EC315 Quantitative Research Methods
PART I: HYPOTHESIS TESTING
PROBLEM 1 (15 pts): A brand of fluorescent light tubes is advertised as having an average illumination lifespan of 2,000 hours. A random sample of 64 bulbs burned out with a mean lifespan 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 onetail hypothesis test to determine if the means are statistically equal using an alpha of 0.05.
n_{1} = 45 n_{2} = 36
xbar_{1}= 64 xbar_{2} = 60
s_{1}=15 s_{2} = 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 twotail hypothesis test, α =.05.
Male GPA’s  Female GPA’s  
Sample Size  17  15  
Sample Mean  3.8  3.95  
Sample Standard Dev  .5  .7  
PROBLEM 5 (20 pts): The NeutraPride 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 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 (f_{o})
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  
Coefficients  Standard Error  t Stat  Pvalue  
Intercept  34.6165  38.3735  0.9021  0.3753 
X1 (Square Feet)  0.1232  0.0184  8.3122  0.0018 
X2 (Lot Size)  .00142  1.7120  5.2583  0.0122 
X3 (Bedrooms)  17.3903  6.8905  2.5238  0.1259 
Answer the following questions, and note that some are twoparters, so answer both!
 Is there a linear relationship in this model? How can you tell?
 Why is the coefficient for lot size a positive number? What is the value (per square foot) of a lot?
 Which is the most statistically significant variable? What evidence shows this?
 Which is the least statistically significant variable? What evidence shows this?
 For a 0.05 level of significance, could any variable(s) be dropped from this model? Why?
 Looking at the associated pvalue, should the Intercept be dropped from this model? Why?
 Using all of the variables: What should be the cost of a 2,000 squarefoot home with a lot size of 5,000 square feet and three bedrooms?
PART III SPECIFIC KNOWLEDGE SHORTANSWER QUESTIONS (50 Points)
Problem 1: In a regression analysis:
 What is the range of an R^{2} value? ________________________
 What does or could a pvalue = 0.18 mean/imply? __________________________________
 What is a DurbinWatson test designed to detect? _________________________________
 How is an Adjusted R^{2} value different from an R^{2} value? ___________________________
Problem 2: Define multicollinearity in the following terms:
 Variables need to be ___________________ in a linear regression model.
 In which type of regression is multicollinearity likely to occur? ________________________
 What is the negative impact of multicollinearity in a regression? ______________________
 How could you identify if it exists? _____________________________________
 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.
 Should Ms. Parker be concerned about Timmy’s reading ability? Why (or why not)?
 What percentage of students did worse than Timmy on this standardized test?
 Brenda’s Mom bragged to Timmy’s Mom that her daughter scored a 96. Could her claim be valid? Why? (Hint: Compute the Zvalue or use a 95% Confidence interval) Would you conclude Brenda’s Mom is a jerk?

Last Updated on March 25, 2019 by Essay Pro