Question

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 210 games. The sample mean and sample standard deviation of the​ point-spread errors are x̄=1.3 and s=12.2. Use this information to test the hypothesis that the true mean​ point-spread error for all games is larger than 0. Conduct the test at α=0.01 and interpret the result.

a.find the rejection region

b. find the value of the test statistic

c. Compare the rejection region result and the test statistic result

Answer 1

Solution :

= 0

= 1.3

s = 12.2

n = 210

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 0

H_a : > 0

a ) =0.01

the critical value for a right-tailed test is t_c​=2.344.

The rejection region for this right-tailed test is R = t:t > 2.344

b) Test Statistics

Test statistic = t

= ( - ) / s / n

= (1.3-0) / 12.2/ 210

= 1.544

c ) Since it is observed that t =1.544 ≤ t_c ​=2.344, it is then concluded that the null hypothesis is not rejected.

P(z > 1.544) = 1 - P(z <1.544 ) = 0.062

P-value = 0.062

p= 0.062 ≥ 0.01, it is concluded that the null hypothesis is not rejected.