Practice Test 1 - AP Statistics

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

The heights of adult male giraffes in a wildlife reserve are approximately Normal with mean $\mu=5.4$ meters and standard deviation $\sigma=0.3$ meters. The normal curve below marks a height of 4.8 meters. Which statement about the marked value is correct?
A company compares two versions of a website checkout page. Visitors are randomly assigned to version A or version B, and the company records whether each visitor completes a purchase (yes/no). After one week, 120 of 400 visitors assigned to A purchase, and 150 of 420 visitors assigned to B purchase. Which inference procedure is most appropriate to test whether the purchase rates differ between the two versions?
A student investigates whether weekly study time (in hours) predicts exam score (out of 100) for a random sample of students at a school and fits a least-squares regression line with exam score as the response. A 95% confidence interval for the population slope is $(1.8,\ 4.6)$ . Which interpretation is correct?
A school district predicts that the distribution of students' primary mode of transportation is 40% bus, 35% car, and 25% walk/bike. A random sample of 120 students is surveyed, and a chi-square goodness-of-fit test is conducted at $\alpha=0.05$ . The summary is below. What conclusion is appropriate? Observed/Expected counts and p-value: - Bus: Observed 44, Expected 48 - Car: Observed 39, Expected 42 - Walk/Bike: Observed 37, Expected 30 - p-value = 0.18
Two independent random samples are taken to compare mean commute times (in minutes) for City A and City B. The samples have sizes $n_A=30$ and $n_B=30$ . Let $\bar{x}_A-\bar{x}_B$ be the difference in sample means. Which statement is correct about the shape of the sampling distribution of $\bar{x}_A-\bar{x}_B$ ?
Two fair six-sided dice are rolled. Let Event A be "the sum is 7" and Event B be "at least one die shows a 4." Which statement about Events A and B is correct?
A public health department wants to estimate the mean number of sugary drinks consumed per week by adults in a city. The plan is to post an online survey link on the department's social media pages and analyze the responses received over one week. The research question is: "What is the mean weekly number of sugary drinks consumed by all adults in the city?" Which aspect is most important to address before collecting data?
A hospital compared mean recovery time (days) for patients receiving a new therapy (N) versus standard therapy (S), using independent random samples. A 95% confidence interval for $\mu_N-\mu_S$ is $( -2.4,\ -0.6)$ days. Which interpretation is correct?
A city compared mean commute times for two independent groups: commuters who use public transit (T) and commuters who drive (D). A 92% confidence interval for $\mu_T-\mu_D$ is $(3,\ 11)$ minutes. Which interpretation is correct?
A restaurant manager studies whether the number of tables served per hour ( $x$ ) predicts average tip amount in dollars ( $y$ ) for servers. The manager suspects that serving more tables per hour is associated with higher tips in the population. Which hypotheses are appropriate for testing this claim about the slope in the regression of $y$ on $x$ ?
A researcher collects data on the preferred type of movie from a sample of moviegoers. The categories are Action, Comedy, Drama, and Sci-Fi. Which of the following is NOT information that can be obtained from a frequency table of this data?
A fitness study compares mean resting heart rate (beats per minute) for people who meditate daily (M) versus those who do not (N). A 95% confidence interval for $\mu_M-\mu_N$ is $(-6.5,\ -1.2)$ . The researchers claim daily meditation is associated with a lower mean resting heart rate. Is the claim supported by the interval?
A random sample of 120 smartphones from a shipment found that 9 have a defective screen. A 90% confidence interval for the true proportion $p$ of all smartphones in the shipment with defective screens is $(0.03,\ 0.12)$ . Which interpretation is correct?
Scores on a district algebra final for all 11th graders are approximately Normal with mean $\mu=72$ points and standard deviation $\sigma=10$ points. A normal curve is shown with the value $92$ marked on the x-axis. Normal curve (scores) | | .-''''-. | .-' '-. | .' '. | / \ |----------|----|----|----|----|----|----|----|----|----> x 42 52 62 72 82 92 102 $\mu=72$ 92 Which statement about the marked value is correct?
A biologist uses linear regression to predict plant height (cm) from hours of sunlight per day for a random sample of 22 plants. A 98% confidence interval for the slope is $(-0.3,\ 1.9)$ cm per hour. Which interpretation is correct?
A hospital tests a new rapid screening tool for sepsis using a sample of emergency-room patients and finds a statistically significant improvement in early detection compared with the current protocol. Based on this inference, administrators must decide whether to replace the current protocol across the hospital. Why is it important to consider potential error when using this statistical result to make the decision, given that missing sepsis can be life-threatening but unnecessary treatment can also cause harm?
A researcher recorded reaction times (in milliseconds) for 64 participants completing a computer task. The summaries were: mean $=312$ ms, median $=305$ ms, SD $=38$ ms, five-number summary $(240,\ 285,\ 305,\ 330,\ 420)$ , and IQR $=45$ ms. Which interpretation is correct?
A business tracks advertising spending (x, in thousands of dollars) and weekly sales (y, in thousands of dollars) over 14 weeks. The scatterplot shows sales increasing slowly at first, then more rapidly, suggesting an upward curve. Which feature suggests a linear model is not appropriate for predicting sales from advertising spending?
A store tracks revenue from online sales $O$ and in-store sales $S$ (in hundreds of dollars) for a day. Assume $O$ and $S$ are independent with $\mu_O=18$ , $\sigma_O=4$ , $\mu_S=30$ , and $\sigma_S=6$ . Define $D=S-O$ , the difference (in-store minus online). Which statement about $D$ is correct?
A student takes a multiple-choice quiz and then reports whether they studied. Let event $A$ be "the student scores at least 90%," and event $B$ be "the student studied." Suppose, for this quiz, studying and scoring at least 90% are independent events (based on a large dataset from past classes). How does knowing that $B$ occurred affect the likelihood of $A$ ?

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