Question about chi-square goodness of fit test

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Apppreciate_your_help

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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.

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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.
 
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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 :)
 
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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.
 
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