Chi–Squares
Which of the following measures is not typically used when setting up a chi-square test?
Mean
Degrees of freedom
Observed frequencies
Expected frequencies
What is a consequence of failing to check the condition that no more than 20% of cells in a contingency table should have expected counts less than five before conducting a chi-square test for homogeneity?
The validity of test results is called into question because the small counts could lead to an increase in Type I error.
More data needs to be gathered beyond the number of observed events, as long as a ratio is maintained.
The results are more prone to be statistically significant since many expected values are below five.
The overall interpretation of the result doesn't change, but additional cells with low counts need to be added.
What is the purpose of a Chi-Square test for independence?
To assess the linear relationship between two quantitative variables.
To determine if there is an association between two categorical variables.
To compare the proportion of successes in one group to that in another group.
To calculate the mean difference between two groups.
Which type of data should be used when performing a Chi-Square test?
Categorical data from one or more samples organized into frequencies and counts.
Continuous numerical data represented by mean and standard deviation figures.
Quantitative data from multiple populations summarized into medians and ranges.
Individual numerical values from repeated measures within an experiment design.
What type of error occurs if we fail to reject the null hypothesis in a chi-square test when there actually is an association between categories?
Sampling error (fluctuations due to unforeseen sampling variability).
Power error (misestimating strength relationship).
Type I error (rejecting true null hypothesis).
Type II error (failing to detect an actual effect).
To determine if a die is fair, a student rolls it 60 times and records the frequency of each result; which of the following chi-square test results suggests that the die may be unfair?
A chi-square test statistic much larger than the critical value at a conventional significance level.
A chi-square test statistic roughly equal to the degrees of freedom.
A small p-value that suggests there is no significant difference from what was expected.
A large p-value indicating strong adherence to the expected frequencies.
In a chi-squared test for independence, which is true about the expected counts?
Expected counts represent the number of observations in each category that would be expected if the null hypothesis is true
Expected counts are calculated based on observed counts and sample size
Expected counts must be at least 10 for the test to be valid
Expected counts should be higher than the observed counts

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In what form must the observed counts be presented before performing a Chi-Square test?
Histogram
Scatterplot
Box plot
Contingency table
When researchers divide the population into strata based on specific characteristics before drawing a simple random sample from each stratum, what kind of sampling method are they using?
Stratified Random Sampling
Cluster Sampling
Convenience Sampling
Multistage Sampling
What are the appropriate hypotheses for a chi-square test for homogeneity?
H0: There is no difference in distributions of a categorical variable across populations or treatments. Ha: There is a difference in distributions of a categorical variable across populations or treatments.
H0: There is no association between two categorical variables in a given population or the two categorical variables are independent. Ha: Two categorical variables in a population are associated or dependent
H0: There is no difference in distributions of a categorical variable across samples. Ha: There is a difference in distributions of a categorical variable across samples
H0: There is no association between two categorical variables in a given sample or the two categorical variables are independent. Ha: Two categorical variables in a sample are associated or dependent