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Homework Help for Statistics

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Statistics

Given independent random variables X and Y with E ( X )=80, σX=10 and E (Y)=85, σY =12 respectively, find the mean and variance of each of the following random variables.

a. W=4X-2Y

b. {X1 ,..., X 100} and {Y1, ...,Y 100} are independent draws from X and Y distributions.

W=y bar -x̅ 

 

c. {X1,..., X10} are independent draws from X distributions.

W =X1+,...,+X10

 

d. W=10X

Answered
28 Mar 2020
Statistics

Never forget that even small effects can be statistically significant if the samples are large. During a three-year period, 8 of the 57 headed by men and 6 of the 35 headed by women failed.

(a) Find the proportions of failures for businesses headed by women and businesses headed by men. These sample proportions are quite close to each other. Give the p-value for the hypothesis that the same proportion of women's and men's businesses fail. (Use two-sided alternative). What can we conclude (use alpha as 0.05)?

The p-value was ___________ so we conclude that ____________.

 

(b) Now suppose that the same sample proportion came from a sample 30 times as large. That is 180 out of 1050 businesses headed by women and 240 out of 1710 businesses headed by men fail. Verify that the proportions of failures are exactly the same as in part (a). Repeat the test for the new data. What can we conclude?

The p-value was ___________ so we conclude that ____________.

c) It is wise to use a confidence interval to estimate the size of an effect rather than just giving a p-value. Give 95% confidence intervals for the difference between proportions of men's and women's businesses that fail for the settings of both (a) and (b).

Interval for smaller samples: ___________ to ___________.

Interval for larger samples: ___________ to ___________.

What is the effect of larger samples on the confidence interval?

 

Answered
16 Mar 2020
Statistics

Suppose you are evaluating a grant proposal. The proposer seeks $250,000 to conduct a series of experiments on patients with a rare kind of brain lesion. Let's say the proposer will measure ability to remember lists of words in the experiment. A very interesting and provocative theory, described clearly in the proposal, predicts that the brain-damaged people should actually remember slightly better than the control group, and so the investigator proposes an experiment to test this prediction. A pilot study shows that among normals, the mean number of words remembered (from a list of 20) is 12.2, and the standard deviation is 3.1. (The SD in the lesion group could be assumed to be bigger, but we'll just assume that it's the same.) The investigator explains that a pool of 24 subjects with brain lesions is already available from a local clinic for the braindamaged group. Suppose that you, as a reviewer of the proposal, want a power of .80 in proposed experiments. What effect size would be required to generate this power? (Assume a Type I error rate, i.e. alpha, of 0.05.) Suppose that the effect size is actually 0.2 (small, as predicted by the proposed theory). What sample size would be needed to achieve a power of .80? (Should you fund the proposal?)

Answered
27 Feb 2020
Statistics

The mean score for a statistics exam is 125 (on a 200 point exam), with a standard deviation of 30. You are told that your score is 1.5 standard deviations above the mean. What is your score?

Answered
18 Jan 2020
Statistics

The elasticity of demand for a product is likely to be greater:

  1. the greater the amount of time over which buyers adjust to a price change.

  2. the smaller the number of substitute products available.

  3. if the product is a necessity, rather than a luxury good.

  4. the smaller the proportion of one's income spent on the product.

Answered
8 Jan 2020
Statistics

Refer to Figure 22.2 for a perfectly competitive firm. The profit-maximizing quantity of output is

  1. C

  2. D

  3. E

Answered
23 Dec 2019
Statistics

The demand for Chocolate Chip Cookie Dough ice cream is likely quite elastic because

  1. ice cream must be eaten quickly.

  2. this particular flavor of ice cream is viewed as a necessity by many ice-cream lovers.

  3. the market is broadly defined.

  4. other flavors of ice cream are good substitutes for this particular flavor.

Answered
20 Dec 2019
Statistics

A sample of n = 25 scores has M = 20 and s2 = 9. What is the sample standard deviation?

 

  1. 3

  2. 4.5

  3. 9

  4. 81

Answered
20 Dec 2019
Statistics

If the supply of a good is inelastic,

  1. producers will not change their quantity supplied by much if the market price doubles.

  2. a small increase in price will lead producers to sharply increase their quantity supplied.

  3. producers have diminishing marginal returns of labor.

  4. producers will increase their quantity supplied in response to sharp drops in the market price.

Answered
17 Dec 2019
Statistics

Fill in the blank:

The relationship between sales and profits can be written as ______.

 

Answered
17 Dec 2019
Statistics

Category of money supply includes money that is quickly and easily accessed  (Currency, Coins, Checks, paper money) is:

  1. M0

  2. M1

  3. M2

  4. M3

Answered
17 Dec 2019
Statistics

All else held constant, an increase in the price of tablets will result in a

 

  1. leftward shift of the demand curve for tablets.

  1. rightward shift of the demand curve for tablets.

  1. decrease in the demand for tablets.

  2. movement up and to the left along the demand curve for tablets.

Answered
17 Dec 2019
Statistics

All else being equal, if the price of a product decreases, we would expect

  1. supply to decrease.

  2. demand to increase.

  1. quantity supplied to increase.

  2. quantity supplied to decrease.

Answered
17 Dec 2019
Statistics

What is the opportunity cost of studying for an economics test if the person can go for watching the movie?

Answered
17 Dec 2019
Statistics

An increase in expected future income will:

  1. increase aggregate demand and aggregate supply.

  2. decrease aggregate demand and aggregate supply.

  1. increase aggregate supply.

  2. increase aggregate demand.

Answered
17 Dec 2019
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