LONG QUESTIONS

1. Following table gives the miles-per-gallon for four brands of cars using three different grades of gasoline. If the Total Sum of Squares equals 270, using the Two-Way ANOVA (at α = 5%), analyze if there is a significant difference in the means of miles/gallon by (a) Brands of Cars; and (b) Grades of Gasoline?

2. There are three brands of TVs in the market. Samsung sells 35% of the market, Sony 40%, and all other brands 25%. Sony announced a special deal for the Holiday Season. To check on sales, a sample of 300 TVs sold was examined. It showed that 135 TVs sold were Sony, 95 were Samsung, and the rest were other brands. Using Chi-square test, can we say that market shares of these brands changed significantly as a result of Sony's special deal? State your null hypothesis, and interpret your results.

3. Estimate the demand curve from the following data where Y is quantity demanded and X is price.

Number of Observation = 101 ∑ Yi = 16,160 ∑Xi = 30,130
∑(Yi-Yhat)2 = 1,960 ∑(Xi-Xbar)2 = 40,000 ∑(Yi-Ybar)2 = 6,400
∑(Xi-Xbar)(Yi-Ybar) = - 12,000
(Use only two decimal places to write your answers)

Estimate the following:
a. Regression line and interpret it.
b. Make ANOVA Table. Write Ho. Calculate F-value and interpret your results.
c. Calculate measure of "goodness of fit" and interpret your results
d. Calculate t-statistic for b1
e. What will be the quantity demanded if Price is 400? Calculate 95% confidence interval of your predicted value.

Bonus: Calculate coefficient of correlation between x and y and test the hypothesis Ho: ρxy = 0 against ≠ 0. OR Calculate σxy, σx and σy.

4. Following table shows results from a survey testing the use of social networking sites by adults in three countries.
Use Social Networking
Countries YES NO
UK 344 456
Russia 201 399
USA 500 500
Perform Chi-square pairwise comparisons at 5% margin of error to test which pair of countries differed in their use of social networking sites. Which country did the most networking?

5. Given below is a liner expenditure equation for 1000 families in its simplified version:
Y = 9.12 + 0.36 Income + 3.21 ?CPI + 1.45 Family Size + 2.33 Race + 0.82 Area R2 = 0.81
(1.66) (2.22) (3.11) (2.62) (2.21) (1.99) F = 218
Where Y is expenditure (thousand $); Income (thousand $); ?CPI change in consumer price index (%), Family-size 2 to 5; Race (0 = Asian, 1 = African-American, 2= Hispanic, 3 = White), and
Area (0 = Township, 1 = Suburb, 2 = Metropolitan).
Calculate the expected expenditure of an African-American family comprising of 4 family members, earning $50 thousand, living in a metropolitan area where the cost of living (measured by ?CPI) increased by 3 percent in one year.
SHORT QUESTION:
1/ You are given the following output from model estimation:

Variables Coeff Sig Odds
Price Increase_Same Model (000) -0.112 0.023 0.894
Gender 1.241 0.041 3.459
Number of Competitive Models 0.161 0.001 1.175
Number of Recalls_Same Model -0.341 0.002 0.711
Constant -1.223 0.011
Nagelkerke R-sq = 0.66

I there are three competitive models in the market, calculate the probability of buying the same model again by a male buyer if the price increase for the same model is five thousand dollars and there were two recalls of the same model for its defective parts.

2/ A text book publishing company finds 15 typos per 1000 pages. What is the probability of finding less than 3 errors in a book of 400 pages?

3/ To analyze the risk and return of GE stocks, Charles Schwab (Jan 2012) reported the stock price change in GE common stocks as follows:

20.0 -21.0 12.0 13.0 11.0 -6.0 -19.0 14.0

Construct the 95% confidence interval of the population variance (and standard deviation) of GE Stocks. (Hint: Use chi-square distribution.)

4/ Consider the following test about the quantity of cough syrup in a bottle,
Ho: μ = 32 fl oz (with σ = 4 fl oz. ) Ha: μ ≠ 32 fl oz
Calculate the sample size be if the FDA is willing to accept only 1% of Type I and Type II error given that random test suggested quantity of cough syrup to be 30 fl oz only.

5/ What is the largest possible sample size if a delegate wants to be 99% sure that his sample proportion will be within 1% of the population proportion.

6/ The makers of a diet supplement claim that one can lose weight up to 10 lbs of their original weight in one month. In a sample study of 20 cases the standard deviation was as high as 30 lbs. Do you believe in their claim? (α = 5%)

7/ Test the following Hypothesis about two variances:
Ho: σ12 = σ22
Ha: σ12 ≠ σ22
A sample 21 observation and 31 observations revealed sample standard deviations as 24 and 19 respectively. Test the null hypothesis at 95% confidence and show your values in a diagram.