Inference for Categorical Data: Proportions

One- and two-sample z-procedures for sample proportions are used with ________ data.

• discrete

• continuous

• categorical

• quantitative

• subspace

Are more than 10% of households now without landline phone service?  2000 American households were surveyed. Which procedure is appropriate?

• t interval for means

• t test for means

• z interval for proportions

• z test for proportions

Are people more likely to die of heart disease or cancer?  20,000 death certificates were examined. Which procedure is appropriate?

• t interval for difference of means

• t test for difference of means

• z interval for difference of proportions

• z test for difference of proportions

Mood can be measured as sad, flat, ambivalent or happy. What type of data is this?

• Numerical

• Categorical

Two large containers, X and Y, contain many colored beads. From a random sample of beads taken from container X, the proportion of blue beads in the sample was recorded as phat_x=0.35. From a random sample of beads taken from container Y, the proportion of blue beads in the sample was recorded as phat_y=0.39. Assuming all conditions for inference are met, which of the following procedures is the most appropriate for estimating the difference between the proportions of all blue beads in the containers?

• A two-sample z-interval for a difference in population proportions

• A two-sample z-interval for a difference in sample proportions

• A one-sample z-interval for a population proportion

• A one-sample z-interval for a sample proportion

• A one-sample z-interval for a difference in population proportions

Answer explanation

A two-sample z-interval is appropriate for estimating the difference between two population proportions.

Two large containers, X and Y, contain many colored beads. From a random sample of beads taken from container X, the proportion of blue beads in the sample was recorded as phat_x=0.35. From a random sample of beads taken from container Y, the proportion of blue beads in the sample was recorded as phat_y=0.39. Assuming all conditions for inference are met, which of the following procedures is the most appropriate for estimating the difference between the proportions of all blue beads in the containers?

• A two-sample z-interval for a difference in population proportions

• A two-sample z-interval for a difference in sample proportions

• A one-sample z-interval for a population proportion

• A one-sample z-interval for a sample proportion

• A one-sample z-interval for a difference in population proportions

Answer explanation

A two-sample z-interval is appropriate for estimating the difference between two population proportions.

An inspector monitors large truckloads of potatoes to determine the proportion p of potatoes with major defects before the potatoes are used to make potato chips. She intends to compute a 95% confidence interval for p. To do so, she selects a simple random sample of 50 potatoes from a truckload of more than 2000 potatoes. Suppose that only 2 of the 50 potatoes sampled are found to have major defects. Which one of the following assumptions for inference about a proportion using a confidence interval is violated?

• Large counts.

• 10% condition.

• There are not violations.

Tina wants to know if the proportion of people who buy burgers is at all affected by her open mic reading. If p=0.8 before her reading, what is an appropriate set of hypotheses?

• Ho: p = 0.8
  Ha: p > 0.8

• Ho: p = 0.8
  Ha: p < 0.8

• Ho: p ≠ 0.8
  Ha: p = 0.8

• Ho: p= 0.8
  Ha: p ≠ 0.8

A credit card company would like to compare the proportion of people who have poor credit to the proportion of people who think they have poor credit. Which of the following is most appropriate?

• Proportion Z-Test

• Proportion Z-Interval

• 2-Proportion Z-Test

• 2-Proportion Z-Interval

A 99% confidence interval found that the true proportion of teens who drink coffee every day is in the interval (0.785, 0.831). What was the p^ value used to determine this interval? 

• 0.8

• 0.808

• 0.825

• 0.831