29 Questions
What does the chi-square formula represent?
The difference between observed and expected values
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
According to the hypotheses mentioned, what does the null hypothesis state?
There is no 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
How does the alternative hypothesis differ from the null hypothesis in a chi-square test?
It asserts a real difference between groups
What is the formula used to calculate chi square?
Σ [ (Oi - Ei)2 / Ei ]
What do the sum of the expected numbers and the sum of the observed numbers have in common?
They are equal
What would be the calculated degrees of freedom for a table with 3 rows and 4 columns?
6
What happens to the sum of the differences between observed and expected numbers?
It always comes to zero
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
What is the reason for not rejecting the null hypothesis in the text?
Calculated χ2 value < Tabulated χ2 value
What type of variables is the chi-square statistic most appropriate for?
Categorical variables
What type of data is used in the computation of the chi-square test statistic?
Frequency data
What are the two sets of frequencies in chi-square analysis?
Observed and calculated frequencies
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
What does the expected number of observations for each cell represent in chi-square testing?
Hypothesized values under the null hypothesis
What value is calculated in chi-square testing to determine the relationship between two categorical variables?
Chi-square test statistic
What is the main purpose of the Chi-Square goodness of fit test?
To determine if sample data align with a hypothesized distribution
How is the Chi-Square test statistic denoted?
Χ²
What does the null hypothesis (Ho) state in a Chi-Square goodness of fit test?
The data align with a specified distribution
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
What formula is used to calculate the test statistic chi-square random variable (Χ2)?
Χ2 = Σ [ (Oi - Ei)2 / Ei ]
When is the Chi-Square goodness of fit test used?
To assess whether data align with a hypothesized distribution
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
What does the alternative hypothesis (Ha) state in a Chi-Square goodness of fit test?
The data do not align with a specified distribution
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
How is the expected number of observations (E) calculated for each level?
Ei = npi
What does the chi-square test statistic represent?
A measure of the discrepancy between observed and expected values
For what purpose can the chi-square distribution be used?
Testing hypotheses when the data are in the form of frequencies
Learn about the Chi square goodness of fit and test for independence of two variables. Understand the concept of the chi-square distribution and its application in analyzing count or frequency data.
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