Practice Test 63 - AP Statistics

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

A biologist observes 400 offspring from a plant cross and records flower color: Red, Pink, or White. A genetics model predicts a 1:2:1 ratio (25% Red, 50% Pink, 25% White). The observed counts are Red 92, Pink 198, White 110. The biologist wants to test whether the observed distribution differs from the predicted ratio. Which inference procedure is most appropriate?
A wildlife biologist studies whether habitat type is associated with the number of frogs found. She visits 30 ponds (observational units). For each pond, she records habitat type (forest, grassland, or urban) and the count of frogs observed during a standardized 10-minute survey. The goal is to see if frog counts differ by habitat. Which classification is correct?
A jar contains 6 red marbles and 4 blue marbles. A student draws exactly 5 marbles without replacement. A success is drawing a red marble and a failure is drawing a blue marble. The student records the number of red marbles drawn in the 5 draws. Does this meet the binomial conditions?
A company is studying whether two different email subject lines affect the proportion of customers who open a promotional email. The company has a list of 50,000 customer email addresses. It randomly assigns 25,000 customers to receive Subject Line A and 25,000 to receive Subject Line B, then records whether each email is opened within 48 hours (response variable: opened/not opened). Which statement is most accurate about conclusions from this study?
A fitness company wants to test whether a new training app increases the number of push-ups users can do in one minute. The company recruited 80 volunteers who responded to an online advertisement. The volunteers were randomly assigned to use either the new app or the standard app for 6 weeks. After 6 weeks, the new-app group had a higher mean push-up count. Which conclusion is justified based on the design of this study?
A student group wants to know whether students who participate in school sports report higher overall happiness. They survey 40 students who play a school sport and 40 students who do not, asking each to rate happiness on a 1–10 scale. The athletes' mean rating is 7.8; the non-athletes' mean rating is 6.9. Which conclusion is supported by the data?
A quality-control manager wants to estimate the probability that at least 3 of the next 10 lightbulbs from a supplier are defective, assuming the defect rate is 8% and each bulb is independent. She runs a simulation of 2000 trials; in each trial she generates 10 random digits (00–99), counts a bulb as defective if the digit is 00–07, and records whether the trial had at least 3 defectives. The simulation produced 146 successes (trials with at least 3 defectives). Which interpretation of the simulation results is correct?
A sports scientist wants to study whether a caffeine-free energy drink improves sprint performance. She randomly samples 60 athletes from a local training club roster. At a lab visit, each athlete is randomly assigned to drink either the energy drink or a placebo drink that tastes similar. After 20 minutes, each athlete runs a 100-meter sprint; the response variable is sprint time in seconds. Which statement is best supported by the design of this study?
A cross-country team recorded the time (in minutes) it took each of 30 runners at the school to complete a 1-mile trial on the same flat course, timing each runner with a stopwatch. The dotplot below shows the distribution of mile times. Which feature of the distribution is most evident?
A nutritionist compares daily sodium intake (mg) and systolic blood pressure (mmHg) for adults. The scatterplot shows a weak positive linear trend with substantial scatter. Which statement about correlation is correct?
An online retailer compares the mean number of items per order for two types of customers. Each week, it takes an independent random sample of $n_1=60$ new customers and $n_2=60$ returning customers and computes $\bar{x}_{new}-\bar{x}_{ret}$ . Which statement is correct about what makes the sampling distribution of $\bar{x}_{new}-\bar{x}_{ret}$ approximately normal?
A company reviews orders and tracks whether an order is returned (event $A$ ) and whether the order was shipped with expedited delivery (event $B$ ). Managers think expedited shipping might be associated with different return behavior. How does knowing that $B$ occurred affect the likelihood that $A$ occurred for a randomly selected order?
A consumer advocate suspects that fewer than 50% of households in a region have access to high-speed internet. A random sample of 220 households finds that 121 have access (so $\hat{p}=0.55$ ). Which hypotheses are appropriate for testing the advocate's suspicion about the population proportion $p$ ?
A company analyzes whether the number of service calls (per month) predicts customer satisfaction score (0–100) using a random sample of 60 customers. A 95% confidence interval for the slope is $(-0.50,\ 0.20)$ satisfaction points per call. Which interpretation is correct?
A city measured daily high temperatures (in $^{\circ}$ F) for 31 days in July. The five-number summary is: min $=71$ , $Q_1=78$ , median $=83$ , $Q_3=88$ , max $=96$ . A boxplot is created from these statistics. Which feature is consistent with the summary statistics?
A delivery service recorded the distance (in miles) of 65 delivery routes in one day. The summary statistics were: mean $= 18.1$ mi, median $= 18.0$ mi, standard deviation $= 4.2$ mi, five-number summary $(8.5, 15.0, 18.0, 21.0, 27.5)$ , and IQR $= 6.0$ mi. Which interpretation is correct?
Which of the following is the best interpretation of the standard deviation of J?
How is the residual for this car calculated?
A sociologist wants to compare the distribution of preferred commuting method (car, public transit, bike, walk) between two cities. Independent random samples are taken: 250 commuters from City 1 and 220 commuters from City 2, and each commuter reports their preferred method. The sociologist wants to test whether the distribution of commuting preference is the same in both cities. Which inference procedure is most appropriate?
A factory machine produces parts, and a technician inspects parts one by one until finding the first part that fails inspection. Assume each inspected part is independent and the probability a part fails is constant. The technician records the number of parts inspected until the first failure. Why is a geometric model appropriate?

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