AP Stats Unit 7

A team of psychologists studied the effect of multitasking on the completion of cognitive tasks. A group of 40 women participated in the study. Each woman owned a smartphone equipped with the same type of keyboard. The women typed a text passage on the phone twice, one time while sitting in a quiet room (a single task) and the other time while walking (a multitask). The order of the single task and the multitask was randomly determined for each woman. The psychologists recorded the time it took each woman to type the text for both tasks. If the conditions of inference are met, which of the following tests is most appropriate to analyze the data?

• A two-sample t-test for a difference between means

• A matched-pairs t-test for a mean difference

• A one-sample z-test for a proportion

• A two-sample z-test for a difference between proportions

• A chi-square test of independence

A polling agency conducted a survey by selecting 100 random samples, each consisting of 1,200 United States citizens. The citizens in each sample were asked whether they were optimistic about the economy. For each sample, the polling agency created a 95 percent confidence interval for the proportion of all United States citizens who were optimistic about the economy. Which of the following statements is the best interpretation of the 95 percent confidence level?

• With 100 confidence intervals, we can be 95% confident that the sample proportion of citizens of the United States who are optimistic about the economy is correct.

• We would expect about 95 of the 100 confidence intervals to contain the proportion of all citizens of the United States who are optimistic about the economy.

• We would expect about 5 of the 100 confidence intervals to not contain the sample proportion of citizens of the United States who are optimistic about the economy.

• Of the 100 confidence intervals, 95 of the intervals will be identical because they were constructed from samples of the same size of 1,200.

• The probability is 0.95 that 100 confidence intervals will yield the same information about the sample proportion of citizens of the United States who are optimistic about the economy

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CCSS.HSS.IC.B.4

A representative of a car manufacturer in the United States made the following claim in a news report. "Ten years ago, only 53 percent of Americans owned American-made cars, but that figure is significantly higher today." A research group conducted a study to investigate whether the claim was true. The group found that 56 percent of a randomly selected sample of car owners in the United States owned American-made cars. A test of the appropriate hypotheses resulted in a p-value of 0.283. Assuming the conditions for inference were met, is there sufficient evidence to conclude, at the significance level of a = 0.05, that the proportion of all car owners in the United States who own American-made cars has increased from what it was ten years ago?

• Yes, because 0.56 > 0.53.

• Yes, because a reasonable interval for the proportion is 0.56 ± 0.283.

• Yes, because 0.56 - 0.53 = 0.03 and 0.03 < 0.05.

• No, because 0.283 < 0.53.

• No, because 0.283 > 0.05.

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CCSS.HSS.IC.B.4

A botanist collected one leaf at random from each of 10 randomly selected mature maple trees of the same species. The mean and the standard deviation of the surface areas for the 10 leaves in the sample were computed.Assume the distribution of surface areas of maple leaves is normal. What is the appropriate method for constructing a one-sample confidence interval to estimate the population mean surface area of the species of maple leaves, and why is the method appropriate?

• The t-interval is appropriate, because the population standard deviation is not known.

• The t-interval is appropriate, because the t-interval is narrower than the z-interval.

• The z-interval is appropriate, because the z-interval is narrower than the t-interval.

• The z-interval is appropriate, because the central limit theorem applies.

• The z-interval is appropriate, because the sample standard deviation is known.

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CCSS.HSS.IC.B.4

A state educational agency was concerned that the salaries of public school teachers in one region of the state,region A, were higher than the salaries in another region of the state, region B. The agency took two independent random samples of salaries of public school teachers, one from region A and one from region B. The data are summarized in the table below. Assuming all conditions for inference are met, do the data provide convincing statistical evidence that the salaries of public school teachers in region A are, on average, greater than the salaries of public school teachers in region B?

• Yes, there is evidence at the significance level of a = 0.001.

• Yes, there is evidence at the significance level of a = 0.01 but not at a = 0.001.

• Yes, there is evidence at the significance level of a = 0.05 but not at a = 0.01.

• Yes, there is evidence at the significance level of a = 0.10 but not at a = 0.05.

• No, there is no evidence at the significance level of a = .10.

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CCSS.HSS.IC.B.4

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

• 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

• Measurements of annual income for each twin for 100 randomly selected pairs of twins

• 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 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

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CCSS.HSS.ID.A.4

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?

• 
• 
• 
• 
• 

A medical doctor uses a diagnostic test to determine whether a patient has arthritis. A treatment will be prescribed only if the doctor thinks the patient has arthritis. The situation is similar to using a null and an alternative hypothesis to decide whether to prescribe the treatment. The hypotheses might be stated as follows.

H_o : The patient does not have arthritis

H_a : The patient has arthritis

Which of the following represents a Type II error for the hypotheses?

• Diagnosing arthritis in a patient who has arthritis

• Failing to diagnose arthritis in a patient who has arthritis

• Diagnosing arthritis in a patient who does not have arthritis

• Failing to diagnose arthritis in a patient who does not have arthritis

• Prescribing treatment to a patient regardless of the diagnosis

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

• 195

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

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CCSS.HSS.IC.B.4