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.

Answers

Answer 1

Answer:

There is a significant relation between weight and price

Step-by-step 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 : [tex]H_0: \mu =0[/tex]

Alternate Hypothesis : [tex]H_a: \mu \neq 0[/tex]

Given : SST=51956800 SSE= 7312286.84 n = 10

SSR = SST-SSE

SSR=51956800-7312286.84

SSR=44644513.16

Level of significance =[tex]\alpha = 0.05[/tex]

[tex]F=\frac{\frac{SSR}{m}}{\frac{SSE}{n-k}}[/tex]

Where m = no. of restrictions

k = No. of independent variables

[tex]F=\frac{\frac{44644513.16}{1}}{\frac{ 7312286.84}{10-2}}[/tex]

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


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Ava read an article claiming that 10% of people in her county were senior citizens, and she wondered if this held true for residents in her city. She took a random sample of 225 people from her city to test H0 : p = 0.10, where p is the proportion of people in her city that are senior citizens. Ava found that approximately 14% of those sampled were senior citizens. She conducted an appropriate significance test, and the resulting test statistic was z ≈ 1.89 z. Assume that the conditions for inference were met.calculate the p-value for Ellie's significance test

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