09 STAT HWB q hypothesis testing one pop

09 STAT HWB q hypothesis testing one pop - Dr. V.R....

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Dr. V.R. Bencivenga Economics 329 PRACTICE ASSIGNMENT #9B: HYPOTHESIS TESTING I For each problem, state the null and alternative hypotheses in terms of the parameter(s) of probability model for the data, and give the test statistic; its sampling distribution; the reason why the sampling distribution is valid; the rejection region; and the conclusion of the test. 1. You are interested in the value of the mean of a normal population whose variance is known to be 100. Consider testing the null hypothesis H 0 : = 0 versus the alternative hypothesis H A : = 2. What is the minimum sample size needed to control the probability of Type I error at 5%, while simultaneously controlling the probability of Type II error at 5%? 2. A manufacturer of pharmaceuticals is concerned about the concentration of impurities in a drug. The standard is that the concentration of impurities should not exceed 2.5 percentage points in the population of batches of the drug produced by this manufacturer. It is known that in this population, the distribution of impurity concentrations is approximately normal with standard deviation .3 percentage point. The null hypothesis is that the population mean impurity concentration is at most 2.5. The alternative hypothesis is that the population mean exceeds 2.5. A random sample of nine batches will be tested. a. What rejection region restricts the probability of Type I error to be at most 10%? b. What rejection region restricts the probability of Type I error to be at most 5%? c. If the population mean is 2.4, what is the probability of Type I error for the test in part b? d. If the population mean is 2.6, what is the power of the test in part b? What is the probability of Type II error? e. Graph the sampling distributions of the sample mean under the null hypothesis (specifically, for a population mean of 2.5) and under the alternative hypothesis (specifically, for a population mean of 2.6). On your graph, represent the null and alternative hypotheses, the acceptance and rejection regions from part b, and the probabilities of Type I and Type II error from parts b and d. f.
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09 STAT HWB q hypothesis testing one pop - Dr. V.R....

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