AP Statistics: Inference for Categorical Data (Proportions) Practice Test
AP Statistics: Inference for Categorical Data (Proportions) Practice Test
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Question 1 of 19
1. Question
A health insurance executive suspects that 50% of insurance applications are incomplete (i.e. critical data is missing from the application). He wants to gather a sample to estimate the true proportion. He wants to be within 5% of the true mean with 95% confidence. What sample size does he need?
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Question 2 of 19
2. Question
In a simple random sample of 1000 people, 261 are lefthanded. Find a 95% confidence interval for the true proportion of lefthanded people in the entire population.
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Question 3 of 19
3. Question
A health insurance executive suspects that 50% of insurance applications are incomplete (i.e. critical data is missing from the application). He wants to gather a sample to estimate the true proportion. He wants to be within 5% of the true mean with 95% confidence. What sample size does he need?
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Question 4 of 19
4. Question
Faith is in charge of a website campaign that shows a banner asking users to make a donation when they visit the site. She has two designs for the banner in mind: design A and design B. She suspects that design A will lead to a larger proportion of users making a donation. She wants to test her hypothesis by randomly assigning each user one of the two designs over the course of a week. Which of the following is an appropriate set of hypotheses for Faith’s significance test?
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Question 5 of 19
5. Question
Erva is a manager in charge of customer satisfaction. Customers who call her
company’s support line are asked if they were satisfied with the service they received at the end of each call. Customers hear music while they are on hold, and Erva wonders if the genre of music has any impact on satisfaction. She plans on randomly assigning customers to hear either jazz or classical, and she’ll test if the proportion who say they were satisfied is significantly different between the groups. Which of the following is an appropriate set of hypotheses for Erva’s significance test?CorrectIncorrect 
Question 6 of 19
6. Question
A political consultant wondered if support for a candidate was significantly different between voters who owned a landline telephone and voters who did not. The consultant surveyed a random sample of voters and found 36 of 75 who owned a landline supported the candidate, while 20 of 100 who did not own a landline supported the candidate. The consultant wants to test if these results suggest a significant difference in support between voters who do and do not own a landline. Assume that all conditions have been met. Which of the following would be an appropriate test statistic for their test?
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Question 7 of 19
7. Question
An egg supplier sources its eggs from two farms—farm A and farm B. The supplier suspects that a larger proportion of eggs from farm A have dangerous amounts of salmonella. The supplier took a random sample of 1000 eggs from each farm. Here the results:
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Question 8 of 19
8. Question
Researchers suspect that myopia, or nearsightedness, is becoming more common over time. A study from the year 2000 showed 132 cases of myopia in 400 randomly selected people. A separate study from 2015 showed 228 cases in 600 randomly selected people.
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Question 9 of 19
9. Question
Nicki’s business ships orders from a location in Chicago and another location in Denver. She suspected that a larger proportion of orders shipped from the Denver location were arriving late. She took a random sample of 100 orders from each location. She found that 20 orders in Denver sample arrived late, and 12 orders in Chicago sample arrived late. She wants to use these results to test if the proportion of orders that arrive late is significantly larger at Denver location. She will test H 0 : p Denver = p Chicago versus H a : : p Denver > p Chicago . Assume that all conditions have been met. What is the Pvalue associated with these sample results?
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Question 10 of 19
10. Question
A university offers a certain course that students can take inperson or in an online setting. Teachers of the course were curious if there was a difference in the passing rate between the two settings. Data from a recent semester showed that 80%, percent of students passed the inperson setting, and 75% percent of students passed the online setting. They were willing to treat these as representative samples of all students who may take each setting of the course. The teachers used those results to make a 95% confidence interval to estimate the difference between the proportions of students who pass in each setting of the course. The resulting interval was approximately (0.04, 0.14). They want to use this interval to test H o : p inperson = p online versus H a : p inperson ≠ p online . Assume that all conditions for inference have been met. Based on the interval, what do we know about the corresponding Pvalue and conclusion at the ∝ = 0.05 level of significance.
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Question 11 of 19
11. Question
Jules works on a small team of 40 employees. Each employee receives an annual rating, the best of which is “exceeds expectations.” Management claimed that 10% of employees earn this rating, but Jules suspected it was actually less common. She obtained an anonymous random sample of 10 ratings for employees on her team. She wants to use the sample data to test H o : p = 0.1 versus H a : p < 0.1, where p is the proportion of all employees on her team who earned “exceeds expectations.” Which conditions for performing this type of test did Jules’ sample meet? Choose all answers that apply.
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Question 12 of 19
12. Question
Quintin read a report claiming that 4% of police officers in the US have had formal complaint filed against them. Quintin suspects that this figure is higher in hisstate. He obtains a random sample of records for 500 officers from the approximately 20,000 officers in his state. He wants to use these data to test H o : p = 0.04 versus H a : p > 0.04, where p is the proportion of officers in Quintin’s state who have had a formal complaint filed against them. Which conditions for performing this type of significance test have been met? Choose all answers that apply.
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Question 13 of 19
13. Question
A professor gives a multiple choice exam where each question has five choices. The professor decides not to count a question against students if the class as a whole does significantly worse on the question than they would have done simply by guessing. In other words, the teacher tests H o : p = 0.20 versus H a : p < 0.20, where p is the proportion of students who would correctly answer the question. Suppose that 14 of 100 students correctly answer a particular question. Assuming that the conditions for inference have been met, calculate the test statistic for the professor’s significance test.
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Question 14 of 19
14. Question
According to a very large poll in 2015, about 90% of homes in California had access to the internet. Market researchers want to test if that proportion is now higher, so they take a random sample of 100 homes in California and find that 96 of them have access to the internet. The researchers will test H o : p = 0.90 versus H a : p > 0.90, where p is the proportion of homes in California that have access to the internet. Assuming that the conditions for inference have been met, calculate the test statistic for the significance test.
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Question 15 of 19
15. Question
Amanda read a report saying that 49% of teachers in the United States were members of a labor union. She wanted to test whether this was true in her state, so she took a random sample of 300 teachers from her state to test H o : p = 0.49 versus H a : p ≠ 0.49, where p is the proportion of teachers in her state who are members of a labor union. The sample results showed 134 teachers were members of a labor union, and the corresponding test statistic was z ≈ 1.50. Assuming that the necessary conditions are met, what is the approximate Pvalue for Amanda’s significance test?
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Question 16 of 19
16. Question
There is a law in ND saying that the ratio of elementary students to teachers can be no more than 22:1. A hypothesis test is performed to determine if the proportion of schools is above 25% using an SRS of 85 schools. At the 0.05 significance level, what conclusion can be made if 32 of the schools surveyed exceed this ratio?
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Question 17 of 19
17. Question
Which of the following best describes a Type I error?
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Question 18 of 19
18. Question
Which of the following best describes a Type II error?
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Question 19 of 19
19. Question
The null hypothesis always contains a/an…
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