Problem 1 A,B,C Inc. produces fresh, a brand of liquid laundry detergent. In order to more effectively manage its inventory and make revenue projections, the company would like to like to better predict demand for Fresh. The company has established the flowing demand equation:
Demand = Bo + B1FreshPrice + B2ComPrice + B3AdvExpend
Your Minitab Output follows:
Regression Analysis: Demand versus FreshPrice, ComPrice, AdvExpend
The regression equation is
Demand = 7.59 - 2.36 FreshPrice + 1.61 ComPrice + 0.501 AdvExpend
Predictor Coef SE Coef T stat Pvalue
Constant 7.589 2.445 3.10 0.005
FreshPrice -2.3577 0.6379 -3.70 0.001
ComPrice 1.6122 0.2954 5.46 0.000
AdvExpend 0.5012 0.1259 3.98 0.000
S = 0.234669 R-Sq = 89.4% R-Sq(adj) = 88.1%
Analysis of Variance
Source DF SS MS F Sign F
Regression 3 12.0268 4.0089 72.80 0.000
Residual Error 26 1.4318 0.0551
Total 29 13.4586
Source DF Seq SS
FreshPrice 1 2.9631
ComPrice 1 8.1907
AdvExpend 1 0.8729
Obs FreshPrice Demand Fit SE Fit Residual St Resid
5 3.60 9.3300 8.8164 0.0864 0.5136 2.35R
R denotes an observation with a large standardized residual.
Predicted Values for New Observations
Obs Fit SE Fit 95% CI 95% PI
1 8.4107 0.0469 (8.3143, 8.5070) (7.9188, 8.9025)
Values of Predictors for New Observations
Obs FreshPrice ComPrice AdvExpend
1 3.70 3.90 6.50
a. Write out the regression equation.
b. Predict the Demand when FreshPrice is 3.70, ComPrice is 3.90 and AdvExpend is 6.50.
c. Using the data from #1 above:
1. Report R-Sq and Adj R-SQ. Explain there differences and explain their meaning in the context of this problem.
2. Test the entire Model for significance. That is, the F test. Let alpha equal .05.
d. Using the t tests on each of the independent variables and also the p values.
n1 = 10 n2 = 10
xbar1= 121.92 xbar2 = 114.81
s1=1.40 s2 = 1.84
PROBLEM 6. American Demographics (Jan. 2002) reported the results of a survey on the planning habits of men and women. In response to the question, "What is your preferred method of planning and keeping track of meetings, appointments and deadlines?" 56% of the men and 46% of the women answered "keep them in my head". A nationally representative sample of 1000 adults participated in the survey; therefore, assume that 500 were men and 500 were women.
a. Set up the null and alternative hypothesis for testing whether the percentage of men who prefer keeping track of appoints in their heads is larger than the corresponding percentage of women.
b. Compute the test statistic for the test.
c. Give the rejection region for the test using alpha = .01.
d. Make the appropriate conclusion.
PROBLEM 7 A study compared three different display panels for use by air traffic controllers. Each display panel was tested in a simulated emergency condition: 12 highly trained air traffic controllers took part in the study. Four controllers were randomly assigned to each display panel. The time (in seconds) deeded necessary to stabilize the emergency conditions were recorded. The results of the computer analysis is below. Carry out the appropriate statistical test to determine if the average time necessary to stabilize the emergency conditions is the same for the three methods. Let alpha = .05. Show the 5 steps for the One Way ANOVA or Single factor ANOVA:
One-way ANOVA: Panel A, Panel B, Panel C
Source DF SS MS F Sign f
Factor 2 500.17 250.08 30.11 0.000
Error 9 74.75 8.31
Total 11 574.92
Step by step method for regression analysis,ANOVA and hypothesis testing are discussed here. Regression coefficients, coefficient of determination, scatter diagram , significance of regression model, test statistic, critical value and p value are explained in the solution.