Question about chi-square goodness of fit test

A

Apppreciate_your_help

New member
Joined
May 2, 2022
Messages
13
Hi all

As a beginner I have a question, where I'm looking for a solution with an explanation:

In 100 tosses of a coin, heads were observed 15 times and tails 85 times. At the 0.05 significance level, test the hypothesis that the coin is fair. Use the chi-square goodness of fit test.

Many thanks for your help. Best regards
 
Hello A_Y_H. Please share what you've learned so far about the Chi-Square Test for goodness of fit. If you're not familiar with that method, then are you needing help finding on-line lectures or videos? Thank you.

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes the main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to...
www.freemathhelp.com
 
I watched some examples on the internet, where the formula is shown. But I don't know for example when a significance level is given too (given im my example). χ2 = ∑(Oi – Ei)2/Ei, where Oi = observed value (actual value) and Ei = expected value
 
Apppreciate_your_help said:
I watched some examples on the internet, where the formula is shown. But I don't know for example when a significance level is given too (given im my example). χ2 = ∑(Oi – Ei)2/Ei, where Oi = observed value (actual value) and Ei = expected value
Click to expand...
Let's ignore the significance level for now. I find it helpful to put it in a table format.

Category​
Observed Data​
Expected ​
(Observed-Expected)^2/Expected​
Head15??
Tail85??

The sum of the last column is your chi-square statistic. We can continue once you computed the chi-square stat.
 
CategoryObserved DataExpected (Observed-Expected)^2/Expected
Head15102,5
Tail85900.2778

The expected values are assumptions

hould I have expected 50 heads and 50 tails? :)
 
100-1=99?

Dear math teacher BigBeachBanana. In fact it's very late here in Europe. Since I need to go to work very early in the morning, I will stop for now! But, I will come back again. I would be really thankful, if you could finish helping me, resolving my question. I wish you a good day, where ever you live on this planet :)
 
Apppreciate_your_help said:
100-1=99?
Click to expand...
Not quite.
For the Pearson's Goodness of Fit test, degree of freedom = k-1, where k is the number of categories. In your example, there are 2 ( head and tail). Thus, your degree of freedom is 2-1=1.
Now, look up the chi-squared value corresponding to 1 degree of freedom and a 5% significance level from either the chi-square distribution table or calculator. I'm not sure what's available to you.
 
Last edited:
Good day teacher

Pearson's Goodness of Fit test --> This is the chi square goodness of fi test right? Pearson's Goodness of Fit test is the English expression of it may? I never heared/read "Pearson".
For the Pearson's Goodness of Fit test, degree of freedom = k-1, where k is the number of categories. In your example, there are 2 ( head and tail). Thus, your degree of freedom is 2-1=1. --> OK, Understood so far.
We can use the chi-square distribution table (lucky me, it's a bit easier...)

1651610413515.png

Do I need to compare with the value of yesterday?
Could you help me out please further?
Many thanks.
 
Apppreciate_your_help said:
Good day teacher

Pearson's Goodness of Fit test --> This is the chi square goodness of fi test right? Pearson's Goodness of Fit test is the English expression of it may? I never heared/read "Pearson".
For the Pearson's Goodness of Fit test, degree of freedom = k-1, where k is the number of categories. In your example, there are 2 ( head and tail). Thus, your degree of freedom is 2-1=1. --> OK, Understood so far.
We can use the chi-square distribution table (lucky me, it's a bit easier...)

View attachment 32547
Click to expand...
There are many "chi-squared" tests for different purposes, and differ in how they define the degree of freedom. The one you're using is Pearson's. I just want to be specific.

The value is correct 3,841. Now compare that that your chi-squared statistic of 49.
If the chi-squared stat > chi-squared critical value, then we reject the null. Otherwise, we accept the null.
 
Good day

Many thanks OK. I understood, it's not that difficult. This is it for my initial question in the beginning? :) I tought there are much much more steps to go :)
 
Last edited:
Null hypothesis, is in my case --> It the coin is fair or not fair?
Alternate hyptothesis --> anything else?

My conclusion: 49 is greater than 3,841. the null hypothesis must be rejected.
 
Apppreciate_your_help said:
Null hypothesis, is in my case --> It the coin is fair or not fair?
Alternate hyptothesis --> anything else?

My conclusion: 49 is greater than 3,841. the null hypothesis must be rejected.
Click to expand...
Hypotheses are statements, not questions.
Null Hypothesis: The coin is fair
Alternate Hypothesis: The coin is not fair

Since 49>3,941. We reject the null at a 5% significance level, meaning you're 95% confident that the coin is not fair.
 
You must log in or register to reply here.
Top