Stats and Financial Analysis

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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 ...