To do inferential procedures comparing two proportions, we need another variance formula (our ruler). This formula is based on what principle?
A) The variance of the difference of two statistics is the difference of the variances of each statistic.
B) The variance of the difference of two statistics is the smaller of the variances of each statistic.
C) The variance of the difference of two statistics is the sum of the variances of each statistic.
D) The variance of the difference of two statistics is the larger of the variances of each statistic.
To determine the correct answer, we need to understand the principle underlying the variance formula for comparing two proportions.
When comparing two proportions, we want to estimate the difference between them and assess whether this difference is statistically significant. To do this, we need to consider the variability in the sample proportions.
The central principle in this context is known as the "variance of the difference of two statistics." This principle tells us how to calculate the variance of the difference between two proportions by considering the variances of each proportion individually.
Now, let's evaluate each answer choice to determine which one aligns with this principle:
A) The variance of the difference of two statistics is the difference of the variances of each statistic.
This answer suggests that the variance of the difference between two proportions is calculated by subtracting the variances of each proportion. However, this is not correct, as it oversimplifies the relationship between the variances.
B) The variance of the difference of two statistics is the smaller of the variances of each statistic.
This answer implies that the variance of the difference between two proportions is the smaller of the two variances of the individual proportions. However, this is not accurate, as it does not accurately capture the relationship between the variances.
C) The variance of the difference of two statistics is the sum of the variances of each statistic.
This answer suggests that the variance of the difference between two proportions is calculated by summing the variances of each proportion. This is the correct principle. When comparing two proportions, we calculate the variance of the difference by adding the variances of each proportion.
D) The variance of the difference of two statistics is the larger of the variances of each statistic.
This answer implies that the variance of the difference between two proportions is the larger of the two variances of the individual proportions. However, this is not accurate, as it does not reflect the correct relationship between the variances.
Based on the explanations above, the correct answer is C) The variance of the difference of two statistics is the sum of the variances of each statistic.