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The mean number of points improved (over the set of five games) was $\bar { x } = 7$ . Assu the standard deviation is $\sigma = 43$ and let $\mu$ be the population mean number of points improved for the set of five games. To determine whether the program is effective, a test is made of the hypotheses $H _ { 0 } : \mu = 0$ versus $H _ { 1 } : \mu > 0$ .

i). Compute the value of the test statistic.

ii). Compute the $P$ -value.

iii). Do you reject $H _ { 0 }$ at the $\alpha = 0.01$ level?

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