Question

Please show work and explain. Thank you.

1. The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of a specialty pet food. Data are collected from a random sample of 8 equal-sized stores, with the following results:

Store	Shelf Space (in square feet)	Weekly Sales (in Dollars)
1	4	120
2	4	150
3	8	160
4	8	180
5	12	200
6	16	210
7	16	240
8	20	260

Use Excel to find the regression results. Please include Excel results.

a. at the 0.05 level of significance, is there evidence of a linear relationship between shelf space and weekly sales?

b. construct a 95% confidence interval estimate of the population slope, β₁.

Answer 1

a) NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

alpha=0.05

t = r*sqrt(n-2)/sqrt(1-r^2)

t= 0.961*sqrt(6)/0.076

t= 8.54

df=6

The p-value is .000141.The result is significant because p < .05.

Decision:REJECT H0

Conclusion: We have sufficient evidence to conclude that there is relationship between two variables

b) 95% confidence interval estimate of the population slope, β1 is (5.43, 9.73)

By using MS EXCEL data analysis tool pack