Question

Consider the following data on x = weight (pounds) and y = price ($) for 10 road-racing bikes.

Brand Weight Price ($)
A 17.8 2,100
B 16.1 6,250
C 14.9 8,370
D 15.9 6,200
E 17.2 4,000
F 13.1 8,500
G 16.2 6,000
H 17.1 2,580
I 17.6 3,500
J 14.1 8,000

Required:
Use the F test to determine whether the weight for a bike and the price are related at the 0.05 level.

Answer 1

There is a significant relation between weight and price

Explanation:

Brand Weight(x) Price ($) (y)

A 17.8 2100

B 16.1 6,250

C 14.9 8,370

D 15.9 6,200

E 17.2 4,000

F 13.1 8,500

G 16.2 6,000

H 17.1 2,580

I 17.6 3,500

J 14.1 8,000

Null Hypothesis :
`H_0: \mu =0`

Alternate Hypothesis :
`H_a: \mu \\eq 0`

Given : SST=51956800 SSE= 7312286.84 n = 10

SSR = SST-SSE

SSR=51956800-7312286.84

SSR=44644513.16

Level of significance =
`\alpha = 0.05`

`F=((SSR)/(m))/((SSE)/(n-k))`

Where m = no. of restrictions

k = No. of independent variables

`F=((44644513.16)/(1))/(( 7312286.84)/(10-2))`

F=48.843

Degree of freedom 1 = 1

Degree of freedom 2 = 10-2=8

Using calculator

p-value is .000114.

p value < α

So, we reject the null hypothesis .

Hence There is a significant relation between weight and price