Question

You may need to use the appropriate technology to answer this question.

Consider the data.

xi	2	6	9	13	20
yi	7	19	10	28	21

(a) What is the value of the standard error of the estimate?

B)Test for a significant relationship by using the t test. Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ ≠ 0
H_a: β₁ = 0

H₀: β₀ = 0
H_a: β₀ ≠ 0    

H₀: β₁ = 0
H_a: β₁ ≠ 0

H₀: β₁ ≥ 0
H_a: β₁ < 0

H₀: β₀ ≠ 0
H_a: β₀ = 0

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

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

p-value =  

c)Use the F test to test for a significant relationship. Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ ≠ 0
H_a: β₁ = 0

H₀: β₀ = 0
H_a: β₀ ≠ 0    

H₀: β₁ ≥ 0
H_a: β₁ < 0

H₀: β₀ ≠ 0
H_a: β₀ = 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 =

Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest).

Brand	Price ($)	Score
A	180	76
B	150	71
C	95	59
D	70	58
E	70	40
F	35	26

(a) The estimated regression equation for this data is  ŷ = 23.528 + 0.315x, where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use α = 0.05.

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 three decimal places.)

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

p-value =  

(b)Test for a significant relationship using the F test. Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ ≠ 0
H_a: β₁ = 0

H₀: β₁ = 0
H_a: β₁ ≠ 0    

H₀: β₀ = 0
H_a: β₀ ≠ 0

H₀: β₀ ≠ 0
H_a: β₀ = 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 =  

(c) Show the ANOVA table for these data. (Round your p-value to three decimal places and all other values to two decimal places.)

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Regression
Error
Total

Answer 1

a)

std error σ              =

=se =√s2=

7.4922

b)

H₀: β₁ = 0
H_a: β₁ ≠ 0

test stat t =	β1/se(β1)=	=	1.472
p value:		=	0.2375

2)

a)

H₀: β₀ = 0
H_a: β₀ ≠ 0

test stat t =	β1/se(β1)=	=	4.391
p value:		=	0.0118

b) H₀: β₀ = 0
H_a: β₀ ≠ 0

value of the test statistic =19.28

p value =0.0118

c)

Source	SS	df	MS	F	p value
regression	1480.74	1	1480.74	19.28	0.012
Residual error	307.26	4	76.82
Total	1788.00	5