Question 1: The average price of a gallon of unleaded regular gasoline was reported to be $3.13 in Illinois. Use this price as the population mean, and assume the population standard deviation is $.20.
a. What is the probability that the mean price for a sample of 30 service stations is within $.03 of the population mean?
b. What is the probability that the mean price for a sample of 50 service stations is within $.03 of the population mean?
c. What is the probability that the mean price for a sample of 100 service stations is within $.03 of the population mean?
d. Which, if any of the sample sixes in parts (a),(b),(c) would you recommend to have at least a .95 probability that the sample mean is within $.03 of the population mean?
Question 2: Times/CNN voter polls monitor public opinion for the presidential candidates during 2000 presidential election campaign. One Time/CNN poll conducted by Yankelovich Partners Inc, used a sample of 589 likely voters. Assume the population proportion for a presidential candidate is p=.50. Let p be the sample proportion likely voters favoring the presidential candidate.
a. Show the sampling distribution of p
b. What is the probability the Times/CNN poll will provide a sample proportion within +-.04 of the population proportion?
c. What is the probability the Times/CNN poll will provide a sample proportion within +-.03 of the population proportion?
d. What is the probability the Times/CNN poll will provide a sample proportion within +-.02 of the population proportion?
Question 3: The national Center for Education Statistics reported that 47% of college students work to pay for tuition and living expenses. Assume that a sample of 450 college students was used in the study.
a. Provide a 95% confidence interval for the population proportion of college students who work to pay for tuition and living expenses.
b. Provide a 99% confidence interval for the population proportion of college students who work to pay for tuition and living expenses.
c. What happens to the margin of error as the confidence is increased from 95% to 99%