# If a researcher aims to make a prediction of the number of failures on the interview before

Examples for Part I

1. If a researcher aims to make a prediction of the number of failures on the interview before

one gets a job, he or she should use:

(a) The negative binomial.

(b) The Poisson.

(c) The binomial.

(d) The discrete uniform.

(e) None of the above.

2. The mean of any distribution is:

(a) The weighted average of all observations

r(1−p)

(b) p

(c) np

(d) λ

(e) None of the above.

3. T/F: In OLS regression, explanatory variables must be linearly independent.

True.

False.

4. T/F: In OLS regression, explanatory variables could be correlated with error term.

True.

False.Examples for PART II

1. (CH 11)

Consider the experiment flipping a coin repeatedly for y + r times and count the number of

heads (successes). Define the random variable as the number of failures before you achieve 2 nd

(y+r−1)!

y+r−1 r

head (success). (Hint: P(Y = y) = (

) p (1 − p) y ) = (r−1)!y! p r (1 − p) y )

r−1

(a) Which distribution is it? (2 Points)

What is the probability that

(b) you have one failure prior to 2 nd success? (5 Points)

(c) you have the second head (success) at fifth trial? (8 Points)

2. (CH 12)

Using the standard normal tables draw the correct curve, shade the area underneath the curve,

and find the probability that Z will fall inside that shaded area:

(a) P[ -∞ ≤ Z ≤ -1]

(b) P[-0.26 ≤ Z ≤ 0.50]

(c) P[0.32 ≤ Z ≤ ∞]Compute the probability that 0.6 ≤ X ≤ 1 for the following probability density functions.

(a) Random variable X is continuous over the range [-1, 1], and has pdf given by f(x) = 1.5x 2 .

(b) Random variable X is continuous over the range [0, 1], and has pdf given by f(x) =

0.75x(2 + x).

Let the random variable X be the amount that parents spend per child on clothes per year.

X is normally distributed with the mean of 527 and standard deviation of 160:

(a) What is the probability that the amount spent is more than $700?

(b) What is the probability that the amount spent is less than $100?3. (CH 14,15)

Suppose that we make a tentative claim that the mean of housing prices in South Dallas is

70,000. A sample of 100 houses in South Dallas is selected by a researcher. Data on houses’

prices will be used to test the following hypothesis. Please write down the null hypothesis and

alternative hypothesis for each of the following scenarios.

(a) The researcher believes that the average house price in South Dallas differs from 70,000.

(b) The researcher believes that the average house price in South Dallas is greater than 70,000.

(c) The researcher believes that the average house price in South Dallas is less than 70,000.

(d) The following table gives hypothesis testing result under scenario (a), interpret the testing

result. (Reject or fail to reject, statistically significant or not) (6 Points)

One-sample t test

Variable Obs Mean

price 100 451146.8

mean = mean(price)

Ho: mean = 70000

Ha: mean < 70000

Pr(T < t) = 0.9998

Std. Err. Std. Dev.

102185.7 1021857

[95% Conf. Interval]

248388.2

t =

degrees of freedom =

Ha: mean != 70000

Pr(|T| > |t|) = 0.0003

653905.4

3.7299

99

Ha: mean > 70000

Pr(T > t) = 0.00024. (CH 16) (HW5)

Answer the following questions according to the table:

(attratio is worker’s attendance rate, dis is a variable indicating a worker is disabled or not)

Source

SS

df

MS

Model

Residual .465966173

4.32959064 2

97 .232983087

.044634955

Total 4.79555681 99 .048439968

attratio Coef.

age

dis

_cons -.0009336

-.1662263

.9855363

Std.

Err.

.0028481

.0539149

.1229061

t

-0.33

-3.08

8.02

Number of obs

F(

2,

97)

Prob > F

R-squared

Adj R-squared

Root MSE

P>|t|

0.744

0.003

0.000

[95%

Conf.

-.0065862

-.2732324

.7416018

=

=

=

=

=

=

100

5.22

0.0070

0.0972

0.0786

.21127

Interval]

.004719

-.0592202

1.229471

(a) Is it simple regression model or multiple regression model?

(b) Write down the regression equation.

(c) Write down the null hypothesis and alternative hypothesis for regression coefficients.

(d) Interpret t-test results for each coefficient respectively.

(e) Explain coefficient for age and dis.

(f) What does R_squared tell you?

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