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Lecture12 - March 19th Example Bayport High was chosen to...

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March 19th Example Bayport High was chosen to participate in a new curriculum program. A year later, 86 Bayport sophomores who participated in this program was randomly selected to take a SAT-I math exam. The national average on this exam was 494 with a standard deviation of 124. The 86 students averaged a score of 528. Can it be claimed at the 0.05 α = level that the new curriculum is effective? (Another question for later, if the true mean is 514, what is the power of the test at 0.05 α = ?) Solution Test on one population mean μ 86, 528, 124, large sample n x σ = = = 0 0 : 494 : 494 a H H μ μ μ = f Test statistic : 0 0 0 (0,1) ~ H X Z N n μ σ - = & 0 528 494 2.54 124 86 z - = = At 0 0.05 0.05, z 2.54 1.645 Z α = = = f Therefore, we reject 0 H and conclude the new curriculum is effective. p-value It is the probability that we observe something at least as extreme as the sample (or test statistic) observed, given that the null hypothesis is true. Example. 1. One-sided to the right 1
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0 0 0 : : a H H μ μ μ μ = f Test statistic : 0 2.54 z = 0 0 0 0 0 0 0 p-value ( | : ) ( 2.54 | : ) ( ) P Z z H p value P Z H example μ μ μ μ =
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