Question

1. Management of a fast-food chain proposed the following regression model to predict sales at outlets:

y = β0 + β1x1 + β2x2 + β3x3 + ε, where

y = sales ($1000s)

x1 = number of competitors within one mile

x2 = population (in 1000s) within one mile

x3 is 1 if a drive-up window is present, 0 otherwise

Multiple regression analysis was performed on a random sample of data collected from 25 outlets.

Given the following portion of an output of the regression software tool, answer the question:

Which of the independent variables are significant at α = 5%?

	Coefficients	Standard Error	t Statistic	P-value
Intercept	39.223	5.942	6.601	0.0000
Competitors	-2.674	1.161	-2.303	0.0316
Population	7.720	2.043	3.779	0.0011
Drive-up	10.682	5.304	2.014	0.0570

Select one:

A Both Population and Competitors

B Drive-up only

C Competitors only

D Population only

E Both Population and Drive-up

F All three variables

2.

Two samples are randomly selected from normal populations. The sample statistics are given below.

n1 = 18 n2 = 13

1 = 535 2 = 520

s1 = 40 s2 = 25

Use α = 0.01 to test the hypothesis that μ1 > μ2.

Select one:

A critical value tc = ±2.763; standardized test statistic t = 1.282; fail to reject H0

B critical value tc = -1.313; standardized test statistic t = -1.282; reject H0

C critical value tc = ±2.771; standardized test statistic t = -1.282; reject H0

D critical value tc = 2.467; standardized test statistic t = 1.282; fail to reject H0

3.

Two samples are randomly selected from normal populations. The sample statistics are given below.

n1 = 18 n2 = 13

1 = 535 2 = 520

s1 = 40 s2 = 25

Use α = 0.01 to test the hypothesis that μ1 > μ2.

Select one:

A critical value tc = ±2.763; standardized test statistic t = 1.282; fail to reject H0

B critical value tc = -1.313; standardized test statistic t = -1.282; reject H0

C critical value tc = ±2.771; standardized test statistic t = -1.282; reject H0

D critical value tc = 2.467; standardized test statistic t = 1.282; fail to reject H0

Answer 1

Ans 1 )

the independent variables are significant at α = 5% is

	Coefficients	Standard Error	t Statistic	P-value
Intercept	39.223	5.942	6.601	0.0000
Competitors	-2.674	1.161	-2.303	0.0316
Population	7.720	2.043	3.779	0.0011
Drive-up	10.682	5.304	2.014	0.0570

D) Population only because p-value is less than

Ans 2 )two samples are randomly selected from normal populations. The sample statistics are given below.

n1 = 18 n2 = 13

1 = 535 2 = 520

s1 = 40 s2 = 25

Separate-Variances t Test for the Difference Between Two Means
(assumes unequal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.01
Population 1 Sample
Sample Size	18
Sample Mean	535
Sample Standard Deviation	40
Population 2 Sample
Sample Size	13
Sample Mean	520
Sample Standard Deviation	25
Intermediate Calculations
Numerator of Degrees of Freedom	18759.6336
Denominator of Degrees of Freedom	657.3944
Total Degrees of Freedom	28.5363
Degrees of Freedom	28
Separate Variance Denominator	11.7032
Difference in Sample Means	15
Separate-Variance t Test Statistic	1.2817
Upper-Tail Test
Upper Critical Value	2.4671
p-Value	0.1052
Do not reject the null hypothesis

D critical value tc = 2.467; standardized test statistic t = 1.282; fail to reject H0

3.

D critical value tc = 2.467; standardized test statistic t = 1.282; fail to reject H0