Question: Point spreads of NFL games. Refer to the Chance (Fall 1998) study of point-spread errors in NFL games, Exercise 7.41 (p. 411). Recall that the difference between the actual game outcome and the point spread established by odds makers—the point-spread error—was calculated for 240 NFL games. The results are summarized as follows: . Suppose the researcher wants to know whether the true standard deviation of the point spread errors exceeds 15. Conduct the analysis using α = 0.10.

The given problem explains the point-spread error in NFL games. The point-spread error was calculated for 240 NFL games.

From the sample, the sample mean is -1.6, and the sample standard deviation is 13.3.

Here, the test is based on the true standard deviation of the point-spread error.

The null hypothesis, which can be further tested with the use of specific statistical tests, is an assumption that must be made before making any choice regarding the true value of the parameters. The choice is then made based on the calculated value of the parameter and critical, which means that if the computed value falls within the critical zone, the null hypothesis is rejected; otherwise, it is accepted.

The null and alternative hypotheses are

Null hypothesis:

H₀ : σ = 15

The true standard deviation of points spread errors is 15.

Alternative hypothesis:

H_a : σ > 15

The true standard deviation of points spread errors exceeds 15.

The level of significance is α = 0.10

Since the test statistic is given by

From the given data sample size n is 240.

By substituting the values,

From the table of for df = 239 and α = 0.10 the critical value for the test is,

The calculated statistics value is less than the critical value. That is .

So, the null hypothesis is rejected at the given level of significance, and we conclude that the true standard deviation of the points spread errors is 15.