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

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.

Key Insights

• 🤏 The chi-square statistic is used in hypothesis testing to compare observed data to expected values.
• 🍹 The degrees of freedom in this test are determined by the number of sums of observed and expected values.
• 🤏 The critical chi-square value is determined by the significance level and degrees of freedom.
• 🤏 If the calculated chi-square statistic is more extreme than the critical value, the null hypothesis is rejected.
• 🥺 In this case, the calculated chi-square statistic is found to be more extreme than the critical value, leading to the rejection of the owner's distribution.
• ❓ This analysis demonstrates the importance of hypothesis testing in evaluating the accuracy of a given distribution.
• 🛄 The results suggest that the owner's claim about the distribution of customers is not supported by the observed data.
• 🎚️ The significance level chosen determines the threshold for rejecting the null hypothesis. In this case, a 5% significance level is used.

Transcript

I'm thinking about buying a restaurant, so I go and ask the current owner, what is the distribution of the number of customers you get each day? And he says, oh, I've already figure that out. And he gives me this distribution over here, which essentially says 10% of his customers come in on Monday, 10% on Tuesday, 15% on Wednesday, so forth, and so... Read More

Questions & Answers

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.