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1. A company manufacturing pacemakers is testing a new electrode. The electrodes must adhere to a silicone substrate for at least 20 years. The company is going to test the hypothesis that the mean adherence time is 20 years vs. the alternative that it is less than 20 years at the significance level 0.05. The experiment will be conducted with a sample of 25 volunteers Assume that the population distribution for the adherence time is approximately normally distributed. The average adherence time for the pacemakers in the 25 volunteers is found to be 18.8 years and the standard deviation of the sample is found to be 3 years. (a) Conduct the tes. What are the assumptions? What is the test statistic? State your decision and conclusion (b) I te company wants to decrease the probability of making a type I error without increasing the sample size, should the critical value be increased or decreased? Justify your answer (c) Find the 95% confidence interval for the population mean adherence time. Interpret this interval in context of the problem
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