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The final scores of games of a certain sport were compared against the final point spreads established by oddsmakers. The difference between the game outcome and point spread (called a point-spread error) was calculated for 230 games. The mean error is  X_bar = -0.7. The population standard deviation of the point-spread error sigma = 14.1. Use this information to test the hypothesis that the true mean point-spread error for all games differs from 0. Conduct the test at alpha =0.01 and interpret the result.

Determine the null and alternative hypotheses. 


The test statistic Z= ___ ?


What is the appropriate conclusion at alpha = 0.01?

 

The null hypothesis in this test represent the claim, H0: mu = 0 against the alternative hypothesis

Ha: mu != 0 The standard normal distribution applies because the population standard deviation has been given.

Z = (X_bar - mu)/(standard deviation/sqrt(n)) z = (-0.7 - 0)/(14.1/sqrt(230)) = -0.75 The critical value can be calculated using the Excel function. =NORM.S.INV(1-0.01/2) = -2.58 of 2.58 The z-score is negative, so compare that with -2.58. Reject the null hypothesis because -2.58 is less than -0.75

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