Hypothesis Testing for ? using Z, T or Bootstrap. Computing power and Sample Size Exercise 1. From extensive testing, the mean drying time of a company’s spray paint product is thought to be normally distributed with mean ? = 100 seconds and standard deviation of ? = 4 seconds. The manager of the research division of the company that produces the paint considers using a different colorant and wants to know whether the mean drying time will change. a. Write out the manager’s question in terms of a null H0 and alternative hypotheses HA about the population mean ? drying time using the new colorant b. If the managers choose to use a significance level of ? = 0.10 and assume ? = 4, identify the power of a Z test to detect a mean increase of 2 seconds (?A = 102). They plan to look at a sample of 25 drying times and do a two-sided hypothesis test. Also identify the probability of making a type 2 error if the true mean drying time with the new colorant is 102 seconds, ?A = 102. c. Describe Type 1 and Type 2 errors of the test in context. d. What sample size should the managers use to ensure their 10% level 2-sided Z test has power of at least 0.9 to detect a true mean drying time of 102 ounces (assuming ? = 4)? e. Use the R function power.t.test() to recompute the power and type 2 error rate in (b) and the sample size in (e) assuming a t test will be run. Discuss how these values compare to the values computed assuming a Z test statistic and why that makes sense based on what we claim to “know” with each of them.
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- Null Hypothesis (\(H_0\)): The mean drying time with the new colorant is 100 seconds. (\(\mu = 100\)) - Alternative Hypothesis (\(H_A\)): The mean drying time with the new colorant is not 100 seconds. (\(\mu \neq 100\)) Show more…
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