Question

1.

The following data on price ($) and the overall score for 6 stereo headphones that were tested by Consumer Reports were as follows.

Brand	Price ($)	Score
Bose	180	72
Scullcandy	162	72
Koss	90	66
Phillips/O'Neill	72	60
Denon	72	42
JVC	36	30

a. Does the t test indicate a significant relationship between price and the overall score?

The test t-Conclusion at = .05

t =   (to 2 decimal places.)

p-value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .1greater than .1Item 2

What is your conclusion? Use = .05.
- Select your answer -There is a significant relationship between price and overall scoreThere is no significant relationship between price and overall scoreItem 3 .

b. Test for a significant relationship using the F test.
p-value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .1greater than .1Item 4

What is your conclusion? Use = .05.

Because p-value is - Select your answer -greater than or equal toless than or equal toequal toItem 5  .05, we - Select your answer -acceptrejectItem 6  H ₀: β ₁ is - Select your answer -greater than or equal to zeroless than or equal to zeroequal to zeroItem 7 .

c. Show the ANOVA table for these data. Round your answers to three decimal places, if necessary.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Regression					- Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .1greater than .1Item 12
Error
Total

2.

Given are five observations for two variables, x and y.

x i	1	2	3	4	5
y i	3	7	5	12	13

Round your answers to two decimal places.

a. Using the following equation:

Estimate the standard deviation of ŷ* when x = 3.

b. Using the following expression:

Develop a 95% confidence interval for the expected value of y when x = 3.

  to  

c. Using the following equation:

Estimate the standard deviation of an individual value of y when x = 3.

Answer 1

1) applying regression from excel: data-data analysis

test stat t=

r*(√(n-2)/(1-r2))=

3.09

t stat is in rejection region

p-value is between 0.025 and 0.05

There is a significant relationship between price and overall score

2)

p-value is between 0.025 and 0.05

because the p value is less than 0.05 , we reject Ho , Beta1 is equal to zero

c)

Source	SS	df	MS	F	p value
regression	1053.730	1	1053.730	9.573	0.036
Residual error	440.270	4	110.068
Total	1494.000	5

2)

a)

std error of confidence interval =

s*√(1/n+(x0-x̅)2/Sxx)=

0.95

b)

for 95 % confidence and 3degree of freedom critical t=						3.1820
95% confidence interval =xo -/+ t*standard error=					(4.98,11.02)

c)

std error of prediction interval=s*√(1+1/n+(x0-x̅)2/Sxx)=

2.32

d)

for 95 % confidence and -2degree of freedom critical t=						3.1820
95% prediction interval =xo -/+ t*standard error=					(0.61,15.39)