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 | 190 | 78 |
Scullcandy | 150 | 76 |
Koss | 85 | 67 |
Phillips/O'Neill | 80 | 57 |
Denon | 80 | 40 |
JVC | 45 | 27 |
a. Does the t test indicate a significant relationship between price and the overall score?
The test t-Conclusion at α = .05
t = (to 2 decimal places.)
p-value is - Select your answer -less than .02, between
.02 and .05, between .05 and .1, between .1 and .2 or greater than
.2.
What is your conclusion? Use α = .05.
- Select your answer -There is a significant relationship between
price and overall score OR There 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 .01, between
.01 and .025, between .025 and .05, between .05 and .1, greater
than .1
What is your conclusion? Use α = .05.
Because p-value is - Select your answer - greater than or equal to, less than or equal to. OR equal to 0.5 - we accept or reject H_{0}: β_{1} is - Select your answer -greater than or equal to zero, less than or equal to zero, equal to zero?
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 .01, between .01 and .025, between .025 and .05, between .05 and .1greater than .1 | ||||
Error | x | ||||
Total | x | x |
Applying regression from excel: data -data analysis: regression:
df | SS | MS | F | Significance F | |
Regression | 1 | 1500.843 | 1500.843 | 10.19842 | 0.033106 |
Residual | 4 | 588.6569 | 147.1642 | ||
Total | 5 | 2089.5 | |||
Coefficients | Standard Error | t Stat | P-value | ||
Intercept | 23.71897 | 11.68002 | 2.030729 | 0.11212 | |
Price | 0.321724 | 0.100744 | 3.193497 | 0.033106 |
from above":
a) The test t =3.19
p-value is between .02 and .05
There is a significant relationship between price and overall score
b)
p-value is between .025 and .05
Because p-value is less than or equal to 0.05 reject H_{0}: β_{1} is equal to zero
df | SS | MS | F | p value | |
Regression | 1500.843 | 1 | 1500.843 | 10.198 | between 0.025 and 0.05 |
Residual | 588.657 | 4 | 147.164 | ||
Total | 2089.500 | 5 |
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