Knowing the average systolic blood pressure of adults is an important medical issue. We do know that adult systolic blood pressure has a normal distribution with unknown mean π known standard deviation π = 9.8. We wish to create a confidence interval for π. We randomly select 17 adults and measure the systolic blood pressure xi of each adult selected. The sample mean was x-bar = 114.9 and the sample standard deviation was s = 9.3 (a) What is the critical value for a 96% confidence interval for π? (b) Create a 96% confidence interval for π (c) How long is the 96% confidence interval for π? (d) How many observations would we need to guarantee that the 96% confidence interval above has a length of 4 or less? (e) Create a 96% prediction interval for π using this data (f) Assuming π is not known, create a 96.0% confidence interval for π using this data (g) What is the length of the confidence interval for part f? (h) Write out R script or any other comments for the above
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