POWERSuppose X1, . . . , X25 represent the IQs of n students sampled from the Cal student body. IQsare standardized to be normal with mean 100 and SD 15. The Cal sample has a mean of 104 andan SD of 14.6.Are Cal students on average smarter than the norm?Null hypothesisAlternative hypothesisTest statisticp-valueNote that we do not reject the null hypothesis. We may ask ourselves, how likely is it that the testwould detect a difference (i.e. reject the null at the α = 0.05 level) when the true mean is 104?P (test statistic ≥ 1.65|µ = 104)In general, we might want to compute this chance for various values of µ to see how sensitive thistest is to departures from the hypothesized mean. A power curve gives us these values. That is, itcomputes P (test statistic ≥ 1.65|µ) for various values of µ.1●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●100 102 104 106 108 1100.0 0.2 0.4 0.6 0.8 1.0Power of z−testTrue value for
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