Chi–Squares
In conducting a chi-square test for goodness of fit using a two-way table, why is considering the variability around the expected counts crucial?
To ensure each variable has at least one category with zero frequency.
To identify which variable has greater predictive power over the other.
To evaluate whether the differences between observed and expected counts are statistically significant.
To calculate the total sum of squares for all categories combined.
A survey was conducted to examine the preference for different smartphone brands among three age groups: teenagers (13-19 years), young adults (20-30 years), and adults (31-50 years). 50 teenagers preferred Apple, 30 teenagers preferred Samsung, 60 young adults preferred Apple, 40 young adults preferred Samsung, 40 adu...
50
44
47
45
If a researcher uses expected counts to assess homogeneity across groups in a two-way table but observes some expected counts below 5, how might this affect their conclusions?
It ensures more accurate results due to smaller count sizes.
It does not affect conclusions as chi-square is robust to such deviations.
It may inflate Type I error rates, falsely suggesting non-homogeneity.
It reduces Type II error rates by increasing sensitivity.
When assessing the independence of two categorical variables in a large sample size contingency table, what is the implication if most of the standardized residuals are greater than 2?
The variables are probably independent.
There is likely an association between the variables.
The larger sample size invalidates the chi-square test.
Standardized residuals do not provide information on variable association.
When should we use a chi-squared test for homogeneity?
When examining the relationship between two categorical variables in a single population.
When two different populations have different amounts for a given categorical variable.
When trying to determine if there is a statistically significant difference in proportion for two variables
When comparing the distribution of a categorical variable between two or more independent groups or populations.
What assumption about variability must hold true when calculating expected frequencies in a two-way table for them to be valid?
No more than 20% of cells have an expected count less than 10.
Each cell's count is large enough, typically at least 5.
Observations must be normally distributed within each cell.
All cells have identical observed frequencies.
Which measurement would NOT be used to examine variability among expected counts within cells?
Correlation coefficient measures variance among expected counts in categorical data.
Standard deviation describes the amount of spread around the mean of observed counts.
Variance effectively summarizes the overall amount of spread in counted data.
Interquartile range (Q) compares the middle portion of frequencies between categories.

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When researchers divide the population into groups based on characteristics and then randomly select from each group, they are using which method?
Cluster sampling
Simple random sampling
Stratified random sampling
Convenience sampling
In a two-way table, what value is used to calculate the expected count for a cell?
The product of the corresponding row and column totals divided by the grand total.
The sum of the corresponding row and column totals divided by the grand total.
The square root of the product of corresponding row and column totals.
The difference between the corresponding row and column totals divided by two.
Researchers investigated the relationship between gender (male and female) and hair color (blonde and brunette). There are 30 male blondes, 45 male brunettes, 20 female blondes, and 35 female brunettes. What is the table total?
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130
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75