Practice Test 10 - AP Statistics

20 questions. Answer them in any order, then submit to see your score and every explanation.

A hospital tracks whether a randomly selected patient arriving at the emergency room on a certain day is admitted or not admitted. Historical data suggest $P(\text{admitted})=0.40$ . Let event $A$ be "the next selected patient is admitted." Which statement correctly describes the probability $P(A)=0.40$ ?
A researcher is studying whether the proportion of adults who have received a flu shot this year is lower among adults who work from home than among adults who work primarily on-site. In a random sample, 55 of 130 work-from-home adults had a flu shot, and 78 of 150 on-site adults had a flu shot. The research claim is that the work-from-home proportion is lower. Which hypotheses are appropriate?
A shipping company finds that 12% of packages handled at a certain distribution center arrive at least one day late. A manager randomly tracks 35 packages from that center, recording whether each package is late or on time. Assume outcomes are independent. Let $X$ be the number of late packages (successes). Which values correctly model this situation with a binomial distribution?
A school counselor estimates the probability that, in a random sample of 6 students, at least one is left-handed. Assume 12% of students are left-handed and students are independent. She simulates 1000 trials; in each trial she generates 6 random integers from 1 to 100 and counts a student as left-handed if the number is 1–12. The simulation produced 534 trials with at least one left-handed student. Which interpretation of the simulation results is correct?
An environmental scientist measured water temperature ( $x$ , in °C, from 6 to 24) and dissolved oxygen ( $y$ , mg/L) at 12 sites in a river. The least-squares regression line predicting dissolved oxygen from temperature is $\hat{y}=12.1-0.18x$ . The purpose of this linear model is to describe the linear association and predict typical dissolved oxygen for temperatures in the observed range. Which interpretation of the model is correct?
A bottled-water company claims its bottles contain a mean of 500 mL. A regulator tests $H_0: \mu = 500$ versus $H_a: \mu \ne 500$ at $\alpha = 0.01$ . The regulator analyzes a random sample and rejects $H_0$ , concluding the mean fill amount differs from 500 mL. In truth, the company's process is properly calibrated and the true mean fill is exactly 500 mL. Which type of error was made?
A school district wants to know whether the mean time students spend on homework per night is more than $\mu=90$ minutes. A random sample of 60 students reports their nightly homework time, and a one-sample $t$ test is conducted with $H_0:\mu=90$ versus $H_a:\mu>90$ at $\alpha=0.10$ . The p-value is 0.072. What conclusion is appropriate?
A sports scientist compares the proportion of athletes who report improved performance after using two different training plans. In random samples, 54 of 90 athletes using Plan A report improvement and 62 of 95 athletes using Plan B report improvement. A 95% confidence interval for $p_A - p_B$ is $(-0.18,\ 0.05)$ . The scientist claims that Plan A leads to a higher improvement rate than Plan B. Is the claim supported by the confidence interval?
A city health department wants to test whether the proportion of adult residents who received a flu shot this season is less than 60%. A random sample of 250 adults is selected from the city, and 132 report having received a flu shot (sample proportion $\hat{p}=0.528$ ). Which hypotheses are appropriate for a one-proportion $z$ test of the department's claim?
A real estate agent models house price (in $1000s) from distance to downtown (miles). The agent claims that being farther from downtown is associated with a lower mean house price. A 95% confidence interval for the slope is $(-12.5,\,-3.0)$ (thousand dollars per mile). Is the claim supported by the confidence interval?
A researcher studied 14 cars and recorded vehicle weight ( $x$ , in thousands of pounds, from 2.2 to 4.6) and highway fuel efficiency ( $y$ , in miles per gallon, from 18 to 41). A least-squares regression line predicting mpg from weight is $\hat{y}=55.0-7.5x.$ The purpose of this linear model is to describe the linear pattern and predict typical mpg for cars within the observed weight range. Which interpretation of the model is correct?
A real estate analyst examined 22 recently sold homes and recorded living area ( $x$ , square feet) and sale price ( $y$ , thousands of dollars). A least-squares regression of $y$ on $x$ was fit. The slope test $H_0: \beta_1=0$ vs. $H_a: \beta_1\ne 0$ produced a p-value of 0.0006 and a positive estimated slope. Using $\alpha=0.01$ , the analyst rejected $H_0$ . What conclusion is appropriate?
A delivery service claims its mean delivery time for local orders is 45 minutes. A random sample of $n=55$ local deliveries has a sample mean time of $\bar{x}=44.2$ minutes. The company wants to test whether the true mean delivery time is 45 minutes or not. Which hypotheses are appropriate for a test of a population mean?
A public health analyst wants to estimate the mean amount of sugar (grams, quantitative) in a particular brand of cereal. A simple random sample of 18 boxes is collected and the sugar content per serving is measured for each box. Which inference procedure is most appropriate to create a confidence interval for the population mean sugar content?
A tech company tracks whether an employee works remotely on a given day (event $R$ ) and whether the employee attends an optional team coffee chat (event $C$ ). Because coffee chats are held in person, remote work may reduce attendance. How does knowing that an employee worked remotely ( $R$ occurred) affect the likelihood that the employee attended the coffee chat ( $C$ )?
A hospital compared mean recovery time (days) for patients receiving Treatment A versus Treatment B. From independent random samples, a 92% confidence interval for $(\mu_{A}-\mu_{B})$ was $( -3.4,\ -0.8)$ . Which interpretation is correct?
A researcher wants to estimate the proportion of adults in a state who support a proposed tax measure. She randomly sampled 1200 adults from a statewide voter registration list and asked whether they support the measure. The sample proportion supporting the measure was 0.54. Which conclusion is justified based on the design of this study?
A nutrition label claims a cereal box contains a mean of $\mu = 14$ oz of cereal. A quality-control analyst tests $H_0: \mu = 14$ versus $H_a: \mu \ne 14$ at $\alpha = 0.05$ using a random sample of boxes and obtains p-value $p = 0.74$ . Which interpretation of the p-value is correct?
A student claims a coin is fair and records the results of 40 flips in order. The sequence begins with 12 Heads in a row, then continues with a mix of Heads and Tails (no other run longer than 5). Under a truly random process, long runs can occur but are less common. Is the pattern consistent with random behavior?
A teacher randomly selects a student and records the number of siblings that student has. Let the discrete random variable $X$ be the number of siblings of the selected student. The probability distribution of $X$ is shown in a table. Which statement correctly interprets the random variable $X$ ?

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