Question

A statistical program is recommended.

A marketing professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 10 students who took the course last quarter follow.

Hours Spent Studying	Total Points Earned
45	40
30	35
90	75
60	65
105	90
65	50
90	90
80	80
55	45
75	65

(a)

Develop an estimated regression equation showing how total points earned can be predicted from hours spent studying. (Round your numerical values to two decimal places.)

ŷ =

(b)

Test the significance of the model with α = 0.05. (Use the F test.)

State the null and alternative hypotheses.

H₀: β₀ = 0
H_a: β₀ ≠ 0

H₀: β₀ ≠ 0
H_a: β₀ = 0  

H₀: β₁ = 0
H_a: β₁ ≠ 0

H₀: β₁ ≠ 0
H_a: β₁ = 0

H₀: β₁ ≥ 0
H_a: β₁ < 0

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Do not reject H₀. We cannot conclude that the relationship between hours spent studying and total points earned is significant.

Reject H₀. We conclude that the relationship between hours spent studying and total points earned is significant.

Do not reject H₀. We conclude that the relationship between hours spent studying and total points earned is significant.

Reject H₀. We cannot conclude that the relationship between hours spent studying and total points earned is significant.

(c)

Predict the total points earned by Mark Sweeney. He spent 85 hours studying. (Round your answer to two decimal places.)

points

(d)

Develop a 95% prediction interval for the total points earned by Mark Sweeney. (Round your answers to two decimal places.)

points to  points

Answer 1

y = 5.85 + 0.83 x

b)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.936862
R Square	0.87771
Adjusted R Square	0.862424
Standard Error	7.523125
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3249.721	3249.721	57.41819	6.44E-05
Residual	8	452.7792	56.59741
Total	9	3702.5
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	5.847009	7.971731	0.733468	0.48421	-12.5358	24.22985	-12.5358	24.22985
X Variable 1	0.829539	0.109474	7.577479	6.44E-05	0.577091	1.081988	0.577091	1.081988