AP Statistics Flashcards: Setting Up a Chi-Square Goodness of Fit Test
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Review key ideas with interactive flashcards. This set includes 19 cards to help you master important concepts.
Chi-Square Statistic
A measure of the distance between observed counts and expected counts, relative to the expected counts.
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Chi-Square Statistic
A measure of the distance between observed counts and expected counts, relative to the expected counts.
Large Counts Condition (Chi-Square)
This condition is met for a chi-square goodness-of-fit test when all expected counts are greater than or equal to 5.
How is the alternative hypothesis (Hₐ) stated for a goodness-of-fit test?
The alternative hypothesis (Hₐ) states that at least one of the category proportions is different from the value specified in the null hypothesis.
What is the formula for calculating expected counts in a goodness-of-fit test?
The expected count for a category is calculated as (sample size) × (null proportion).
To test if the distribution of student grade levels (Freshman, Sophomore, Junior, Senior) at a rally matches the overall school enrollment proportions, what test should be used?
The appropriate method is a chi-square test for goodness of fit, as it compares the distribution of one categorical variable to a hypothesized distribution.
Under what circumstances is a chi-square goodness-of-fit test the appropriate testing method?
This test is appropriate when you have count data for one categorical variable and want to test a claim about its distribution of proportions.
Describe the key characteristics of chi-square distributions.
Chi-square distributions are always positive and are skewed to the right.
A company claims its bag of candies contains 30% red. In a random sample of 200 candies, what is the expected count for red candies?
The expected count is the sample size times the null proportion, so 200 × 0.30 = 60 red candies.
What is the relationship between observed counts, expected counts, and the chi-square statistic?
The chi-square statistic quantifies the total difference between the observed counts and the expected counts across all categories.
In a chi-square test, the expected counts for three categories are 10, 12, and 4. Does this meet the large counts condition?
No, the large counts condition is not met because one of the expected counts (4) is less than 5.
What is the purpose of a Chi-Square Goodness of Fit Test?
It is used to test how well the distribution of proportions for a single categorical variable matches a hypothesized distribution.
In a chi-square test, the expected counts for four categories are 15, 8, 5, and 22. Does this meet the large counts condition?
Yes, the large counts condition is met because all expected counts (15, 8, 5, 22) are greater than or equal to 5.
What does a large chi-square statistic value indicate?
A large chi-square value indicates a significant difference between the observed and expected counts, providing evidence against the null hypothesis.
What are the two primary conditions to verify for a chi-square goodness-of-fit test?
The two main conditions to check are the independence of observations and the large counts condition.
How is the null hypothesis (H₀) stated for a goodness-of-fit test?
The null hypothesis (H₀) specifies the proportion of observations that will fall into each possible category.
How do degrees of freedom affect a chi-square distribution's shape?
As the degrees of freedom increase, the skewness of the chi-square distribution lessens and it becomes more symmetric.
What kind of data is analyzed using a chi-square test for goodness of fit?
This test is used for analyzing the distribution of proportions in categorical data from a single variable.
Expected Counts
The counts that would be consistent with the null hypothesis, calculated as the sample size multiplied by the hypothesized probability for each category.
What is the primary difference in the statements of H₀ and Hₐ for a goodness-of-fit test?
H₀ specifies the exact value for every category proportion, while Hₐ simply states that the distribution is not what is specified in H₀.