Sample Test for Proportion

In 1975, a random sample of 1484 adult U.S. citizens was surveyed, and 193 strongly agreed with the statement, "People should take care of themselves". Then, in 1991, a survey of 1013 adult U.S. citizens showed that only 61 strongly agreed with the statement. Does this indicate that the proportion of U.S.adults who strongly agree with the given statement has dropped?

• Two-Sample Z Test for the Difference in Proportions

• Two-Sample T Test for the Difference in Means

• Matched Pairs T Test for a Mean

• One-Sample T Test for a Mean

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

Which of the following is true pertaining to a 2-proportion z-interval?

• There are no restrictions on sample size 

• This interval can be found even if the samples are not random

• The population should be large, relative to each of the sample sizes

• So long as all conditions are met for one sample, you do not need to check conditions for the other sample

What additional condition must be checked for a 2-proportion test or interval compared to a 1-proportion test or interval?

• You must make sure that the samples are random

• You must make sure that the two samples are independent from one another

• You must make sure that the sum of the samples' sizes are smaller than 10% of the whole population

• The conditions are exactly the same

In a past General Social Survey, a random sample of men and women answered the question “Are you a member of any sports clubs?” Based on the sample data, 95% confidence intervals for the population proportion who would answer “yes” are .13 to .19 for women and .247 to .33 for men. Based on these results, you can reasonably conclude that 

• At least 25% of American men and American women belong to sports clubs.

• At least 16% of American women belong to sports clubs. 

• There is a difference between the proportions of American men and American women who belong to sports clubs.

• There is no conclusive evidence of a gender difference in the proportion belonging to sports clubs

As part of a national sleep study, a random sample of adults was selected and surveyed about their physical activity and the number of hours they sleep each night. Of the 183 adults who exercised regularly (exercisers), 59 percent reported sleeping at least seven hours at night. Of the 88 adults who did not exercise regularly (nonexercisers), 52 percent reported sleeping at least seven hours at night. Which of the following is the most appropriate standard error for a confidence interval for the difference in proportions of adults who sleep at least seven hours at night among exercisers and nonexercisers?

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A random sample of 100 people from Country S had 15 people with blue eyes. A separate random sample of 100 people from Country B had 25 people with blue eyes. Assuming all conditions are met, which of the following is a 95 percent confidence interval to estimate the difference in population proportions of people with blue eyes (Country S minus Country B) ?

• (-0.01, 0.21)

• (-0.15,-0.05)

• (-0.19,-0.01)

• (-0.21, 0.01)

• (-0.24,0.04)

A wildlife biologist is doing research on chronic wasting disease and its impact on the deer populations in Colorado. To estimate the difference between the proportions of deer with chronic wasting disease in two different regions, a random sample of 200 deer was obtained from one region and a random sample of 197 deer was obtained from the other region. The biologist checked for the following (see pic). Which of the following conditions for inference was the biologist checking?

• The population of deer within each region is approximately normal.

• It is reasonable to generalize from the samples to the populations.

• The samples are independent of each other.

• The observations within each sample are close to independent.

• The sampling distribution of the difference in sample proportions is approximately normal.

At a baseball game, 42 of 65 randomly selected people own an iPad. At a rock concert occurring at the same time across town, 34 of 52 randomly selected people own an iPad. A researcher wants to test the claim that the proportion of iPad owners at the two venues is different. A 90% confidence interval for the difference in population proportions(game − concert) is (−0.154, 0.138). Which of the following gives the correct outcome of the researcher’s test of the claim?

• Because the confidence interval includes 0, the researcher can conclude that the proportion of iPod owners at the two venues is the same.

• Because the center of the interval is –0.008, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.

• Because the confidence interval includes 0, the researcher cannot conclude that the proportion of iPod owners at the two venues is different.

• Because the confidence interval includes more negative than positive values, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.

In 1975, a random sample of 1484 adult U.S. citizens was surveyed, and 193 strongly agreed with the statement, "People should take care of themselves". Then, in 1991, a survey of 1013 adult U.S. citizens showed that only 61 strongly agreed with the statement. Does this indicate that the proportion of U.S. adults who strongly agree with the given statement has dropped?

• Two-Sample Z Test for the Difference in Proportions

• Two-Sample T Test for the Difference in Means

• Paired Data one-sample T Test for a difference in Means

• One-Sample T Test for a Mean