AP Statistics Unit 6

From a random sample of 50 people, sitting pulse rates and standing pulse rates were measured for each person. A coin was flipped to determine whether the sitting or the standing pulse rate would be measured first. Let μ_sitting represent the mean sitting pulse rate in the population, μ_standing represent the mean standing pulse rate of the population, and μ_d represent the mean difference between the sitting and standing (sitting – standing) pulse rates of the population. Which of the following represents an appropriate test and hypotheses to determine if there is a difference in mean pulse rates between sitting and standing in the population?

• A two-sample t-test with

  H₀ : μ_sitting = μ_standing

  H_A : μ_sitting ≠ μ_standing

• A two-sample t-test with

  H₀ : μ_sitting = μ_standing

  H_A : μ_sitting < μ_standing

• A matched-pairs t-test with

  H₀ : μ_d = 0

  H_A : μ_d ≠ 0

• A matched-pairs t-test with

  H₀ : μ_d = 0

  H_A : μ_d < 0

A matched-pairs t-test is NOT an appropriate way to analyze data consisting of which of the following?

• Measurements of annual income for both individuals in pairs formed by assigning 100 people to pairs at random

• Measurements of annual income recorded for both spouses of 100 randomly selected married couples

• Measurements of annual income for both individuals in pairs formed by matching 100 people from State A and 100 people from State B based on level of education

• Measurements of annual income taken both before and after a two-year training course for a random sample of 100 people who took the course

A national health study reported that the proportion of students with elevated blood pressure is 0.15. The principal of a local high school believes that the proportion of students in the school with elevated blood pressure is greater than 0.15. If a large random sample is used, which of the following is the most appropriate test to investigate the principal’s belief?

• A z-test for a proportion

• A z-test for the difference between two proportions

• A t-test for a mean

• A matched-pairs t-test

A large city newspaper periodically reports the mean cost of dinner for two people at restaurants in the city. The newspaper staff will collect data from a random sample of restaurants in the city and estimate the mean price using a 90 percent confidence interval. In past years, the standard deviation has always been very close to $35. Assuming that the population standard deviation is $35, which of the following is the minimum sample size needed to obtain a margin of error of no more than $5 ?

• 90

• 112

• 133

• 147

A 95 percent confidence interval for the mean time, in minutes, for a volunteer fire company to respond to emergency incidents is determined to be (2.8, 12.3). Which of the following is the best interpretation of the interval?

• The probability is 0.95 that a randomly selected time for response will be between 2.8 minutes and 12.3 minutes.

• We are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes.

• Ninety-five percent of the time the mean time for response is between 2.8 minutes and 12.3 minutes

• We are 95% confident that a randomly selected time for response will be between 2.8 minutes and 12.3 minutes.

A two-sample t-test of the hypotheses

H₀ : μ₁ - μ₁ = 0 versus H_A : μ₁ - μ₁ > 0 produces a p-value of 0.03. Which of the following must be true?

I. A 90 percent confidence interval for the difference in the means will contain the value 0.

II. A 95 percent confidence interval for the difference in the means will contain the value 0.

III. A 99 percent confidence interval for the difference in the means will contain the value 0.

• I only

• I and II only

• II and III only

• I, II, and III

A biologist wants to estimate the difference between the mean body lengths of green and brown stinkbugs. A random sample of 20 green stinkbugs has a mean body length of 16.22 mm and a standard deviation of 1.34 mm. A random sample of 20 brown stinkbugs has a mean body length of 13.41 mm and a standard deviation of 0.73 mm. What is the standard error of the difference (green – brown) between the sample means?

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A machine is designed to dispense at least 12 ounces of a beverage into a bottle. To test whether the machine is working properly, a random sample of 50 bottles was selected and the mean number of ounces for the 50 bottles was computed. A test of the hypotheses H₀ : μ = 12 versus H_A : μ < 12 was conducted, where μ represents the population mean number of ounces of the beverage dispensed by the machine. The p-value for the test was 0.08. Which of the following is the most appropriate conclusion to draw at the significance level of α = 0.05 ?

• Because the p-value is greater than the significance level, there is not convincing evidence that the population mean number of ounces dispensed into a bottle is less than 12 ounces.

• Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is less than 12 ounces.

• Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.

• Because the p-value is less than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.

An airline claims that the mean flight time between City X and City Y is 38 minutes. After taking many flights, a local business group believes that the claim is unrealistic and that the actual mean flight time is greater than 38 minutes. If the group conducts a study to investigate its belief, which of the following hypotheses should be tested?

• H₀ : x̄ = 38

  H_A : x̄ ≠ 38

• H₀ : x̄ = 38

  H_A : x̄ > 38

• H₀ : μ = 38

  H_A : μ ≠ 38

• H₀ : μ = 38

  H_A : μ > 38