A restaurant association says that households in the United States headed by people under the age of 25 spend less on food away from home than households headed by people ages 55-64. The mean amount spent per year by 32 households headed by people under the age of 25 is $2015 and the sample standard deviation is $113. The mean amount spent by 32 households headed by people ages 55-64 is $2715 and the sample standard deviation is $97. At α = 0.05, can you support the restaurant association’s claim?

In reference to the year 2000 national census, the distribution of United States households according to type of living arrangement is given in the table below. An SRS of 500 households gives the observed frequencies, by household type, for the city of Aurora, Illinois.

Ethnic Origin    Census Percent    Observed frequency from sample

Married, with children                        25%                                                  95

Married, with no children                    20%                                                110

Single parent                                    5%                                                    35

Single individual                               15%                                                 65

One person                                      20%                                                 120

Other (roommate, etc.)                      15%                                                   75

Using a significance level of 0.05, test the claim that the Aurora distribution fits the distribution obtained by the census personnel.

Several geothermal power plants are in operation in the united states and more are being built since the heat source of a geothermal plant is hot geothermal water which is “free energy.” An 8-MW geothermal power plant is being considered at a location where geothermal water 160 degrees C is available. Geothermal water is to serve as the heat source for a closed Rankine power cycle with refringent 134a as the working fluid. Specify suitable temperature and pressures for the cycle, and determine the thermal efficiency of the cycle. Justify your selection.

The mean cost of domestic airfares in the United States rose to an all-time high of $385 per ticket.† Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $110.

(a)

What is the probability that a domestic airfare is $561 or more? (Round your answer to four decimal places.)

(b)

What is the probability that a domestic airfare is $230 or less? (Round your answer to four decimal places.)

(c)

What is the probability that a domestic airfare is between $300 and $480? (Round your answer to four decimal places.)

(d)

What is the minimum cost in dollars for a fair to be included in the highest 3% of domestic airfares? (Round your answer to the nearest integer.)

The mean cost of domestic airfares in the United States rose to an all-time high of $370 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $100. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $530 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $240 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $320 and $480 (to 4 decimals)?

d. What is the cost for the 4% highest domestic airfares? (rounded to nearest dollar)

1. policymakers, and politicians often argue that rising healthcare costs in the United States are bad, and use this to argue for policies to try to reduce prices. Using economics and the supply and demand framework:

   • Explain why you should not reason or make policy based on the fact that prices are rising/falling. (2 points)

   • Give two demand side and two supply side factors that might explain rising prices in the US (4 points)

New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $205 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $53. Use Table 1 in Appendix B.

a. What is the probability that a hotel room costs $224 or more per night (to 4 decimals)?

b. What is the probability that a hotel room costs less than $139 per night (to 4 decimals)?

c. What is the probability that a hotel room costs between $201 and $299 per night (to 4 decimals)?

d. What is the cost of the 20% most expensive hotel rooms in New York City? Round up to the next dollar.

Returns on common stocks in the United States and overseas appear to be growing more closely correlated as economies become more interdependent. Suppose that the following population regression line connects the total annual returns (in percent) on two indexes of stock prices:

MEAN OVERSEAS RETURN = ?0.07 + 0.20 ? U.S. RETURN

1. What does this number say about overseas returns when the U.S. market is flat (0% return)? (Fill in blanks)

This says that the mean overseas return is ______ % when the U.S. return is 0%.

2.What does this number say about the relationship between U.S. and overseas returns? (Fill in blanks)

This says that when the U.S. return changes by 1%, the mean overseas return changes by ______ %.

3.We know that overseas returns will vary in years when U.S. returns do not vary. Write the regression model based on the population regression line given above. (Fill in blanks)

y_i = _____+ ______ x_i + ?_i, where y_i and x_i are observed overseas and U.S. returns in a given year, and ?_i are independent N(0, ?) variables.

The travel-to-work time for residents of the 15 largest cities in the United States is reported in the 1998 Information Please Almanac. Suppose that a preliminary simple random sample of residents of San Francisco is used to develop a planning value of 6.25 minutes for the population standard deviation. If we want to estimate the population men travel-to-work time for San Francisco residents with a margin of error of 2 minutes, what sample size should be used? Assume a 95% confidence interval