The following data show the brand, price, and the overall score for six stereo headphones that were tested by consumer reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 to 100.

Price Score

Bose 180 76

Skullcandy 150 71

Koss 85 61

Phillips/O'Neill 70 56

Denon 70 40

JVC 35 26

a). Develop the estimated regression equation that could be used to predict the score given the price.

b). Compute the coefficient of determination.

c). What is the value of the sample correlation coefficient?

d). Does the t test indicate a significant relationship between price and the overall score? What is your conclusion? Use α=0.05

e). Test for a significant relationship using the F test. What is your conclusion? Use α= 0.05

f). Develop a point estimate of the score for a headphone with a price of 100.

g). Develop a 95% confidence interval for the mean score for all headphones with a price of 100.

Suppose that market for good X is free and competitive, where the equilibrium price and quantity are $30 per tops and 10 million tons per year respectively. The producers of good X complain to the government that the current market price is too low to provide them with sufficient income, and they want the government to set a price floor of $40 per ton and to purchase all resulting surplus in order to guarantee that the price support is maintained. Some government advisors are concerned by the fact that elasticities of demand and supply for good X are unknown and therefore, this price support policy could be too costly for the government.

The question:
Could the impact of the price floor on the consumers of good X (in terms of the loss of consumer surplus) be more than $100 million, or less than $100 million, or equal to $100 million? What conditions would your answer depend on?
(Hint: make some reference to elasticity.)
Explain your reasoning carefully, and illustrate with an appropriate diagram(s) using demand and supply curves.

maximum 400 words.

Suppose that the economy has 10 workers. The supply curve of workers is given by: P=0.1Q+100. Also, there are two types of consumers: A and B. Each A has the following demand curve: Q=1000-5P. The demand curve of B given by: Q=100-0.5P. Assume that there are 10 A and 100 B in this market.

a. Calculate the aggregate demand and aggregate supply curves.

b. Calculate the equilibrium price and quantity.

c. Calculate the consumer's surplus, the producer's surplus and total surplus.

d. Suppose that the government decides to subsidize product. How much subsidy is needed for lowering the market price to 100 (for consumers). Calculate the consumer, producer and society surplus.

e. (ignore d) Suppose that the government impose tax of 20 RMB per product. Calculate the new price and quantity at equilibrium. Calculate the deadweight loss of the economy.

Calculating the Inflation Rate

Using the simple percent change formula above and the annual CPIs in the table below, it becomes possible to calculate the inflation rate between any two years.

For example, the inflation rate from 1990 to 1991 was 4.2 percent:

CPI (1991) − CPI (1990) X100

            CPI(1990)

=   136.2 – 130.7 X 100

            130.7

= 5.5/130.7 × 100

= 0.420 × 100

= 4.2%

Use the annual CPI data in the Table below to complete the inflation rate calculations for each year in Table A.

Table A: Calculating Inflation Rates

1. If you earned $10 an hour in 1994, how much would you have to earn in 1995 for your wage to have the same purchasing power?

2. If you saved $100 in 2018, how much interest would you have to earn in order for the savings to have the same purchasing power in 2019?

Table: Annual Average CPI (1982–1984 to 2012)

*Average CPI for 1982, 1983, and 1984; base level = 100.

How Much Did Things Cost in the “Good Old Days”?

Have you ever heard your parents or grandparents say, “Back in my day, a loaf of bread only cost a nickel and a gallon of gas only cost a quarter”? How can it be that things were so much cheaper back then? Were they really cheaper? You will try to answer this question by comparing modern prices to historical prices and calculating the percent increase in prices. To do so, you will examine prices of two goods: movie tickets and a McDonald’s Big Mac®.

Calculating Percent Change in Price

Percent change in price is calculated by dividing the amount of change in price by the original price and multiplying the result by 100. If the price has increased, percent change will be positive, and if the price has decreased, the percent change will be negative. The formula for calculating percent change in price:

New price – Old price × 100       OR        Price (Year 2) – Price (Year 1) × 100

Old price                                               Price (Year 1)

Historic Prices

1. Which item had the largest percent increase in price?

2. Prices seem so low in 1967. Were people much better off then? What else would

you need to know to draw a conclusion?

Studies indicate that the probability that a married man votes is 0.45, the probability that a married woman votes is 0.40, and the probability that a married woman votes given that her husband does is 0.60. Compute the following probabilities:
(a) Both a man and his wife vote.
(b) A man votes given that his wife does.

Aaron acted as an agent and purchased some goods on behalf of Martin at RM100,000. Later, seller of goods was informed by Martin’s wife that her husband passed away. George then offered the seller RM200,000 for the same goods. Can seller sell to George, or is seller bound to sell to Aaron? State the legal implications.

A psychologist wants to know whether wives and husbands who both serve in a foreign war have similar levels of satisfaction in their marriage. To test this, six married couples currently serving in a foreign war were asked how satisfied they are with their spouse on a 7-point scale ranging from 1 (not satisfied at all) to 7 (very satisfied). The following are the responses from husband and wife pairs.

(a) Test whether or not mean ratings differ at a 0.05 level of significance. State the value of the test statistic. (Round your answer to three decimal places.)

=?

State the decision to retain or reject the null hypothesis.

Retain the null hypothesis

or

Reject the null hypothesis

(b) Compute effect size using eta-squared. (Round your answer to two decimal places.)

=?

Suppose the price of one typical stock could only increase by 2 or decrease by 1 in one day. From the historical data, we somehow know that this stock goes up with probability 0.7, goes down with probability 0.3. Suppose the initial price is 100. Suppose we want to study the price behavior for that stock for one week(5-weekdays). (Round your answer in 3 decimal Places) This question is just for setting up the model.

what is the probability of the stock price close up at 102 at the end of Monday?

what is the probability of the stock price close up at 99 at the end of Monday?

Which of the following distribution bear the most resemblance to the distribution of stock price on Monday?

what is the probability of the stock price close up at 107 at the end of Friday?

Which of the following distribution bear the most resemblance to the distribution of stock price at the end of Friday?

what is the probability of the stock price close up at 108 at the end of Friday?

what is the probability of the stock price close up at most as 107 (include 107 itself) at the end of Friday?

what is the probability of the stock price close up at least as 108 (include 108 itself) at the end of Friday?

what is the probability of the stock price close up at least as 107 (include 107 itself) at the end of Friday?

what is the probability of the stock price close up at most as 100 (include 100 itself) at the end of Friday?

Suppose that Intel currently is selling at $50 per share. The rate on margin loan is 8%. Investor A purchased 100 shares using 60% margin. Investor B sold 100 shares using 60% margin. The maintenance margin is 40%. 1. Calculate the margin call price for Investor A 2. Calculate the margin call price for Investor B