Practice Test 55 - AP Statistics

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

A city's transit authority claims riders use 5 payment methods with the following population proportions: 40% Card, 25% Mobile, 20% Cash, 10% Pass, 5% Other. In a random sample of 400 rides, the observed counts are: Card 150, Mobile 120, Cash 70, Pass 45, Other 15. A chi-square goodness-of-fit test of $H_0$ : the population proportions match the claimed values gives $p$ -value = 0.003. Expected counts under $H_0$ are: Card 160, Mobile 100, Cash 80, Pass 40, Other 20. What conclusion is appropriate at $\alpha=0.01$ ?
A company randomly sampled employees and recorded department (Sales, Engineering, HR) and whether the employee prefers remote work (Yes/No). The two-way table is shown. A chi-square test of independence resulted in $p$ -value $=0.67$ . What conclusion is appropriate at the 5% significance level?
An environmental agency tests whether the mean lead concentration in a river exceeds the legal limit of 15 ppb. They test $H_0: \mu=15$ vs. $H_a: \mu>15$ using $\alpha=0.02$ . They fail to reject $H_0$ and conclude there is not convincing evidence the river exceeds the legal limit. In reality, the true mean is $\mu=18$ ppb. Which type of error was made?
A school district wants to know whether students' preferred lunch option differs by grade level. A random sample of students is selected from each of three grades (6th, 7th, 8th), and each student reports one preference (Pizza, Salad, or Sandwich). The results are shown in the two-way table. Which chi-square test is appropriate, and what are the correct hypotheses?
A student takes 16 shots at a target and records whether each shot hits the bullseye. A success is "bullseye," and exactly 16 shots are taken, but the student adjusts their aim after each miss, increasing the chance of a bullseye over time. Does this meet binomial conditions?
A researcher studied 13 cars and recorded vehicle weight ( $x$ , in thousands of pounds, from 2.4 to 4.8) and highway fuel economy ( $y$ , miles per gallon). The least-squares regression line predicting mpg from weight is $\hat{y}=46.0-5.2x$ . The purpose of this linear model is to describe the linear association and predict typical fuel economy for weights in the observed range. Which interpretation of the model is correct?
A nutritionist studies whether daily fiber intake in grams ( $x$ ) predicts LDL cholesterol level in mg/dL ( $y$ ). The nutritionist expects that higher fiber intake is associated with lower LDL cholesterol in the population. Which hypotheses are appropriate for testing this expectation about the slope in the regression of $y$ on $x$ ?
A public health student fits a least-squares regression line to predict systolic blood pressure (mmHg) from age (years) using a random sample of 80 adults. A 95% confidence interval for the slope is $(0.15,\ 0.65)$ mmHg per year. Which interpretation is correct?
A standardized test administrator states that the probability a randomly selected student arrives late to the test is $0.05$ . The random process is selecting one student at random from all test takers; the sample space is {late, on time}. Which statement correctly describes the probability $0.05$ ?
A restaurant owner claims that the proportion of customers who leave a tip is higher when the receipt includes a suggested tip amount than when it does not. One week, a random sample of 260 receipts with suggested tips showed 221 customers tipped; another week, a separate random sample of 240 receipts without suggested tips showed 190 customers tipped. Which hypotheses are appropriate for a test of this claim?
A hospital reports that the mean length of stay for patients undergoing a certain procedure is 3.5 days. A random sample of $n=28$ recent patients shows a mean stay of $\bar{x}=3.9$ days. An administrator wants to test whether the true mean length of stay has increased above 3.5 days. Which hypotheses are appropriate for a test of a population mean?
The distribution of weights (in grams) of apples from a large orchard is approximately Normal for the population of all apples harvested. The mean is $\mu=150$ g and the standard deviation is $\sigma=10$ g. The interval from 130 g to 170 g is marked on the normal curve. Which statement about the marked interval is correct?
A bookstore owner compares mean amount spent per customer on weekdays versus weekends. Independent random samples were taken (weekday: $n=25$ ; weekend: $n=27$ ). A two-sample $t$ test for $\mu_{weekend}-\mu_{weekday}$ used $H_0:\mu_{weekend}-\mu_{weekday}=0$ and $H_a:\mu_{weekend}-\mu_{weekday}>0$ . The p-value was 0.073. At $\alpha=0.05$ , what conclusion is appropriate?
A sports scientist claims that a higher proportion of runners will experience muscle cramps when they drink water only compared with a sports drink during a race. In a random sample of 120 runners who drank water only, 42 reported cramps; in a separate random sample of 130 runners who drank a sports drink, 30 reported cramps. Which hypotheses are appropriate for a test of this claim?
A runner's time for the first half of a race is $A$ minutes and for the second half is $B$ minutes. Suppose $A$ and $B$ are independent with $\mu_A=24.0$ , $\sigma_A=1.5$ , $\mu_B=25.0$ , and $\sigma_B=1.8$ . Let $T=A+B$ be the total time. Which statement about $T$ is correct?
A restaurant chain is estimating the mean time (in minutes) customers wait for takeout orders at a particular location. On Monday, a random sample of 50 orders has a mean wait of 12.6 minutes. On Tuesday, an independent random sample of 50 orders from the same location has a mean wait of 14.1 minutes. Assume the ordering process did not change. Why might the sample results differ?
A hospital tracks the next 30 patients who arrive at the emergency room. For each patient, a success is "patient is admitted to the hospital" and a failure is "patient is treated and released." The hospital records the number admitted among these 30 patients. Does this meet binomial conditions?
A marketing firm wants to estimate the mean amount spent per visit by customers at a grocery chain. They randomly select 25 stores from all stores in the chain and then record the total spent by every customer who shops at those stores on a single Saturday. Which conclusion is justified based on the design? (Assume the 25 stores are selected by simple random sampling.)
A nutrition researcher models systolic blood pressure (mmHg) as a linear function of daily sodium intake (mg) using a random sample of adults. A 90% confidence interval for the population slope is $(0.002,\ 0.006)$ . Which interpretation is correct?
A coach analyzes the relationship between practice sessions attended ( $x$ ) and free-throw percentage ( $y$ ) for 18 players. A 90% confidence interval for the true slope is $( -0.5,\ 2.0)$ percentage points per session. Which interpretation is correct?

Practice tests