Solve the following problems:
A) These are heights and weights for five randomly-selected adults. Units are centimeters and kilograms, respectively.
height 183 172 190 167 193
weight 91 83 99 83 104
a. Find a linear regression equation which predicts weight as a function of height. Be sure to define your variables clearly.
b. According to your equation, what should a 160-centimeter adult weigh?
c. Explain why the prediction in part (b) is likely to be close to correct, or explain why it probably is not.
B)Here are the weights of two samples of nuts:
S = {1.07, 1.15, .99, 1.41, 1.26, 1.09, 1.16, 1.2}
T = {1.21, .7, 1.55, 1.19, .9, 1.38, 1.15, 1.01}
a. Demonstrate that it is not unreasonable to believe that the samples are drawn from normal populations.
b. Can you be 99% certain that the samples came from populations with different means? Justify your answer. Include a statement in plain English.
c. Can you be 95% certain that the standard deviation of the population from which S was drawn is less than the standard deviation of the population from which T was drawn? Justify your answer. Include a statement in plain English.
c) A randomly-selected group of 21 people were each asked to play a new video game. Below are the numbers of points they scored. The scores are grouped according to the age, in years, of the players.
below 20 {23, 51, 42, 36, 29, 44, 53}
20 to 40 {42, 33, 20, 45, 55, 22, 30}
above 40 {31, 25, 24, 36, 27, 37, 22}
Is it 95%-certain that the three mean scores of all potential players below 20, all potential players between 20 and 40, and all potential players above 40 are not the same? Explain how you proved your answer.