AP Stats Assessment

Since 2020, more Americans believe social media companies wield too much political power. 78% of Americans say these companies have too much power and influence in politics today, according to a new survey of 10,133 randomly selected U.S. adults conducted in 2024. The 95% confidence interval for this study is (0.7719, 0.7871). Which of the following is a correct statement, based on this situation?

• If this poll were repeated in the same way, many times, 95% of them would capture the true proportion of Americans who believe social media companies have too much power and influence in politics.

• We are 95% confident that the sample proportion of those who believe that social media companies have too much power and influence in politics is between 0.7719 and 0.7871.

• If this poll were repeated in the same way, many times, 95% of them would find that 78% of Americans sampled would believe that social media companies have too much power and influence in politics.

• We are 95% confident that the sample proportion of Americans who believe social media companies have too much power and influence in politics is 78%.

A local financial advisor is looking into what proportion of their customers struggle with paying their bills on time. Out of their 5,000 customers, he needs to randomly select a certain number of them to create a confidence interval with a margin of error of 5%. Because he is unsure of the proportion of his customers who will struggle with paying their bills on time, he uses an estimate of \( \hat{p} = 0.50 \). Which of the following represents the sample size he will need to get the margin of error he desires with 95% confidence?

• 242

• 385

• 500

• The financial advisor should send a survey to all 5,000 of his customers, and construct a confidence interval with those who respond.

A significance test is conducted to test the following hypotheses: H₀: p = 0.45 Hₐ: p < 0.45 The test statistic is z = -1.61. Which of the following contains the correct p-value and interpretation of the p-value?

• Our p-value of 0.107 is the probability of obtaining a test statistic of -1.61 or lower if the true population proportion is 0.45.

• Our p-value of 0.054 is the probability of obtaining a test statistic of -1.61 or lower if the true population proportion is 0.45.

• Our p-value of 0.107 is the probability of obtaining a sample proportion lower than 0.45 if the true population proportion is 0.45.

• Our p-value of 0.054 is the probability of obtaining a test statistic of 1.61 (or higher) or -1.61 (or lower) if the true population proportion is 0.45.

• Our p-value of 0.027 is the probability of obtaining a sample proportion lower than 0.45 if the true population proportion is 0.45.

From a sample of 150 adults, 68 said that they believe the education system is generally going in the wrong direction. Which of the following will correctly calculate this z test statistic?

Which of the following is the correct conclusion in the context of this problem, if your significance level is set at 0.05?

• Our p-value is less than α = 0.05, we would reject H₀. We have convincing evidence that less than 51% of adults in our town believe education system is generally going in the wrong direction.

• Our p-value is less than α = 0.05, we would fail to reject H₀. We do not have convincing evidence that less than 51% of adults in our town believe education system is generally going in the wrong direction.

• Our p-value is greater than α = 0.05, we would reject H₀. We have convincing evidence that less than 51% of adults in our town believe education system is generally going in the wrong direction.

• Our p-value is greater than α = 0.05, we would fail to reject H₀. We do not have convincing evidence that less than 51% of adults in our town believe education system is generally going in the wrong direction.

• None of the above gives the correct conclusion because we will apply these findings to every American adult, not just the adults in our hometown.

Which of the following is a correct description of a Type II error?

• We concluded that the proportion of adults in our town who believe the education system is generally going in the wrong direction is less than 0.51, when it actually is 0.51.

• We concluded that the proportion of adults in our town who believe the education system is generally going in the wrong direction is not less than 0.51, when it actually is less than 0.51.

• We conclude that the proportion of adults in our town who believe the education system is generally going in the wrong direction is less than 0.51, when it actually is greater than 0.51.

• We conclude that the proportion of adults in our town who believe the education system is generally going in the wrong direction is not less than 0.51, when it actually is 0.51.

• We conclude that the proportion of adults in our town who believe the education system is generally going in the wrong direction is not less than 0.51, when it actually is greater than 0.51.

If all other aspects of a test remain the same, which of the following will NOT increase the probability of a Type II error?

• Decreasing the sample size

• Decreasing the significance level

• Increasing the standard error

• Having a sample statistic close to the null

• Increasing the power of a test

A recent survey of 950 teenagers found that 78% of them work a part-time job while in high school. Which of the following represents the 92% margin of error for the proportion of all teenagers who work a part-time job?

• ± 2.35%

• ± 3.25%

• ± 2.63%

• ± 3.07%

• ± 1.34%

For which of the following situations is a one-sided hypothesis test appropriate?

• A double-blind experiment to determine what effects a new drug has on blood pressure.

• You select a random sample of students at your school to see if the support for a student council president candidate has changed from the previous support proportion of 55%.

• The CDC wants to examine the impacts of a new anti-vaping campaign by conducting a large-scale survey of teenagers aged 14 to 18 by recording the proportion of teenagers who have vaped after the campaign started.

• You select a random sample of students at your school to see if the support of a new initiative by the administrators has improved by more than 5%.

• A large-scale survey of young adults aims to see if there is a strong, positive correlation between a student’s GPA and the amount of sleep they get each night, on average.

Jessica conducted a survey for her final project in AP Statistics. She took an SRS of 50 senior students and found that 42 of them planned on attending college after graduation. Is it appropriate for her to use a Normal distribution to create a 95% confidence interval to capture the true proportion of senior students at the school who plan on attending college after graduation?

• Yes, because she took an SRS.

• Yes, because np̂ is greater than 10.

• Yes, because a Normal distribution always applies to confidence intervals for proportions.

• No, because we do not know if 50 is less than 10% of all senior students at her school.

• No, because n(1 − p̂) is less than 10.