Practice Test 13 - AP Statistics

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

A delivery company randomly samples 36 packages and records delivery times (in days). A one-sample $t$ interval gives a 95% confidence interval for the population mean delivery time of $(2.4,\ 2.9)$ days. Which interpretation is correct?
A city council wants to know whether a majority of residents support a proposed recycling ordinance. A random sample of 400 residents found 228 in favor. A one-sample $z$ test for a population proportion was conducted at significance level $\alpha=0.05$ to test $H_0: p=0.50$ versus $H_a: p>0.50$ . The test produced a $p$ -value of 0.018, so the council rejected $H_0$ . Which conclusion is appropriate?
A track coach times 40 athletes in the 100-meter dash (seconds) during tryouts and wants a model to estimate what fraction run under a certain cutoff time. The histogram of times is unimodal and approximately symmetric. Why is a normal model reasonable here?
An environmental scientist models the relationship between daily high temperature ( $x$ , in $^0$ F) and electricity use ( $y$ , in kWh) for 30 randomly selected days. A 90% confidence interval for the population slope is $(-1.5, 0.4)$ kWh per $^0$ F. Which interpretation is correct?
A card is drawn at random from a standard 52-card deck. Let Event A be "the card is a heart" and Event B be "the card is a face card (J, Q, or K)." Which statement about Events A and B is correct?
A college investigates whether attending review sessions ( $x$ , number of sessions) predicts final course grade ( $y$ ) for 55 students. The professor claims that each additional session increases the mean grade by more than 2 points. A 95% confidence interval for the slope is $(1.1, 2.6)$ grade points per session. Is the claim supported by the confidence interval?
A farmer measures the weights (in pounds) of 50 pumpkins harvested from one field. The five-number summary is: min $=6.2$ , $Q_1=8.5$ , median $=10.1$ , $Q_3=12.4$ , max $=18.0$ . A boxplot is constructed from these values (no outliers marked). Which feature is consistent with the summary statistics?
A company advertises that 95% of its shipments arrive on time. A quality-control analyst randomly selects 150 shipments and finds 135 arrived on time. A one-sample $z$ test for a population proportion is run with $H_0: p=0.95$ and $H_a: p\ne 0.95$ at $\alpha=0.10$ . The test yields a $p$ -value of 0.072, so the analyst rejected $H_0$ . Which conclusion is appropriate?
A public health researcher compares the proportion of adults who got a flu shot this year in two counties. From independent random samples, a 90% confidence interval for the difference in proportions (County A minus County B) is $(-0.11, 0.03)$ . Which interpretation is correct?
A wildlife biologist expects, based on a long-term model, that sightings of a bird species across 5 habitats occur in proportions: 0.15 Wetland, 0.25 Forest, 0.20 Grassland, 0.30 Shrubland, 0.10 Urban. In a random sample of 500 sightings, the observed counts are: Wetland 92, Forest 118, Grassland 93, Shrubland 146, Urban 51. A chi-square goodness-of-fit test gives $p$ -value = 0.049. Expected counts under $H_0$ are: Wetland 75, Forest 125, Grassland 100, Shrubland 150, Urban 50. What conclusion is appropriate at $\alpha=0.05$ ?
A city bus arrives at a stop, and one passenger is randomly selected from those who board. Let event $A$ be "the passenger pays with a student pass" and event $B$ be "the passenger pays with cash." The fare system allows a passenger to use exactly one payment method when boarding. Are the two events mutually exclusive?
A school librarian records the number of pages in 32 randomly selected mystery novels. The five-number summary is: min $=120$ , $Q_1=210$ , median $=280$ , $Q_3=360$ , max $=980$ . A modified boxplot (1.5·IQR rule) is drawn. Which feature is consistent with the summary statistics?
A company advertises that 62% of its customers renew their subscription. A statistician takes many random samples of $n=100$ customers and records $\hat p$ each time. Which statement about the sampling distribution is correct?
A botanist records the height (cm) of a random sample of 25 sunflowers grown with a new fertilizer. The botanist wants to test the claim that the mean height of sunflowers grown with this fertilizer is greater than 180 cm. No population standard deviation is known. Which inference procedure is most appropriate?
A student repeatedly rolls a standard six-sided die 25 times and records whether the result is a 6. A success is "roll a 6," and exactly 25 rolls are made. Does this meet binomial conditions for the number of successes?
A website shows exactly 40 visitors a new page layout. For each visitor, the site records whether the visitor clicks the "Buy" button (success) or does not click (failure). The site uses the same layout for all 40 visitors and assumes each visitor's decision is independent of the others. Does this meet the binomial conditions?
A public health team is investigating whether the proportion of residents who regularly wear a seat belt differs between residents in rural counties and residents in urban counties. In a survey, 162 of 200 rural residents reported regularly wearing a seat belt, and 190 of 220 urban residents reported regularly wearing a seat belt. The research claim is that the proportions differ. Which hypotheses are appropriate?
A health clinic wants to estimate the proportion of adults in its county who received a flu shot this season. A nurse sampled 300 patients who came to the clinic during a two-day period and found that 64% reported receiving a flu shot. The clinic concluded that "about 64% of adults in the county received a flu shot this season." Which statement explains whether the conclusion is valid?
A website monitors whether a randomly selected visitor makes a purchase (P) or not (N), so the sample space is $\{P, N\}$ . Over a long period, the site estimates $P(P)=0.15$ . Which statement correctly describes the probability $0.15$ in this context?
A university wants to know whether a brief mindfulness session reduces test anxiety. From all students enrolled in Intro Psychology (about 1200 students), the researchers take a simple random sample of 200 students. These 200 students are then randomly assigned to either (1) attend a 10-minute guided mindfulness session right before an exam or (2) sit quietly for 10 minutes right before the exam. Immediately after the exam, students complete a standardized anxiety questionnaire. Which conclusion is justified based on the design?

Practice tests