econ 385 final

how to calculate expected value of X

X times probability of X, add all the X's times their probabilities together to get the total

how to construct a 95% confidence interval

Y bar +- t critical value ((S*/Square root of n))

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. So, 50% of the possible Z values are between __________ and __________ a) -∞ and 0 b) 0 and ∞ c) -0.675 and 0.675 d) all of the above

It would be d, this is because it is asking to find where exactly 50% of data would be found. In a, it would be found from - infinity to 0 since 50% of the data is on the left of mean. B is also correct because 50% of data is on the right of the mean. C is correct because if you change it to a percentage instead of proportion, you are stating that you can find 50% of the possible data within -67.5% and 67.5%.

how do you calculate expected value?

Multiply X (times you did leg day or the amount of times a certain company's fridge needs repair in one year) by the probability of it happening, add these together, get the final result of the total expect value.

Standard deviation calculations

First take all the "times you did leg day" or "amount of times your fridge needs to be repaired" and square them. Then multiply them by their probabilities and add them all together to get a value. After getting that value (lets call it z), square the original expected value and subtract it from z to get the variance. Take the square root of that to get the sd.

Conduct a formal hypothesis test to test the following claim: "A father will have one fewer child for every four additional years of education he obtains" against the alternative that the effect is smaller. Draw a diagram of the p-value for this test.

H0: b2 = -.25 H1: b2<-.25 B2--.25/se = _____ If it falls in the middle then we fail to reject the null hypothesis, if it does not fall in the middle then we reject the null. Falls in middle of +/- t values = fail to reject. * actualb2 = mean * calculated b2 =whereever it falls on number line. below b2 line comes the t score, actual is in the middle, calculated is where it 'belongs'

assumption 1

model is linear in parameters.

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 64 fish yields a mean of 3.4 pounds, what is probability of obtaining a sample mean this large or larger?

((False mean - true mean.))/ (sd)/(square root of n) = a z score, using this z score go to the table to get the z value.

how do you calculate the width of a 90% confidence interval.

(z score of n-1) * (SD)/(square root of N). this equals one tailed width, since our tails are 5% and 5%, we need one for two tail's width; would be

Does a mother's schooling have a statistically significant effect on the number of children in a family? Explain

- Yes, the p value is less than 0.05 and the t value is greater than 2. Could also test this using h0: b2 =0 and h1: b2=/= 0, find the t crit value at 5% and go from there. Equation set up is ((b2 - null))/ s.e, if it is greater than the t crit then it is stat significant.

three to know facts about the standard deviation of the mean

- is never larger than the standard deviation of the population - decreases as sample size increases - measures variability of sample mean from sample to sample

) Construct a 95% confidence interval for the true β2 and give a written interpretation of the interval.

B hat 2 +/-(( tc (standard error of B hat 2))) = then you subtract and add that Tc value from Bhat2 to get the interval in which the mean is going to be in.

Does a father's schooling have a statistically significant effect on the number of children in a family? Explain.

H0: b2 = 0 H1: b2 =/= 0 B2-0/s.eb2 = ____ and if the t value is larger than +/- the t crit then it will result in a stat significant and you can use the t value or p value.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z values are larger than __________ is 0.3483.

In order to do this: - subtract 0.3483 from 1 (1-0.3483) - get the answer - look for that on the z score table and find your value

Show how R2 can be calculated from the numbers in the "Sum of Squares" column.

R squared is equal to ESS/TSS. In the order on regression output, ESS is the model, RSS is the error, and TSS is the corrected total.

f Z is a random variable generated by adding together X and Y which are also random variables, what do we know about Var(Z) if X and Y are positively correlated? a) Var (Z) = Var(X) + Var(Y) b) Var (Z) < Var(X) + Var(Y) c) Var (Z) > Var(X) + Var(Y) d) Var (Z) = Var(X) * Var(Y)

The correct answer would be C

for some value of z, the value of the cumulative standardised normal distribution is 0.2090, what is the value of Z if the probability of Z1 in this expression is Z<z1 is .2090 : P(Z<z1) = .2090?

The value of Z since we are given Z1 would be 1-.2090. Basically the 'expected value' if you will.

why did we try to log both sides instead of taking the derivatives to find elasticity?

We logged both sides to help ensure that there was a linear relationship between x and y since that helps our assumption of homoskedasticity.

how to calculate variance

X squared times probability of X. Add them all up. Subtract the mean of X squared from it to get the variance.

how do we reduce interval width?

increasing sample size

Which of the following is NOT equal to Cov(X,Y)? a) σxy b) E[(X - μx)(Y - μy)] c) E[XY] - μxμy d) ρxy

d

a 99% confidence interval estimate can be interpreted to mean that

if all possible samples of size n are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval. And we have a 99% confidence that we have selected a sample whose interval does include the population mean.

Imperfect Multicollinearity

some independent variables have a linear relationship meaning they are correlated with each other but not perfectly so

SD = 4, mean = 3, if ages above 11 get a certain benefit, what proportion is that?

that would be 50 + 34.1 + 13.6, which is equal to 97.7. 100-97.7 = 2.3, 2.3/100 = 0.023. This would mean that 0.023 would be the proportion that receives said benefits.

If P(X = x|Y-=y) = P(X=x), then ________________ a) Y is the dependent variable b) X and Y are positively correlated c) X and Y are statistically independent d) Y must be a discrete random variable

the correct answer is c that they are statistically independent of one another.

assumption 2

there does not exist an exact linear relationship among regressors in the sample.

in order to find the mean and the standard deviation using what you have already calculated, you..

to find the mean, you multiply the expected value times the charge. Then you add that to the one time fee. This gives you the mean of how much people will spend. The standard deviation is the calculated standard deviation times plus the fee that is added onto the one time fee each time service is needed.

if the expected value if a sample statistic is equal to the parameter it is estimating then we call it

unbiased