10.1 Understanding Confidence Intervals for Two Proportions

What is the primary difference between confidence intervals for one proportion and two proportions?

• There is no difference; the same equations are used.

• One proportion uses a Z-score while two proportions use a T-score.

• Two proportions involve comparing two different populations.

• Two proportions require a larger sample size.

What condition must be met for the sampling distribution of p1 - p2 to be approximately normal?

• The samples must come from normally distributed populations.

• The populations must be independent.

• n*p and n*q for both samples must all be at least 10.

• The sample sizes must be equal.

Why is randomization important in conducting a two-proportion Z-test?

• It allows us to generalize the results to the entire population.

• It guarantees the sampling distribution is normal.

• It reduces the standard error of the mean.

• It ensures the sample size is large enough.

What does the two-proportion Z interval estimate?

• The mean difference between two populations.

• The difference in proportions between two populations.

• The total proportion of success in both populations.

• The standard deviation of the difference between two samples.

How do you determine the z-score for a 95% confidence interval?

• By subtracting the confidence level from 1.

• By dividing the confidence level by 2.

• By using a standard normal distribution table.

• By calculating the mean of the two sample proportions.

What is the purpose of adding and subtracting the margin of error in a confidence interval?

• To find the mean of the sample data.

• To calculate the standard deviation.

• To establish the range within which the true population parameter lies.

• To determine the sample size needed.

In the context of the example provided, what does a positive interval indicate about adult and teen Facebook usage?

• Teens use Facebook more than adults.

• The data is inconclusive.

• Adults and teens use Facebook equally.

• Adults use Facebook more than teens.

How does reversing the order of subtraction (teens minus adults) affect the interpretation of the confidence interval?

• It indicates a higher proportion of teens using Facebook compared to adults.

• It reverses the interpretation, showing how much lower the teen proportion is compared to adults.

• It does not change the interpretation of the results.

• It shows the proportion of adults using Facebook is lower.