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 α = 0.05.
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.
(c) Find the predicted value of Y given X = 75. Give an interpretation of the predicted value in the context of the problem.
(d) Construct an ANOVA table and attach the summary output.