Comparing two Proportions by David Spade, PhD

About the Lecture

The lecture Comparing two Proportions by David Spade, PhD is from the course Statistics Part 2. It contains the following chapters:

Comparing Two Proportions
Assumptions and Conditions
Hypothesis Testing
Snoring Example
Example: Mechanics and Conclusion

Included Quiz Questions

What is true regarding the variability in the difference between sample proportions?

We usually do not know the population proportions, so finding the standard deviation is not possible and we have to estimate it using the standard error.
The standard deviation of the difference in the proportions is simply the difference between the standard deviations of the two proportions.
The standard deviation of the difference in the proportions is simply the sum of the standard deviations of the proportions.
The standard error of the difference in the proportions is the sum of the standard errors of the individual proportions.
The standard error is a measure that accounts for the entire population.

What is not one of the conditions for the two-proportion procedure?

The groups we are comparing are linearly related to each other.
Each group’s observations are independent or are randomly selected.
We need to observe at least 10 successes and 10 failures in each group.
The sample sizes should not be larger than 10% of the respective population sizes.
The sample sizes cannot be larger than 25% of the population size.

What is an appropriate interpretation of the 95% confidence interval for p1 - p2 based on the difference ˆp1 -ˆp2 and given by (a ,b)?

We are 95% confident that p1 - p2 is between a and b.
We know that the difference between the population proportions falls between a and b.
The value ˆ p 1 - ˆ p 2 is a more plausible value for the difference in the population proportions than are values near a or near b.
We are 95% certain that p 1 - p 2 is between a and b.
We know that a and b are representative of 95% of the population.

What is true of the hypothesis test for a difference in two population proportions?

We do not know either population proportion under the null hypothesis, so we construct a pooled estimate based on the two sample proportions.
The procedures described in this chapter can be used if the groups are not independent.
The procedures described in this chapter can be used if the individuals in the study are not randomly sampled.
We do not know either sample proportion under the null hypothesis, so we have to construct a pooled estimate based on the population proportions.
A best guess at the difference between two population proportions is as accurate as a pooled estimate based on the sample proportions.

What is the correct interpretation when we reject the null hypothesis?

Based on the data we observed, the null hypothesis is not a reasonable explanation of the behavior between the two populations
We are certain that there is a difference between the two population proportions.
We are certain that there is no difference between the two population proportions.
We have evidence that there is no difference between the two population proportions.
The null hypothesis is false.

Suppose proportion 1 = 0.54, sample size 1 = 450, proportion 2 = 0.37, and sample size 2 = 280. What is the confidence interval for the difference in proportions?