For all hypothesis tests, be sure to include information for all 7 steps. For any two-sample or paired t-tests that you perform, in Step 6, show the decision rule based on BOTH the critical value and the p-value. Use the online app for the t-distribution to compute your p-values.

The Bayley Scales of Infant Development yield scores on two indices – the Psychomotor Development Index (PDI) and the Mental Development Index (MDI) – that can be used to assess a child’s level of functioning at approximately one year of age. As part of a study investigating the development and neurologic status of children who had undergone reparative heart surgery during the first three months of life, the Bayley Scales were administered to a sample of one-year-old infants born with congenital heart failure. The children had been randomized to one of two different treatment groups, known as “circulatory arrest” (n₁ = 73) and “low-flow bypass” (n₂ = 70).

The groups differed in the specific way in which the reparative surgery was performed. Unlike circulatory arrest, low-flow bypass maintains continuous circulation through the brain; although it is felt to be preferable by some physicians, it also has its own associated risk of brain injury.

Here we focus on the MDI score only. The data for this study are on MDI scores is given in the table below:

At the 5% significance level, test the null hypothesis that the mean MDI score at one year of age for the circulatory arrest treatment group is equal to the mean MDI score for the low-flow group. Also provide and interpret the corresponding 95% confidence interval.

7) Name two different types of soil degradation. For each type give a description of how or why it happens (what causes it) AND what the negative effects are (why is it bad).

1) a) A drawer contains 9 white socks and 7 black socks. Two different socks are selected from the drawer at random. What is the probability that both of the selected socks are white?

b) A box contains 10 white marbles and 7 black marbles. Suppose we randomly draw a marble from the box, replace it, and then randomly draw another marble from the box. (This means that we might observe the same marble twice). What is the probability that both the marbles are white?

c) Suppose that 3.4 % of the items produced by a factory are defective. If 5 items are chosen at random, what is the probability that none of the items are defective?

d) Suppose that 5.7 % of the items produced by a second factory are defective. If 5 items are chosen at random from the second factory, what is the probability that exactly one of the items is defective?

2) a) Suppose that 8.8 % of the items produced by a third factory are defective. If 5 items are chosen at random from the third factory, what is the probability that exactly two of the items are defective?

b) Suppose that 5.1 % of the items produced by a fourth factory are defective. If 5 items are chosen at random from the fourth factory, what is the probability that at least two of the items are defective?

c) Suppose that 9.6 % of the items produced by a fifth factory are defective. If 6 items are chosen at random from the fifth factory, what is the expected value (or mean value) for the number of defective items?

d) In a certain town, 19 % of the population develop lung cancer. If 25 % of the population are smokers and 85% of those developing lung cancer are smokers, what is the probability that a smoker in this town will develop lung cancer?

e) . A certain kind of light bulb has a 8.5 percent probability of being defective. A store receives 54 light bulbs of this kind. What is the expected value (or mean value) of the number of light bulbs that are expected to be defective?

7.

Suppose a firm has access to two production processes with the following marginal cost curves: MC₁ = 2Q₁ and MC₂ = 3Q₂

If it wants to produce 30 units of output, how much should it produce with each process?

8.

Output for a simple production process is given by Q = 2KL, where K denotes capital and L denotes labor. The price of capital is $25 per unit and capital is fixed at 5 units in the short run. The price of labor is $5 per unit. What is the variable cost of producing 80 units of output? Explain how you calculated your answer.

A box contains 10 items, of which 3 are defective and 7 are non-defective. Two items are randomly selected, one at a time, with replacement, and x is the number of defective items in the sample. To look up the probability of a defective item being drawn from the box, using a binomial probability table, what would be the values of n, x and p to look up?

True/False

6.A trade between two people is an example of an externality.

7.If a pure public good is provided by voluntary contributions, economic theory predicts that in general too little will be supplied.

8.Economists define public goods to be those goods that are supplied by the government and private goods to be those goods that are supplied by the private sector.

9.A life insurance company must be concerned about the possibility that the people who buy life insurance may tend to be less healthy than those who do not. This is an example of adverse selection.

10.An insurance company must be concerned about the possibility that someone will buy fire insurance on a building and then set fire to it. This is an example of adverse selection

Problem #7

Suppose we are deciding between two alternative investments for the coming year. The first investment is a mutual fund that consists of shares which do well when economy is strong. The second investment is a mutual fund that consists of shares that do well when economy is weak. Your estimate of returns per each investment is provided below with a probability of their occurrence. Calculate the correlation between these mutual funds and interpret.

Mark is a single dad with two dependent children: Joey, age 7, and Sonny, age 3. He has an AGI of $39,000 and paid $4,300 to a qualified daycare center for the two children. What amount can Jamison receive for the child and dependent care credit?

7) You are trying to decide between two mobile phone carriers. Carrier A requires you to pay $200 for the phone and monthly charges of $60 for 24 months. Carrier B wants you to pay $100 for the phone and monthly charges of $70 for 12 months. Assume you will keep replacing the phone after your contract expires. Your cost of capital is 3% APR, compounded monthly.