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Chi Square Statistical Analysis
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Chi Square Statistical Analysis
Chi Square Statistical Analysis
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1
Question
What type of data are chi-square tests primarily used to analyze?
Answer
Categorical data, such as survey responses, age groups, or product preferences.
2
Question
What is the basic idea behind chi-square tests?
Answer
They compare observed counts to expected counts; large differences suggest something interesting is happening.
3
Question
What are the two main types of chi-square tests discussed?
Answer
Chi-square goodness-of-fit test and chi-square test of independence.
4
Question
What does the chi-square goodness-of-fit test assess for a single categorical variable?
Answer
Whether the observed distribution matches a claimed or expected distribution.
5
Question
What does the chi-square test of independence determine about two categorical variables?
Answer
Whether the two variables are related or independent.
6
Question
How is the chi-square test statistic calculated in both types of tests?
Answer
Sum over categories of (observed count minus expected count squared, divided by expected count).
7
Question
What does a larger chi-square value indicate about the data?
Answer
A bigger mismatch between observed and expected counts.
8
Question
Why are chi-square tests used in market-share studies?
Answer
To check if observed product preferences match expected proportions from claimed market shares.
9
Question
How are expected counts calculated in the goodness-of-fit test?
Answer
Expected count for each category equals total sample size times the claimed probability for that category.
10
Question
What is the null hypothesis for the chi-square goodness-of-fit test?
Answer
The population proportions match the claimed values.
11
Question
What is a multinomial experiment in the context of goodness-of-fit?
Answer
Fixed number of independent trials with several possible categories and constant category probabilities.
12
Question
What condition must expected counts usually meet for chi-square goodness-of-fit?
Answer
Expected counts should be at least 5 in each category; combine categories if necessary.
13
Question
How are degrees of freedom calculated for goodness-of-fit test?
Answer
Number of categories minus 1.
14
Question
Why might categories need to be combined in goodness-of-fit tests?
Answer
To ensure expected counts are at least 5 in each category for the test's validity.
15
Question
In the restaurant survey example, what was the sample size and p-value?
Answer
250 customers surveyed, p-value of 0.089.
16
Question
What conclusion was drawn from the restaurant survey chi-square test?
Answer
Do not reject the null hypothesis because p=0.089 > 0.05; observed close to expected.
17
Question
How are expected counts computed in the test of independence?
Answer
Row total times column total divided by the grand total for each cell.
18
Question
What is the null hypothesis for the chi-square test of independence?
Answer
The two categorical variables are independent.
19
Question
What is the alternative hypothesis for the test of independence?
Answer
The two categorical variables are related.
20
Question
How are degrees of freedom calculated for test of independence?
Answer
(number of rows minus 1) times (number of columns minus 1).
21
Question
Give an example of degrees of freedom for a contingency table.
Answer
A three-by-two table has 2 degrees of freedom.
22
Question
In what fields is the test of independence commonly used?
Answer
Health, marketing, and social science to check category connections.
23
Question
What was the chi-square statistic, df, and p-value in the fitness center example?
Answer
Chi-square = 14.945, 2 degrees of freedom, p-value = 0.001.
24
Question
What conclusion was reached in the fitness center chi-square test?
Answer
Reject independence because p=0.001 < 0.05; age group and enrollment are related.
25
Question
What were the observed enrollments by age group in the fitness study?
Answer
24 under age 30, 72 for ages 30 to 50, 44 over age 50.
26
Question
What is the sample size in the fitness center open-house study?
Answer
400 attendees grouped by age and enrollment status.
27
Question
How does the chi-square goodness-of-fit test differ from the test of independence?
Answer
Goodness-of-fit tests one variable against a claimed distribution; independence tests association between two variables using a contingency table.
28
Question
Why is the chi-square statistic adjusted by dividing by expected count?
Answer
To standardize the squared deviations, accounting for category size; larger categories tolerate bigger absolute gaps.
29
Question
If observed counts are close to expected, what happens to the chi-square p-value?
Answer
The p-value is large, supporting the null hypothesis (no rejection).
30
Question
If the chi-square p-value is below the significance level, what do we conclude for independence test?
Answer
The variables are associated; reject null of independence.