Take Home Exam-Fall 2012, EC351, Due: September 26, 2013 at 3:30pm.
I, ________________________, did not receive or give help to any other student on this exam.
1. Professor Hardnose teaches at Sheetrock University (football team name: The
Plasterers) On a recent test, Professor Hard-nose gave 1 A, 3 Bs, 22 Cs, 5 Ds, and 4 Fs. a. If we assign points to the letter grades according to A=4 points, B=3 points, C=2 points, D=1 point, and F=0 points, what is the mean grade (in points)? mean=___________ b. What is the range? c. Given your answer in part a., calculate the sample variance and sample standard deviation. sample variance=____________ e. sample standard deviation=_________ d. Construct a 95% confidence interval for the population mean given a sample size of 35 students.
If the true population mean at Sheetrock University is 2.5, does Professor
Hardnose deserve his name given your answer in d.?

3.
2. The population mean level of income is

=$20,000 with a population standard deviation of

=$2000. If a random sample of 25 is drawn from the population, what is the probability that the sample mean will be between $19,600 and
$20,400? (Use the z-table)
Researchers are interested in the difference in spending patterns between college students aged 20-25 and the population of all spenders aged 20-25. A random sample of n=25 college students has mean spending of x =$30 per week and sample variance of s
2
=$56.25 (s=$7.5) per week.
Suppose that population mean spending among 20-25 year olds is $33. Identify the criticalt value for a 5% significance level for a two-tailed test from the table and then calculate the actual t -value to test the null hypothesis that mean college student spending is different from the population mean. critical t (5%) = _____________ calculated t=_______________
Reject or do not reject?

4.
As the sales manager of Rudolph’s Brewery you are required to make a sales forecast of beer sales. You have fifty-nine monthly observations available beginning with January 1995. The data are in the file beer.xls
on the class website. The table below partially lists the data for the variables SALES: monthly beer sales (in tons),
TEMP: average monthly temperature (degrees F), PRECIP1=monthly precipitation on
Mondays-Wednesdays, PRECIP2=monthly precipitation on Thursdays-Sundays, and
SUN: Monthly total hours of sunlight.
Month SALES TEMP PRECIP1 PRECIP2 SUN
1 2312.0 31.0 0.038 0.074 104.8
2 2580.5 28.9 0.062 0.142 108.3
3 3079.9 32.8 0.143 0.010 153.0
.
Import the data into GRETL by choosing the dataset structure "time series" and "monthly". The start data is 1995:01.
A.
Estimate a regression of beer sales as the dependent variable, and TEMP,
PRECIP1, PRECIP2, and SUN as the independent variables.
The equation to estimate is
Sales
  o
 
1

TEMP
 
2

PRECIP 1
 
3

PRECIP 2
 
4

SUN
 
Test whether each coefficient for the independent variables are significantly different from zero using a t -test.
B. Test whether the set of coefficients are significantly different from zero using an F-test. (Refer to p. 161-162 if you need help on this test.) That is, use an F-test to test the composite hypothesis that
H o
:

1
 
2
 
3
 
4

0
Identify the calculated F and the critical F for a 5% significance level.
C. Interpret the R
2
for the model.
D. Test whether the effect of precipitation on beer sales is significantly different from zero using an F-test. The composite null hypothesis is
H o
:

2
 
3

0
Identify the calculated F and the critical F for a 5% significance level.
E. Using the model estimated in part A, forecast beer sales for a month when the average temperature is 58 degrees, 0.1 inch of rain falls on Monday-
Wednesday, 0.3 inches of rain fall on Thursday-Sunday, and the average sunlight is 140 hours.

5. Let the random variable X take a value x=0 if a woman does not have breast cancer and let x=1 if a woman does have breast cancer. Let the random variable Y take a value of y=0 if a mammogram does not detect breast cancer and let y=1 if a mammogram indicates the presence of cancer.
Y y=0 x=0
X x=1 y=1
You are given the following information. i. The probability that a woman has cancer f(x=1)=0.30. ii. The probability that a test does not detect cancer is f(y=0)=0.65. iii. A mammogram does not always detect cancer in women who have cancer with probability of 0.1. iv. Sometimes a mammogram detects cancer in women who do not have cancer with probability of 0.15. a. b.
Complete the table.
Calculate f(x=0|y=1). Explain what this probability means. c. Calculate f(x=1|y=1). Explain what this probability means. d. Calculate f(f(x=1|y=0). Explain what this probability means.