Reference no: EM1314393

1. A survey conducted by the American Automobile Association showed that a family of four spends an average of $215.60 per day while on vacation. Suppose a sample of 64 families of four vacationing at Niagara Falls resulted in a sample mean of $252.45 per day and a sample standard deviation of $74.50.

a. If the amount spent by a family of four while vacationing at Niagara Falls is skewed to the right, would you expect the median amount spent to be greater than or less than $252.45?  Explain.

b. Is it necessary to assume a normal distribution on the population to estimate the value of the mean spending per day?  Explain.

c. Use the sample data to construct a 95% confidence interval estimate for the mean amount spent per day by a family of four visiting Niagara Falls.

d. Based on the confidence interval from part c), does it appear that the population mean amount spent per day by families visiting Niagara Falls differs from the mean reported by the American Automobile Association?  Explain.

2. A shop manual gives 6.5 hours as the average time required to perform a 30,000 mile major maintenance service on a Porsche 911.   Last month a mechanic performed 11 such services, and his required times were as follows.

6.3  6.6  6.7  5.9  6.3  6.0  6.5  6.1  6.2  6.4  6.3

Is there sufficient evidence at the α = 0.05 level of significance to conclude that the mechanic can perform this service in less time than specified by the service manual?

3. On January 7, 2000, the Gallup Organization released the results of a poll comparing lifestyles of today with that yesteryear.  Then poll results were based in telephone interviews with a randomly selected national sample of 1,031 adults, 18 years and older, conducted December 20-21, 1999. One question asked if the respondent had vacationed for six days or longer within the last 12 months.  Suppose that we will attempt to use the poll's results to justify the claim that more than 40 percent of U.S. adults have vacationed for six days or longer within the last 12 months. The poll actually found that 42 percent of the respondents had done so. Would you conclude that more than 40 percent of U.S. adults have vacationed for six days or longer within the last 12 months? Explain.