Question

Question 1)

College basketball, and particularly the NCAA basketball tournament, is a popular venue for gambling, from novices in office betting pools to high rollers. To encourage uniform betting across teams, Las Vegas oddsmakers assign a point spread to each game. The point spread is the oddsmakers’ prediction for the number of points by which the favored team will win. If you bet on the favorite, you win the bet provided the favorite wins by more than the point spread; otherwise, you lose the bet. Is the point spread a good measure of the relative ability of the two team? Two researchers obtained the difference between the actual margin of victory and the point spread, called the point-spread error, for 101 college basketball games. The sample mean point-spread error was found to be -0.2 point with a sample standard deviation of 10.9 points. For a particular game, a point-spread error of 0 indicates that the point spread was a perfect estimate of the two teams’ relative abilities. At the 5% level of significance, perform the test of hypothesis (five steps) that the mean point-spread error differs from 0.

Question 2)

The U.S. Department of Agriculture reports in Food Consumption, Prices, and Expenditures that the average American consumed 33 lb of cheese in 2010. Suppose that you want to decide whether last year’s mean cheese consumption is greater than the 2010 mean. The preliminary research indicated that population standard deviation is known to be 6.9 lb. Suppose that you decide to use a z-test with 10% level of significance and a sample size of 65.

(1) Find the power if in fact the last year’s mean cheese consumption is 36.2 lb.
(2) Find the power if in fact the last year’s mean cheese consumption is 33.7 lb.
(3) Use results from (1) & (2) above to interpret the relationship between true mean and power.

Answer 1

SOLUTION 1: NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

Level of significance=0.05

t= -0.2/1.08

t= -0.1844

(TWO TAILED TEST)

DEGREES OF FREEDOM= n-1= 101-1=100

P value= 0.8541

Since P value GREATER THAN 0.05 THEREFORE NOT SIGNIFICANT

DECISION: DO NOT REJECT NULL HYPOTHESIS H0.

CONCLSION: Since we don't have sufficient evidence to conclude that he mean point-spread error differs from 0.

NOTE: AS PER THE GUIDELINES I HAVE DONE THE FIRST QUESTION PLEASE RE POST THE REST.