Confidence Intervals for the Difference Between 2 Proportions

A 95% confidence interval for p, the proportion of all shoppers at a large grocery store who purchase cookies, was found to be (0.236, 0.282).

The point estimate and margin or error for this interval are:

• .236 and .282

• .236 and .046

• unknown and .023

• .259 and .046

• .259 and .023

Which assumptions do we check when comparing 2 proportions? Select ALL that apply.

• Independent groups

• Independence

• Nearly Normal

• 10% Condition

• Randomization

If the difference of two proportions (p₁-p₂) shows a confidence interval of (-0.13, 0.32), what would have been our decision from the 2-prop z-test?

• Fail to reject Ha since 0 is in the interval

• Fail to reject Ho since 0 is in the interval

• Reject Ho since 0 is in the interval

• Reject Ha since 0 is in the interval

A survey asked people “On what percent of days do you get more than 30 minutes of vigorous exercise?” Using their responses we want to estimate the difference in exercise frequency between men and women. We should use a

• 2-prop z-interval

• 1-sample t-interval

• 2-sample t-interval

• Paired t-interval

If a test statistic, z or t, is beyond the bounds of -2 or +2, will the p-value be a small or large number?

• Small, because more than 2 standard deviations from the mean does not happen often

• Large, because more than 2 standard deviations from the mean does not happen often

• Small, because more than 2 standard deviations from the mean does happen often

• Large, because more than 2 standard deviations from the mean does happen often

Suppose the P-value for a hypothesis test is 0.0304. Using a = 0.05, what is the appropriate conclusion?

• reject the null, the probability of getting results like this given the null is true is 3.04% which is less than 5%.

• reject the alternative, the probability of getting results like this given the alternative is true is 3.04% which is less than 5%.

• Accept the null, a 3.04% chance is really not that bad.

• Fail to reject the alternative but still don't accept the null.

Which of the following is NOT a null hypothesis?

• Cats are no smarter than dogs

• Americans enjoy hot dogs twice as much as hamburgers

• There is no difference in test scores of students who drink coffee and those that don't

• Students spend as much time on TikTok as on Instagram

• NO, because any proportion must always be positive.

A student project tried to determine if males and females have the same brand preference between Nike and Adidas. The students took separate random samples of 40 females and 30 males from a large high school and asked them if they prefer Nike or Adidas. Of the females, 55% preferred Nike, compared to 80% of the males preferred Nike. Are all conditions satisfied in order to calculate a confidence interval for the difference of the 2 proportions?

• Yes, all conditions are satisfied

• No, the success/failure condition is not satisfied

• No, the random sample condition is not satisfied.

• No, the 10% condition is not satisfied.

A Pew Research Center poll asked independent random samples of working women and men how much they value job security. Of the 806 women, 709 said job security was very or extremely important, compared with 802 of the 944 men surveyed. Calculate a 95% confidence interval for the difference in the proportions.

• (-0.002, 0.062)

• (0.002, 0.062)

• (0.003, 0.056)

• (0.216, 0.272)