AP Statistics Confidence Intervals — practice questions
52 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP Statistics Confidence Intervals in the app →What is a point estimate, as used to introduce confidence intervals?How does a confidence interval differ from a point estimate?What is the general form used to build a confidence interval?α is related to the confidence level CL by α + CL = 1. What does α represent?A sample produces x-bar = 7 with an error bound of EBM = 2.5. What is the resulting confidence interval?Statistics exam scores are normally distributed with a known population standard deviation of three points. A Continuing the exam-score example, σ = 3, n = 36, x-bar = 68, and z(0.05) = 1.645 for a 90% confidence level. Cell phone SAR levels have a known population standard deviation of σ = 0.337. A sample of 30 phones gives x-bThe same exam-score data (σ=3, n=36, x-bar=68) gives a 90% CI of (67.18, 68.82). Raising the confidence level Starting from the exam-score example with n=36 and EBM=0.8225 at 90% confidence, what happens to the error bouYou are told only that a confidence interval is (67.18, 68.82), with no sample mean given. Using the shortcut The population standard deviation for the age of Foothill College students is 15 years. To be 95% confident thYoung adult male heights have a known standard deviation of 2.5 inches. A researcher wants the sample mean heiAmong various ethnic groups, height standard deviation is about three inches. For 48 randomly surveyed male SwFor the Swedish male height example, σ = 3 inches, n = 48, x-bar = 71 inches, and CL = 95% so z(0.025) = 1.96.For a sample of 40 House candidates, x-bar = $568,873 with a known σ = $909,200 to the nearest hundred. At 95%An accounting firm surveys 100 people and finds a sample mean tax-form time of 23.6 hours, with a known σ = 7.A camp director surveys 20 campers about letters sent home, finding x-bar = 7.9 with a known σ = 2.5. For a 90The empirical rule used in the iTunes example says that for a bell-shaped distribution, the sample mean will fWhen statisticians replaced the unknown population standard deviation σ with the sample standard deviation s wOlder statistical practice used the normal approximation for large samples and the Student's t-distribution onFor a Student's t-distribution with n - 1 degrees of freedom, why is the number of degrees of freedom exactly Which property correctly describes how the Student's t-distribution compares to the standard normal distributiAs the degrees of freedom of a Student's t-distribution increase, what happens to its shape?In a study of acupuncture, 15 subjects give a sample mean sensory rate of x-bar = 8.2267 and sample standard dFor the acupuncture study, n = 15, x-bar = 8.2267, s = 1.6722, df = 14, and a 95% confidence level gives t(0.0A study of 20 newborns' cord blood finds x-bar = 127.45 targeted chemicals with s = 25.965, df = 19. For a 90%A tranquilizer's effect on nine patients gives x-bar = 2.51 hours and s = 0.318 hours, so df = 8. For a 95% coA political action committee (PAC) sample of 30 gives x-bar = $251,854.23 and s = $521,130.41, so df = 29. ForA quality-control specialist samples 12 servings of soda, finding x-bar = 13.30 and s = 1.55, so df = 11. For How can you tell a confidence-interval problem is really about a population proportion rather than a populatioThe sample proportion is written p' = x/n. What do x and n represent in this formula?A condition governs when a normal-based confidence interval for a proportion is valid. What must be true of npA market research firm surveys 500 adult residents and finds 421 own cell phones, so p' = 0.842 and q' = 0.158A political science student surveys 500 students and finds 300 are registered voters, so p' = 0.600 and q' = 0What adjustment does the 'plus four' method make to a proportion confidence interval, and why is it applied?Under what conditions is the 'plus four' method recommended for a proportion confidence interval?Six of 25 surveyed statistics students report smoking in the past week. Using the plus-four method, the workinIn a group of 50 teens, 13 report more than 500 Facebook friends. Using the plus-four method, x=15 and n=54, gA mobile phone company wants to be 90% confident its estimated proportion of text-messaging customers aged 50+Using p' = q' = 0.5, z(0.05) = 1.645 for 90% confidence, and a target error bound of EBP = 0.03, the formula nInsurance companies want to know what proportion of drivers always buckle up, aiming for 95% confidence withinA survey of 1,200 people finds 61% feel the president is doing an acceptable job. For a 90% confidence level, A telephone poll of 1,000 adult Americans finds that 20% consider crime the main problem facing the country. FA survey of 200 households finds that in 120 of them, the woman makes the majority of purchasing decisions, soA poll of 1,200 voters finds 65% name the economy as the most significant election issue. For a 90% confidenceAt the Ice Chalet, a randomly selected beginning skating class of 80 children has 64 girls and 16 boys, so p' A Field Poll finds that 400 out of 506 surveyed California adults, about 79%, feel education is a top issue. WContinuing the Field Poll example, p' = 0.79 from 400 of 506 surveyed. For a 90% confidence level, z(0.05)=1.6Of 511 southern California homes surveyed for earthquake preparedness, 338 did NOT meet minimum recommendationIn a Zogby poll of 48 respondents, nine rated a terrorist attack in their community as likely or very likely. A campus survey wants to estimate, with 95% confidence and a margin of error no greater than 5%, the true prop