# Which in turn means we cannot support h 1 this means

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which, in turn, means we cannot support H1.This means there is insufficientevidence to conclude thatthe unknown population mean is different than 10.3.(B). The 95% confidence interval [10.4, 11.2] does not containthe hypothesized value of 10.This meanswe reject Ho which, in turn, means we support H1.This means there is sufficientevidence to concludethat the unknown population mean is different than 10.4.(D). The 95% confidence interval [9.8, 10.4] containsthe hypothesized value of 10.This means wecannot reject Ho which, in turn, means we cannot support H1.This means there is insufficientevidenceto conclude that the unknown population mean is different than 10.Note: the burden of proof is always on H1so we always say “insufficientevidence exists to conclude H1…”when wedo notreject Ho.We always say “sufficientevidence exists to conclude H1...” when werejectHo.Weneverconclude that something is exactlyequalto a hypothesized value (since equality is always in thenullhypothesis which is always rejected or not rejected, but it is never supported or taken to be true).Jury Trial Example: Ho: Defendant is innocent, H1: Defendant is guilty.The jury decision is either“sufficient evidence exists to find the defendant guilty” (if Ho is rejected) or “insufficient evidence exists tofind the defendant guilty” (if Ho is not rejected).The defendant is never found innocent, just not guilty.5.(B). Type I error is a “false alarm”, which is the smoke detector sounding when there’s not really a fire.6.(A). Power is the probability of the smoke detector sounding when there really is a fire.Also, Power = 1– Probability(Type II Error), where a Type II error is a “missed alarm” (i.e., smoke detector not soundingwhen there really is a fire).7.(A). The sample meanxis always in the center of a confidence interval, since a confidence interval isdeveloped by taking the sample meanx(which is a point estimate of the unknown population mean) andthen subtracting the margin of error to get the lower confidence interval value and adding the margin oferror to get the upper confidence interval value.8.(C). Type I error and Type II error probabilities move in opposite directions (all else equal).So if theprobability of a Type I error goes up, the probability of a Type II error will go down (all else equal).Think of a smoke detector: if we make it more sensitive (easier to go off), the probability of a false alarm(Type I error) will increase but the probability of a missed alarm (Type II error) will decrease.9.(B). By definition, the level of significance represents the probability of a Type I error.So if α = 0.01,this means the probability of a Type I error = 0.01.10. (D). Increasing sample size will reduce the width (increase the precision) of a confidence interval.Just
examine the confidence interval formula to see why this has to be true.Answer choices B & C actuallyincrease the width of a confidence interval.Answer choice A (sample mean) has nothing to do with thewidth of a confidence interval.

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Statistical hypothesis testing