Difference in Proportions and Means

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

To compare 2 dog-training programs, an obedience school trained 43 dogs using Program A and 41 dogs using Program B. For Program A, the average number of training hours required was 24.8 with a standard deviation of 3.1 hours. For Program B, the mean was 22.9 hours with a standard deviation of 3.3 hours. Is there a significant difference between the two programs?

• One-Sample Z Test for a Proportion

• One-Sample Z Test for a Mean

• Two-Sample T Test for the Difference in Means

• Two-Sample Z Test for the Difference in Means

Are people who have pets more likely to be left-handed than people who don't have pets?

• one-sample z test for a proportion

• one-sample z interval for a proportion

• two-sample z test for the difference of proportions

• two-sample z intervalfor the difference of proportions

Answer explanation

This is a yes/no question, so a test is required rather than an interval. There are two separate populations: people who have pets vs people who don't, so a two-sample test is needed.

How much more likely are teenagers to use TikTok compared to people over the age of 20?

• one-sample z test for a proportion

• one-sample z interval for a proportion

• two-sample z test for the difference of proportions

• two-sample z interval for the difference of proportions

Answer explanation

The question asks for the size of the difference, so an interval is needed rather than a test. There are two separate populations: teenagers and people over the age of 20.

If p₁ - p₂ = 0, is in the 90% confidence interval, what can we conclude at α = 0.10?

• Reject H₀, there is sufficient evidence to conclude H_a

• Reject H₀, there is NOT sufficient evidence to conclude H_a

• Fail to reject H₀, there is sufficient evidence to conclude H_a

• Fail to reject H₀, there is NOT sufficient evidence to conclude H_a

Are robin eggs more likely then stellar jay eggs to hatch early during a wet spring?  Eggs of 82 robins and 75 stellar jays were observed this spring. Which procedure is appropriate?

• t test for means

• t test for difference of means

• z test for proportions

• z test for difference of proportions

How much faster do people who own sports cars drive on the freeway compared to people who own economy cars.  520 sports cars and 890 economy cars were clocked as they passed by on the freeway. Which procedure is appropriate?

• t interval for means

• t interval for difference of means

• z interval for proportions

• z interval for difference of proportions

Are African Americans taller than Caucasians? 10,000 African Americans and 10,000 Caucasians were measured.

• Hypothesis Test for a Population Mean

• Hypothesis Test for a Population Proportion

• Hyp. Test for the Difference Between 2 Means (Independent Samples)

• Hyp. Test for Paired Data (Dependent Samples)

• Hyp. Test for the Difference Between 2 Proportions

Are tourists on the North Shore more likely to rent a boat than tourists on the South Shore? 50 North Shore tourists and 50 South Shore tourists were surveyed.

• Hypothesis Test for a Population Mean

• Hypothesis Test for a Population Proportion

• Hyp. Test for the Difference Between 2 Means (Independent Samples)

• Hyp. Test for Paired Data (Dependent Samples)

• Hyp. Test for the Difference Between 2 Proportions

Is a man who walks into a car dealership more likely to purchase an automobile than a woman? 70 men and 60 women were observed.

• Hypothesis Test for a Population Mean

• Hypothesis Test for a Population Proportion

• Hyp. Test for the Difference Between 2 Means (Independent Samples)

• Hyp. Test for Paired Data (Dependent Samples)

• Hyp. Test for the Difference Between 2 Proportions