Discuss the below:
Q1. Money magazine reported that the average price of gallon of gasoline in the United States during the first quarter of 2001 was $ 1.46. Assume the price reported by Money is the population mean, and the population standard deviation is $ 0.15.
a) What is the probability that the mean price for a sample of 30 gas stations is within $ 0.03 of the population mean?
b) What is the probability that the mean price for a sample of 50 gas stations is within $ 0.03 of the population mean?
c) What is the probability that the mean price for a sample of 100 gas stations is within $ 0.03 of the population mean?
d) Would you recommend a sample size of 30, 50 or 100 to have at least a 0.95 probability that the sample mean is within $ 0.03 of the population mean?
Q2.The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries (U.S.A Today, June 21, 1994). Assume the population proportion is p=0.17 and a simple random sample of 800 households will be selected from the population.
a. Show the sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries.
b. What is the probability that the sample proportion will be within plus/minus 0.02 of the population proportion?
c. Answer part (b) for a sample of 1600 households.