Chi-Square Test Concepts

The video tutorial explains how to solve a Chi-Square equation, detailing its components such as observed and expected frequencies, and the sum of differences squared over expected values. It covers degrees of freedom, critical values, and the null hypothesis. An example using a coin flip demonstrates the application of the Chi-Square test, including calculations and hypothesis testing. The tutorial emphasizes the importance of having two outcomes, using a 0.05 critical value, and having 30 or more data points for the Chi-Square test.

What does the 'O' represent in the Chi-Square equation?

• Sum of frequencies

• Degree of freedom

• Expected frequency

• Observed frequency

Which of the following is a key component of the Chi-Square equation?

• Sum of squared differences divided by expected frequency

• Sum of observed frequencies

• Product of observed and expected frequencies

• Difference between observed and expected frequencies

What is the critical value for a degree of freedom of one at a 0.05 significance level?

• 5.99

• 3.84

• 2.71

• 7.81

What is the null hypothesis in a Chi-Square test?

• There is a significant difference between observed and expected frequencies.

• There is no significant difference between specified populations.

• The observed frequency is always greater than the expected frequency.

• The Chi-Square statistic is always less than the critical value.

How do you determine the degree of freedom in a Chi-Square test?

• By multiplying the number of categories by two

• By dividing the number of categories by two

• By adding one to the number of categories

• By subtracting one from the number of categories

Which of the following is NOT a condition for applying the Chi-Square test?

• Having two outcomes

• Using a critical value of 0.05

• Using observed and expected frequencies

• Having less than 30 data points

In the coin flip example, what were the expected frequencies for heads and tails?

• 3 heads, 7 tails

• 5 heads, 5 tails

• 7 heads, 3 tails

• 6 heads, 4 tails

What is the Chi-Square statistic calculated from the coin flip example?

• 0.95

• 2.5

• 3.84

• 1.6

What should you do if the Chi-Square statistic is less than the critical value?

• Recalculate the expected frequencies

• Increase the sample size

• Accept the null hypothesis

• Reject the null hypothesis

What is the purpose of using a critical value in a Chi-Square test?

• To decide whether to accept or reject the null hypothesis

• To determine the expected frequency

• To calculate the observed frequency

• To find the degree of freedom