You are conducting a Goodness of Fit hypothesis test for the claim that all 5 categories are equally

drulluna60h

drulluna60h

Answered question

2022-03-09

You are conducting a Goodness of Fit hypothesis test for the claim that all 5 categories are equally likely to be selected. Complete the table. Report all answers correct to three decimal places.
 Category  Observed Frequency  Expected Frequency  (obs-exp)^2/exp  A 15 B 19 C 23 D 18 E 5
What is the chi-square test-statistic for this data?χ2=
At the alpha = 0.05 level, what is the conclusion for this test?
Fail to reject the null hypothesis
Reject the null hypothesis
Report all answers accurate to three decimal places.

Answer & Explanation

Donovan Acevedo

Donovan Acevedo

Beginner2022-03-10Added 1 answers

The hypotheses are given below:
Null hypothesis:
H0: All five categories are equally likely to be selected.
Alternative hypothesis:
H1: All five categories are not equally likely to be selected.
The chi-square test is appropriate in this situation:” 
The test statistic is given below:
χ2=(OiEi)2Eiχ{(k=1)}2
Where
Oi Observed frequency
Ei Expected frequency
k=Number of observations
The expected frequency is obtained as given below:
E=Observedn=805=16
Test statistic
 Category  Observed Frequency  Expected Frequency  (obs-exp)^2/exp  A 15160.063 B 19160.563 C 23163.063 D 18160.25 E 5167.563
The chi-square test-statistic for this data:
χ2=0.063+0.563+3.063+0.25+7.563=11.5.
P-value:
The P-value of the sample statistic is obtained using Excel formula.
From EXCEL formula “=CHISQ.DIST.RT(11.5, 4)”, the P-value is 0.021.
Decision rule:
1. If the P-value is less that the significance level, reject the null hypothesis.
2. Otherwise fail to reject the null hypothesis.Conclusion:
Here, the P-value is less than the significance level (=5%).
Therefore, by the decision rule, Reject the null hypothesis.

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?