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Need to understand these statistics questions. The question involve scatter diagrams, correlation coefficients, ANOVA tables, mean absolute deviation, revenue and cost functions, maximizing profits, and payoff tables.

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Problem 1
The average prices for a product in twelve stores in a city are shown below.
$1.99, $1.85, $1.25, $2.55, $2.00, $1.99, $1.76, $2.50, $2.20, $1.85, $2.75, $2.85
Test the hypothesis that the average price is higher than $1.87. Use level of significance  = 0.05.

Ho: µ=1.87
Ha: µ>1.87
This is a one tailed t test.
Degree of freedom: 12-1=11.
Mean: (1.99+1.85+1.25+2.55+2.00+1.99+1.76+2.50+2.20+1.85+2.75+2.85)/12=2.128
Standard deviation: sqrt(((1.99-2.128)^2+(1.85-2.128)^2+...+(2.85-2.128)^2)/(12-1))=0.462
Test value t=(2.128-1.87)/(0.462/sqrt(12))=1.934
P value=Tdist(1.934,11,1)=0.0396 (Tdist is a function in excel, 11 is the degree of freedom, 1 means one tailed test).
Since P value is less than 0.05, we reject Ho.
Based on the test, we could conclude that the average price is higher than $1.87.

Problem 2
A store wants to predict net profit as a function of sales for next year. Historical data for 8 years is given in the table below.

Year Sales
(thousands of dollars) Net Profit
1 59 5.0
2 50 8.4
3 51 9.5
4 65 8.6
5 80 1.5
6 85 -2.1
7 95 1.2
8 90 1.8

(a) Make a scatter diagram for the data, using Sales for the independent variable and Net Profit for the dependent variable. Insert the trend line and add the equation and R2 value to the diagram.

(b) Determine the correlation coefficient. Comment on the value of the correlation coefficient.
First, from the scatter plot, we could see that there is a negative correlation between sales and net profits.
Therefore, correlation coefficient: -sqrt(0.7467)=-0.864.
Since the value is close to -1, it suggests a strong negative correlation between sales and net profits.

(c) Find the predicted value of Y given X = 75. Give an interpretation of the predicted value in the context ...

Solution Summary

The examined examines statistics and financial analysis for ANOVA tables. The payoff tables are provided.

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14. Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The X column indicates the number of client contacts last month, and the Y column shows the value of sales ($ thousands) last month for each client sampled.

Number of Sales Number of Sales
Contacts, ($ thousands), Contacts, ($ thousands),
14 24 23 30
12 14 48 90
20 28 50 85
16 30 55 120
46 80 50 110

a. Determine the regression equation.
b. Determine the estimated sales if 40 contacts are made.

22. Refer to Exercise 14.
a. Determine the standard error of estimate.
b. Suppose a large sample is selected (instead of just 10). About 95 percent of the predictions regarding sales would occur between what two values?

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