EC315 Quantitative Research Methods
Name: _____________________
PART I: HYPOTHESIS TESTING
PROBLEM 1 (15 pts): A brand of fluorescent light tubes is advertised as having an average illumination life-span of
2,000 hours. A random sample of 64 bulbs burned out with a mean life-span of 1,970 hours and a sample standard deviation
of 80 hours. With a 95% level of significance, test the claim that the advertised mean equals 2,000.
PROBLEM 2 (15 pts): Given the following data from two independent data sets, conduct a one-tail hypothesis test to
determine if the means are statistically equal using an alpha of 0.05.
n1 = 45
xbar1= 64
s1=15
n2 = 36
xbar2 = 60
s2 = 12
PROBLEM 3 (15 points): A test was conducted to determine if the gender of a spokesperson affected the likelihood that
consumers would prefer a new product. A survey at a trade show employing a female spokesperson determined that 60 out
of 200 customers preferred the product, while 72 of 180 customers preferred the product when a male spokesperson was
employed. At the 0.05 level of significance, do the samples provide sufficient evidence to indicate that, in this situation, the
gender of the spokesperson matters to consumers?
PROBLEM 4 (15 points): Assume the population variances are equal for Male and Female GPA’s. Test the sample
data to see if Male and Female PhD candidate GPA’s (Means) are equal. Conduct a two-tail hypothesis test, α =.05.
Sample Size
Sample Mean
Sample Standard Dev
Male GPA’s
17
3.8
.5
Female GPA’s
15
3.95
.7
PROBLEM 5 (20 pts): The Neutra-Pride Bottling Company wants to determine if their soda has appeal to the general
public. A sample of 500 individuals were selected and asked to indicate the soda they preferred. Each volunteer sampled 5
2
brands of soda. Conduct a Hypothesis test at α =.05 to determine if the preference of sodas is uniform (or if there appears to
be some preference).
Brand of Soda Observed (fo)
A
115
B
80
C
105
D
130
E
70
PART II REGRESSION ANALYSIS (40 points): A real estate investor has devised a simple model to
estimate home prices in a fancy, new suburban development. Data from a random sample of 32 homes
were gathered on the selling price of the home ($ thousands), the home size (in square feet), the lot size
(in square feet), and the number of bedrooms. The following Excel Output Summary was generated:
Regression Statistics
Multiple R
0.9647
R Square
0.9307
Adjusted R Square
0.9227
Standard Error
26.0389
Observations
32
Intercept
X1 (Square Feet)
X2 (Lot Size)
X3 (Bedrooms)
Coefficients
34.6165
0.1232
.00142
17.3903
Standard
Error
38.3735
0.0184
1.7120
6.8905
t Stat
-0.9021
8.3122
5.2583
2.5238
P-value
0.3753
0.0018
0.0122
0.1259
Answer the following questions, and note that some are two-parters, so answer both!
a. Is there a linear relationship in this model? How can you tell?
b. Why is the coefficient for lot size a positive number? What is the value (per square foot) of a lot?
c. Which is the most statistically significant variable? What evidence shows this?
d. Which is the least statistically significant variable? What evidence shows this?
e. For a 0.05 level of significance, could any variable(s) be dropped from this model? Why?
f.
Looking at the associated p-value, should the Intercept be dropped from this model? Why?
g. Using all of the variables: What should be the cost of a 2,000 square-foot home with a lot size of
5,000 square feet and three bedrooms?
PART III SPECIFIC KNOWLEDGE SHORT-ANSWER QUESTIONS (50 Points)
3
Problem 1: In a regression analysis:
a. What is the range of an R2 value? ________________________
b. What does or could a p-value = 0.18 mean/imply? __________________________________
c. What is a Durbin-Watson test designed to detect? _________________________________
d. How is an Adjusted R2 value different from an R2 value? ___________________________
Problem 2: Define multicollinearity in the following terms:
a. Variables need to be ___________________ in a linear regression model.
b. In which type of regression is multicollinearity likely to occur? ________________________
c. What is the negative impact of multicollinearity in a regression? ______________________
d. How could you identify if it exists? _____________________________________
e. If multicollinearity is found in a regression, how is it eliminated? ___________________
Problem 3: The mean (average) is an indicator of central tendency. However, it tells us nothing about
the variation in our population. What is used as a good indicator of variation? _____________
Problem 4: The game is tied at the sound of the horn…but wait…Tim Duncan has been fouled and will
have a chance to shoot the winning basket. During past games, Tim has only made 12 out of 28 freethrows. Based on past experience: What is the probability he will miss the shot and the game will go
into overtime? _____________
Problem 5: Using a standardized test, Ms. Parker determined the average reading score for her third
grade students was 72 with a standard deviation of 12. Timmy got a 58 on the test.
a. Should Ms. Parker be concerned about Timmy’s reading ability? Why (or why not)?
b. What percentage of students did worse than Timmy on this standardized test?
c. Brenda’s Mom bragged to Timmy’s Mom that her daughter scored a 96. Could her claim be valid?
Why? (Hint: Compute the Z-value or use a 95% Confidence interval) Would you conclude Brenda’s Mom is a
jerk?
4
PART IV: T/F, Binomial Distribution and Short Essay (30 points)
A. If the average time to finish this exam is 2 hour and 40 minutes, with a standard deviation of 30
minutes, everyone (99.7%) should be complete before how long?
Section A - True or False (1 point each)
If the statement is false, correct it to make it true OR I will consider it wrong!
T
T
T
T
T
T
T
T
T
T
F 1. In a regression, a t-value less than α means the variable is significant.
F 2. A chi-square value may be positive or negative.
F 3. Bragging is not important to the set-up of an alternate hypothesis.
F 4. In a 6 X 5 contingency table the degrees of freedom will be 30.
F 5. Multicollinearity occurs when 2 (or more) variables have a cascading relationship.
F 6. Bias is good because it can focus the research towards expected results.
F 7. A hypothesis test can often completely prove if the null hypothesis is true or false.
F 8. Linear regression is also called the method of Hollywood Squares.
F 9. The Empirical Rule says: 45% of your data will fall within 2σ of the mean.
F 10. A Durbin-Watson statistic must be computed for all types of regressions.
If you knew nothing about statistics (and guessed at each of the above T/F questions), how many
should you get correct?
What would be the probability of guessing and getting all of them correct?
(Do not round off…at least 3 decimal places are needed)
END!
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