Chi-square goodness-of-fit example | AP Statistics | Khan Academy

TL;DR

This analysis examines the results of a chi-squared goodness-of-fit test for a sample of 24 rock-paper-scissors games to determine if the distribution of outcomes disagrees with an even distribution.

Transcript

• [Instructor] In the game rock-paper-scissors, Kenny expects to win, tie, and lose with equal frequency. Kenny plays rock-paper-scissors often, but he suspect his own games were not following that pattern. So he took a random sample of 24 games and recorded their outcomes. Here are his results. So out of the 24 games, he won four, lost 13, and tie... Read More

Key Insights

• 🤏 Kenny's chi-squared test statistic is 5.25, indicating a deviation from an equal distribution of outcomes.
• 🏆 The P-value for the test falls between 0.05 and 0.10, suggesting that there is not enough evidence to reject the null hypothesis at a significance level of 5%.
• 🤏 The analysis demonstrates the process of conducting a chi-squared goodness-of-fit test and highlights the importance of meeting the necessary conditions.
• 🪡 This type of analysis can be applied to other scenarios where the distribution of outcomes in different categories needs to be assessed.

Questions & Answers

Q: What is the null hypothesis in Kenny's chi-squared goodness-of-fit test?

The null hypothesis is that all outcomes in the rock-paper-scissors games have equal probability.

Q: How many categories are considered in this test?

There are three categories: wins, losses, and ties.

Q: What are the conditions that need to be met for a chi-squared goodness-of-fit test?

The conditions are: 1) random sample, 2) large counts (expected number in each category is at least 5), and 3) independence (sample size is no more than 10% of the population).

Q: How is the chi-squared test statistic calculated in this analysis?

The chi-squared test statistic is calculated for each category by taking the difference between the observed and expected values, squaring it, and dividing by the expected value.

Summary & Key Takeaways

• Kenny took a random sample of 24 games of rock-paper-scissors and recorded the outcomes: 4 wins, 13 losses, and 7 ties.

• He wants to use these results to determine if the distribution of outcomes deviates from an equal probability for each category.

• The analysis calculates the chi-squared test statistic and the corresponding P-value to make inferences about the null hypothesis.