Pearson's chi square test (goodness of fit) | Probability and Statistics | Khan Academy | Summary and Q&A

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November 10, 2010
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Pearson's chi square test (goodness of fit) | Probability and Statistics | Khan Academy

TL;DR

A restaurant owner provides a distribution of customers over the week, but a hypothesis test reveals it is not a good fit for observed data.

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Q: What does the restaurant owner provide as the distribution of customers over the week?

The owner gives a distribution of percentages, stating that 10% of customers come in on Monday, 10% on Tuesday, 15% on Wednesday, and so on.

Q: How does the observer test the owner's distribution?

The observer collects data on the number of customers coming in each day of the week and compares it to the expected values based on the owner's distribution.

Q: What is the null hypothesis in this hypothesis test?

The null hypothesis is that the owner's distribution is correct, accurately representing the distribution of customers.

Q: What is the alternative hypothesis?

The alternative hypothesis is that the owner's distribution is not correct and should be rejected.

Summary & Key Takeaways

• The owner provides a distribution of customer percentages over the week, claiming it is accurate.

• Observed data on the number of customers is collected to test the owner's distribution.

• A hypothesis test using the chi-square statistic is conducted to determine if the owner's distribution is valid.

• The calculated chi-square statistic is compared to the critical chi-square value, and it is found that the owner's distribution is not a good fit for the observed data.