Question

A local grocery store wants to predict the monthly sales in dollars. The manager believes that the amount of newspaper advertising significantly affects the store sales. The manager randomly selects 10 months of data consisting of monthly grocery store sales (in thousands of dollars) and advertising expenditures (in thousands of dollars). See the following data:

If the advertising expenditures increase by one thousand of dollars, estimate the average increase in sales with 95% confidence.

The next month, the grocery store wants to invest 3230 dollars in advertising. Predict the total sales for that specific month with 95% confidence.

At the 5% level of significance, conduct the F test to test the overall significance of the model. Is the current model a significant predictor of of the monthly grocery store sales?

Advertising	2.74	2.87	2.93	2.87	2.98	3.09	3.36	3.61	3.75	3.95
Sales	99.9	97.9	98.9	87.9	92.9	97.9	100.6	104.9	105.3	108.6

Answer 1

First enter Data into EXCEL

We have to find the sample mean.

Excel command is =AVERAGE(Select data)

sample mean for advertising = 3.215

sample mean for sales = 99.48

Now we have to find sample standard deviation.

Excel command is =STDEV(Select data)

standard deviation for advertising = 0.424

standard deviation for sales = 6.061

n1 = 10

n2 = 10

s1 = 0.424

s2 = 6.061

Null and alternative hypothesis is

H0 :u1 = u2

Vs

H1 :u1 u2

Level of significance = 0.05

Before doing this test we have to check population variances are equal or not.

Null and alternative hypothesis is

Vs

Test statistic is

F = Larger variance / Smaller variance = 36.731 / 0.179 = 205.20

Degrees of freedoms

Degrees of freedom for numerator = n1 - 1 = 10 - 1 = 9

Degrees of freedom for denominator = n2 - 1 = 10 - 1 = 9

Critical value = 3.179 ( using f-table )

F test statistic > critical value , Reject Ho

we reject null hypothesis