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

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 + ...