Question

Please review the following case information and determine what the t test means. The t test is already calculated but I need to know what role in plays in this case analysis for the regression analysis. Thanks in advance!

In this case, Armand's Pizza Parlors is a chain of Italian-food restaurants located in five-state area. Their most sucessful locations are the ones near college campuses. The null hypothesis is that the managers believe that quarterly sales for these restaurants (y) are related positively to the size of the student population (x). Thus, the restaurants that are near college campuses with a larger student population tend to generate more sales than the restuarants near campuses with a small student population. The alternative hypothesis is that the restaurants near college campuses with a larger student population do not generate more sales than the restaurants near college campuses with a smaller student population.

Restaurant

Population

Sales

1

15

148

2

22

134

3

2

54

4

13

136

5

13

142

6

8

109

7

10

169

8

19

128

9

3

99

10

24

142

11

25

149

12

10

142

13

15

156

14

22

139

15

8

104

16

17

134

17

15

166

18

23

127

19

14

151

20

3

115

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 99.0%	Upper 99.0%
Intercept	103.4275	11.41902	9.057477	4.01E-08	79.43703	127.418	70.55853	136.2965
Population	2.047865	0.729014	2.809089	0.011608	0.516264	3.579466	-0.05056	4.146288

Answer 1

Null hypothesis H₀: The student population have no significant impact on the sale. .

Alternate hypothesis H₁: The student population have significant positive impact on the sale. .

Test and Test statistic: The appropriate test the t-test and the test statistic for regression is

Result:

The regression coefficient table show that the t-stat for the slope coefficient of population is 2.809 with a p-value 0.0116. The 95% confidence interval for the slope coefficient is (0.516, 3.579) which does not contain zero. So there is strong evidence at 5% level of significance against the null hypothesis and so it can rejected. It can be concluded that the student population have significant positive impact on the sales of Pizza.