1. Part of an ANOVA table is shown below.
Source of Variation Sum of Squares Degrees of Freedom Mean Square F
Between treatments 90 3 _____? _____?
Within treatments (Error) 120 20 _____?
Total _____? _____?
a. Compute the missing values and fill in the blanks in the above table. Use a = .01 to determine if there is any significant difference among the means. b. How many groups have there been in this problem?
c. What has been the total number of observations?
2. The sales records of a major auto manufacturer over the past 10 years are shown below.
Number of Cars Sold
Year (t) (in 1000s of Units)
1 195
2 200
3 250
4 270
5 320
6 380
7 440
8 460
9 500
10 500
Develop a linear trend expression and project the sales (the number of cars sold) for time period t = 11.
3. The following data represent the number of flash drives sold per day at a local computer shop and their prices.
Price (x) Units Sold (y)
$34 3
36 4
32 6
35 5
30 9
38 2
40 1
a. Perform an F test and determine if the price and the number of flash drives sold are related.
Let a = .01.
Perform a t test and determine if the price and the number of flash drives sold are related. b.
Let a = .01.
4. In a completely randomized experimental design, 14 experimental units were used for each of the five levels of the factor (i.e., five treatments). Fill in the blanks in the following ANOVA table.
Source of Variation Sum of Squares Degrees of Freedom Mean Square F
Between treatments _____? _____? 800.00 _____?
Within treatments (Error) _____? _____? _____?
Total 10,600 _____?
5. Halls, Inc. has three stores located in three different areas. Random samples of the sales of the three stores (In $1,000s) are shown below.
Store 1 Store 2 Store 3
46 34 33
47 36 31
45 35 35
42 39
45
At a 5% level of significance, test to see if there is a significant difference in the average sales of the three stores.
6. The marketing department of a company has designed three different boxes for its product. It wants to determine which box will produce the largest amount of sales. Each box will be test marketed in five different stores for a period of a month. Below is the information on sales.
Store 1 Store 2 Store 3 Store 4 Store 5
Box 1 210 230 190 180 190
Box 2 195 170 200 190 193
Box 3 295 275 290 275 265
a. State the null and alternative hypotheses.
b. Construct an ANOVA table.
c. What conclusion do you draw?
7. Three different brands of tires were compared for wear characteristics. For each brand of tire, 10 tires were randomly selected and subjected to standard wear testing procedures. The average mileage obtained for each brand of tire and sample standard deviations (both in 1000 miles) are shown below.
Brand A Brand B Brand C
Average mileage 37 38 33 Sample variance 3 4 2
Use the above data and test to see if the mean mileage for all three brands of tires is the same. Let a = .05.
8. John has collected the following information on the amount of tips he received from parking cars the last seven nights.
Day Tips
1 18
2 22
3 17
4 18
5 28
6 20
7 12
a. Compute the three-day moving averages for the time series.
b. Compute the mean square error for the forecasts.
c. Compute the mean absolute deviation for the forecasts.
9. The Very Fresh Juice Company has developed a regression model relating sales (y in $10,000s) with four independent variables. The four independent variables are price per unit (x1, in dollars), competitor's price (x2, in dollars), advertising (x3, in $1000s), and type of container used (x4) (1 = Cans and 0 = Bottles). Part of the regression results is shown below.
Source of Variation Degrees of Freedom Sum of Squares Mean F
Square
Regression 4 283,940.60
Error 18 621,735.14
Total
a. Compute the coefficient of determination and fully interpret its meaning.
b. Is the regression model significant? Explain what your answer implies. Let a = .05.
c. What has been the sample size for this analysis?
10. The prices of Rawlston, Inc. stock (y) over a period of 12 days, the number of shares (in 100s) of the company's stocks sold (x1), and the volume of exchange (in millions) on the New York Stock Exchange (x2) are shown below.
Day (y) (x1) (x2)
1 87.50 950 11.00
2 86.00 945 11.25
3 84.00 940 11.75
4 83.00 930 11.75
5 84.50 935 12.00
6 84.00 935 13.00
7 82.00 932 13.25
8 80.00 938 14.50
9 78.50 925 15.00
10 79.00 900 16.50
11 77.00 875 17.00
12 77.50 870 17.50
Excel was used to determine the least squares regression equation. Part of the computer output is shown below.
ANOVA
df SS MS F Significance F
Regression 2 118.8474 59.4237 40.9216 0.0000
Residual 9 13.0692 1.4521
Total 11 131.9167
Coefficients Standard Error t Stat P-value
Intercept 118.5059 33.5753 3.5296 0.0064
(x1) –0.0163 0.0315 –0.5171 0.6176
(x2) –1.5726 0.3590 –4.3807 0.0018
Use the output shown above and write an equation that can be used to predict the price of the a.
stock.
b. Interpret the coefficients of the estimated regression equation that you found in part (a).
c. At 95% confidence, determine which variables are significant and which are not.
If on a given day, the number of shares of the company that were sold was 94,500 and the
d. volume of exchange on the New York Stock Exchange was 16 million, what would you expect the price of the stock to be?