You are conducting a test of independence for the daim that there is an association between morning

Dawson Riggs

Dawson Riggs

Answered question

2022-03-06

You are conducting a test of independence for the daim that there is an association between morning beverage and age.
 Juice  Coffee  Pop  Tea  less that 25 1918532 25 or older 2730243
What is the chi-square test-statistic and the corresponding p-value for this data?
χ2=?, [three decimal accuracy]
p-value=?, [three decimal accuracy]

Answer & Explanation

oighreacha12

oighreacha12

Beginner2022-03-07Added 2 answers

a) Null and alternative hypothesis:
H0: There is no association between the morning beverage and age.
Hα: There is association between the morning beverage and age.
b) Observed frequency (O) table:
 Juice  Coffee  Pop  Tea  less that 25 191853274 25 or older 2730243102 Total 46487753176
The Expected frequency (E) table: This is a Chi-square test
Expected frequencies and Test statistics can be calculated as follow:
Expected frequency = (row total*column total)/Grand total
 Juice  Coffee  Pop  Tea  less that 25 19.34120.1822.94331.53474 25 or older 26.65927.8184.05743.466102 Total 46487753176
Chi-square test statistic χ2=(OE)2E
The Chi-square test statistic = 28.2658
4) df=n-1=3-1=2, α=0.05. The P-value is 0.00001
5) P-value < 0.05 we reject the null hypothesis.
c) Chi-square test statistic (χ)2:
 Observed frequency (O)  Expected frequency (E)  (O-E)^2  (O-E)^2/E 1919.340.11560.01341820.184.75240.235552.944.24361.44343231.530.22090.00702726.660.11560.00433027.824.75240.170824.064.24361.04524343.470.22090.0051 Chi-square test statistic (χ2)2.9247
degree of freedom (df) = (row-1)*(column -1)
= (2-1)*(4-1)
= 3
significance level α=0.05
d) P-value = 0.403
e) SInce P- value > significance level (α),we fail to reject the null hypothesis.
There is no association between the morning beverage and age.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?