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Quiz 7 Key MA 223 1. We would take H0 : µ = 375 versus Ha : µ ̸= 375, where µ is the population mean for all of the bulbs in the shipment. x̄−375 √ 2. Under H0 we find that Z = s/ is standard normal, and so with 100 probability 0.95 we will have −1.96 < Z < 1.96 for an IID sample of 350−375 √ 100 bulbs. In our case Z = 100/ = −2.5, outside the range required. 100 We reject H0 . The p-value for this two-sided test is p = 0.0124. 3. Circle true or false: TRUE: In part (2) we could have made a type I error (since we may have erroneously rejected H0 ). FALSE: In part (2) we could NOT have made a type II error (that means accepting H0 when in fact H0 is false). FALSE: If we decrease α the probability of making a type II error cannot decrease, and will likely increase. 1