Confidence Intervals and Sample Size Calculations

CHAPTER 8 (Confidence Intervals and Sample Size Calculations) & CHAPTER 9 (Hypothesis Testing) Chapter 8 & 9 Cheat Sheet Case A: Observations are normally distributed or n > 30, AND ? is known Confidence Interval: Hypothesis test: If you don't know if the observations are normally distributed, you can do a normal probability plot to find out. Sample size determination: Z-Test & Zinterval Case B: Observations are normally distributed or n > 30 AND ? is not known Confidence Interval: Hypothesis test: T-Test & TInterval Case C: Binomial observations with np > 5 and n(1-p) > 5 Confidence Interval: Hypothesis Test: Sample size calculation: or or 1-ProbZTest & 1-PropZInt Margin of Error = MOE = traditionally 95% confidence interval Homework Chapter 8 7. a. How large a sample should be selected so that the margin of error of estimate for a 98% confidence interval for p is 0.045 when the value of the sample proportion obtained from a preliminary sample is .53? b. Find the most conservative sample size that will produce the margin of error fofr a 98% confidence interval for p, is equal to 0.045. 8. In a random sample of 50 homeowners selected from a large suburban area, 19 said that they had serious problems with excessive noise from their neighbors. a. Make a 99% confidence interval for the percentage of all homeowners in this suburban area who have such problems. b. Suppose the confidence interval obtained in part (a) is too wide. How can the width of this interval be reduced? Discuss all possible alternatives. Which option is best? 9. The management of a health insurance company wants to know the percentage of its policly holders who have tried alternative treatments (such as acupuncture, herbal therapy, etc.). A random sample of 24 of the companyâ??s policy holders were asked whether or not they have ever tried such treatments. The following are their.