Question

The table below shows the number of cars sold last month by seven employees at Concord Motors and their number of years of sales experience.

Experience	Sales
1	8
2	6
2	7
4	14
5	9
6	13
8	10

Management would like to use simple regression analysis to estimate monthly car sales using the number of years of sales experience. The 95% confidence interval for the regression slope is ________.

Group of answer choices

a (-1.842, 3.158)

b (-0.481, 1.797)

c (0.058, 1.258)

d (0.408, 0.908)

The table below shows the number of cars sold last month by seven employees at Concord Motors and their number of years of sales experience.

Experience	Sales
1	8
2	6
2	7
4	14
5	9
6	13
8	10

Management would like to use simple regression analysis to estimate monthly car sales using the number of years of sales experience. Which one of the following statements describes the results of the hypothesis test that the population slope is not equal to zero using alpha = 0.05?

Group of answer choices

a Because the absolute value of the test statistic is less than the absolute value of the critical value, we fail to reject the null hypothesis and cannot conclude that the population slope is not equal to zero.

b Because the absolute value of the test statistic is less than the absolute value of the critical value, we can reject the null hypothesis and conclude that the population slope is equal to zero.

c Because the absolute value of the test statistic is greater than the absolute value of the critical value, we can reject the null hypothesis and conclude that the population slope is not equal to zero.

d Because the absolute value of the test statistic is greater than the absolute value of the critical value, we fail to reject the null hypothesis and conclude that the population slope is equal to zero.

Answer 1

X	Y	XY	X²	Y²
1	8	8	1	64
2	6	12	4	36
2	7	14	4	49
4	14	56	16	196
5	9	45	25	81
6	13	78	36	169
8	10	80	64	100
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
28	67	293	150	695

Sample size, n =	7
x̅ = Ʃx/n = 28/7 =	4
y̅ = Ʃy/n = 67/7 =	9.57142857
SSxx = Ʃx² - (Ʃx)²/n = 150 - (28)²/7 =	38
SSyy = Ʃy² - (Ʃy)²/n = 695 - (67)²/7 =	53.7142857
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 293 - (28)(67)/7 =	25

Slope, b = SSxy/SSxx = 25/38 = 0.6578947

y-intercept, a = y̅ -b* x̅ = 9.57143 - (0.65789)*4 = 6.9398496

Regression equation :

ŷ = 6.9398 + (0.6579) x

Sum of Square error, SSE = SSyy -SSxy²/SSxx = 53.71429 - (25)²/38 = 37.26692

Standard error, se = √(SSE/(n-2)) = √(37.26692/(7-2)) = 2.73009

Standard error for slope, se(b1) = se/√SSxx = 2.73009/√38 = 0.44288

a)

df = n-2 = 5

Significance level, α = 0.05

Critical value, t_c = T.INV.2T(0.05, 5) = 2.5706

95% confidence interval for slope:

Lower limit = b1 - tc*se(b1) = 0.6579 - 2.5706*0.4429 = -0.481

Upper limit = b1 + tc*se(b1) = 0.6579 + 2.5706*0.4429 = 1.797

Answer: B. (-0.481, 1.797)

------

b)

Null and alternative hypothesis:

Ho: β₁ = 0

Ha: β₁ ≠ 0

Test statistic:

t = b1/se(b1) = 0.6579/0.4429 = 1.4855

Critical value, t_c = T.INV.2T(0.05, 5) = +/- 2.5706

Conclusion:

Answer: A. Because the absolute value of the test statistic is less than the absolute value of the critical value, we fail to reject the null hypothesis and cannot conclude that the population slope is not equal to zero.