Chi Square Test and Distribution

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What does the chi-square formula represent?

The sum of squared errors
The difference between observed and expected values (correct)
The product of observed and expected values
The correlation between two variables

How is the number of degrees of freedom calculated for the chi-square test statistic?

By subtracting one from the product of rows and columns (correct)
By subtracting the sample size from the total population
By subtracting the number of rows from the number of columns
By subtracting the number of categories from the sample size

According to the hypotheses mentioned, what does the null hypothesis state?

The samples come from the same population
All observations are statistically significant
There is no difference in distribution among social classes (correct)
There is a significant difference in distribution among social classes

What is the purpose of calculating the expected value for each cell in a chi-square test?

To compare observed and expected values (C) Signup and view all the answers

How does the alternative hypothesis differ from the null hypothesis in a chi-square test?

It asserts a real difference between groups (A) Signup and view all the answers

What is the formula used to calculate chi square?

Σ [ (Oi - Ei)2 / Ei ] (A) Signup and view all the answers

What do the sum of the expected numbers and the sum of the observed numbers have in common?

They are equal (C) Signup and view all the answers

What would be the calculated degrees of freedom for a table with 3 rows and 4 columns?

6 (B) Signup and view all the answers

What happens to the sum of the differences between observed and expected numbers?

It always comes to zero (C) Signup and view all the answers

How are the differences between samples A and B related?

Each difference in A matches the same figure but with the opposite sign in B (D) Signup and view all the answers

What is the reason for not rejecting the null hypothesis in the text?

Calculated χ2 value < Tabulated χ2 value (A) Signup and view all the answers

What type of variables is the chi-square statistic most appropriate for?

Categorical variables (B) Signup and view all the answers

What type of data is used in the computation of the chi-square test statistic?

Frequency data (B) Signup and view all the answers

What are the two sets of frequencies in chi-square analysis?

Observed and calculated frequencies (C) Signup and view all the answers

If a data sample is sorted into a 2x2 contingency table based on two factors with two levels each, what is the total number of cells in the table?

4 (A) Signup and view all the answers

What does the expected number of observations for each cell represent in chi-square testing?

Hypothesized values under the null hypothesis (D) Signup and view all the answers

What value is calculated in chi-square testing to determine the relationship between two categorical variables?

Chi-square test statistic (D) Signup and view all the answers

What is the main purpose of the Chi-Square goodness of fit test?

To determine if sample data align with a hypothesized distribution (C) Signup and view all the answers

How is the Chi-Square test statistic denoted?

Χ² (D) Signup and view all the answers

What does the null hypothesis (Ho) state in a Chi-Square goodness of fit test?

The data align with a specified distribution (D) Signup and view all the answers

What is the significance level used for in a Chi-Square goodness of fit test?

To establish the cutoff point for acceptance/rejection of the null hypothesis (D) Signup and view all the answers

What formula is used to calculate the test statistic chi-square random variable (Χ2)?

Χ2 = Σ [ (Oi - Ei)2 / Ei ] (A) Signup and view all the answers

When is the Chi-Square goodness of fit test used?

To assess whether data align with a hypothesized distribution (A) Signup and view all the answers

When comparing the P-value to the significance level, what action is taken if the P-value is less than the significance level?

Reject the null hypothesis (B) Signup and view all the answers

What does the alternative hypothesis (Ha) state in a Chi-Square goodness of fit test?

The data do not align with a specified distribution (B) Signup and view all the answers

In which situation is the chi-square goodness of fit test appropriate?

When the expected value of the number of sample observations in each level is at least 5 (B) Signup and view all the answers

How is the expected number of observations (E) calculated for each level?

Ei = npi (D) Signup and view all the answers

What does the chi-square test statistic represent?

A measure of the discrepancy between observed and expected values (B) Signup and view all the answers

For what purpose can the chi-square distribution be used?

Testing hypotheses when the data are in the form of frequencies (B) Signup and view all the answers