	570.769	451.706
Obese	20	431.356	594.369	411.919

(a)	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?    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?
(b)	State the null and alternative hypotheses. H0: μ1 = μ2 Ha: μ1 > μ2H0: μ1 ≠ μ2 Ha: μ1 = μ2    H0: μ1 = μ2 Ha: μ1 ≠ μ2H0: 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 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.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.

Answer 1

(a)	the practical question that requires a statistical test is Do lean and obese people differ in the average time they spend lying down?
(b)	the null and alternative hypotheses. H0: μ1 = μ2 Ha: μ1 ≠ μ2
(c)	using minitab>stat>basic stat>two sample t we have Two-Sample T-Test and CI: Lie, Group Two-sample T for Lie SE Group N Mean StDev Mean Lean 10 502.1 52.3 17 Obese 10 489.7 45.2 14 Difference = μ (Lean) - μ (Obese) Estimate for difference: 12.4 95% CI for difference: (-33.5, 58.3) T-Test of difference = 0 (vs ≠): T-Value = 0.57 P-Value = 0.578 DF = 18 Both use Pooled StDev = 48.8888 Find the size, mean and standard deviation of each group. n x s Lean 10 502.1 52.3 Obese     10 489.7 45.2 (d) the test statistic. t =0.57
(e)	Describe your results in this setting. 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.