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Questions and Answers
What is the conclusion if the P-value is between 0.0025 and 0.005 at a significance level of 5%?
What is the conclusion if the P-value is between 0.0025 and 0.005 at a significance level of 5%?
In the context of the chi-square goodness-of-fit test, what does a P-value greater than the significance level imply?
In the context of the chi-square goodness-of-fit test, what does a P-value greater than the significance level imply?
What is the sample outcome in the example of the coin flip test?
What is the sample outcome in the example of the coin flip test?
Using the two-tailed test for a proportion based on normal distribution, what is the P-value calculated in the coin flip scenario?
Using the two-tailed test for a proportion based on normal distribution, what is the P-value calculated in the coin flip scenario?
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At what significance level was the coin spinning test conducted?
At what significance level was the coin spinning test conducted?
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What is the purpose of the Chi-square test for goodness of fit?
What is the purpose of the Chi-square test for goodness of fit?
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What is the necessary condition for rejecting the null hypothesis in hypothesis testing?
What is the necessary condition for rejecting the null hypothesis in hypothesis testing?
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How many steps are involved in carrying out a significance test using the Chi-square method?
How many steps are involved in carrying out a significance test using the Chi-square method?
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What conclusion can be drawn if the evidence supports that local births are not equally likely on all days of the week?
What conclusion can be drawn if the evidence supports that local births are not equally likely on all days of the week?
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In the context of the Chi-square test for goodness of fit, what does 'k' represent?
In the context of the Chi-square test for goodness of fit, what does 'k' represent?
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What type of test is equivalent to the chi-square test for two categories?
What type of test is equivalent to the chi-square test for two categories?
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If a sample shows a P-value of $0.0014$, what can be concluded regarding the hypothesis test at a significance level of 0.05?
If a sample shows a P-value of $0.0014$, what can be concluded regarding the hypothesis test at a significance level of 0.05?
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What value indicates the degrees of freedom in the Chi-square goodness of fit test if k equals 7?
What value indicates the degrees of freedom in the Chi-square goodness of fit test if k equals 7?
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What conclusion can be made if the Chi-square statistic value is high?
What conclusion can be made if the Chi-square statistic value is high?
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In the birth example provided, what evidence was gathered regarding births across the week?
In the birth example provided, what evidence was gathered regarding births across the week?
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What is the first step in carrying out a significance test?
What is the first step in carrying out a significance test?
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If there are 700 births recorded, what is the expected count for each day if the distribution is even?
If there are 700 births recorded, what is the expected count for each day if the distribution is even?
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What is the role of the P-value in the Chi-square test for goodness of fit?
What is the role of the P-value in the Chi-square test for goodness of fit?
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What is the highest frequency of births recorded on a single day in the provided birth data?
What is the highest frequency of births recorded on a single day in the provided birth data?
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Study Notes
Chi-Square Test for Goodness of Fit
- Previously we tested if there is a relationship between two categorical variables - chi-square test for independence
- Now, we will test if a categorical variable has a specific distribution - chi-square test for goodness of fit
Steps of the Goodness of Fit Test
- State the null and alternative hypotheses
- Check conditions and calculate the test statistic
- Find the p-value using the appropriate distribution
- Make a decision and state a conclusion
Births Example
- The example looks at birth distribution across days of the week
- It is hypothesized that there are fewer births on the weekend
- A sample of 700 births was collected to test the hypothesis
Chi-Square Statistic
- The chi-square statistic is calculated based on the observed and expected frequencies
- The degrees of freedom are (k - 1) where k is the number of categories
Decision & Conclusion
- The decision is based on comparing the p-value and alpha (significance level)
- If the p-value is less than or equal to alpha, reject the null hypothesis
- If the p-value is greater than alpha, do not reject the null hypothesis
- The conclusion is stated in the context of the specific setting of the test
- For the birth example, the p-value was less than 0.05, so the null hypothesis was rejected - births were not equally likely on all days of the week
Comparison with a Two-Tailed z-Test for Two Categories
- The two-tailed z-test for proportions and the chi-square test for two categories are equivalent
- The coin spinning example tests if a coin has a 50-50 distribution of heads and tails
- Both methods, the z-test and the chi-square test, come to the same conclusion that the sample contradicts a 50-50 distribution
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Description
This quiz covers the Chi-Square Test for Goodness of Fit, focusing on how to state hypotheses, compute test statistics, and interpret p-values. An example involving birth distributions across the days of the week is provided for practical understanding.
