Practice Test 39 - AP Statistics

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

A fair six-sided die is rolled once. Let Event A be "the result is even" and Event B be "the result is greater than 4." Which statement about Events A and B is correct?
A city health department collected data on neighborhood type (Urban or Suburban) and whether residents get a flu shot (Yes or No). The results are shown in a table. Which comparison is appropriate for assessing the relationship between neighborhood type and flu-shot status using conditional distributions?
A school district wanted to study whether a new online homework platform improves Algebra 1 test scores. From all 12 Algebra 1 teachers in the district, the district randomly selected 6 teachers to use the new platform for one semester; the other 6 teachers continued with the usual platform. All students in each selected teacher's classes used that teacher's assigned platform. At the end of the semester, the mean test score was higher in classes using the new platform. Which conclusion is justified based on the design of this study?
A company recorded the number of emails received per day by 40 employees. The summary statistics were: mean $= 58$ , median $= 57$ , standard deviation $= 11$ , five-number summary $(32, 50, 57, 65, 83)$ , and IQR $= 15$ . Which interpretation is correct?
A school cafeteria manager claims that students choose among four lunch options in the following distribution: Pizza 40%, Salad 25%, Sandwich 20%, and Pasta 15%. On a randomly selected day, the manager records the lunch choices of $n=200$ students with the observed counts shown in a table. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the manager's claim?
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 call center tracks the length of individual customer calls (in minutes). The population mean is $\mu=8.0$ minutes with population standard deviation $\sigma=5.0$ minutes, and the population distribution is strongly right-skewed. Each day, a supervisor takes a simple random sample of $n=25$ calls and computes the sample mean $\bar{x}$ . Over many days, which statement about the sampling distribution of $\bar{x}$ is correct?
A gym manager wants to study whether class format is associated with how many days per week members attend. For each of 120 randomly selected members, the manager records the member's primary class format (coded 1 = cycling, 2 = yoga, 3 = strength) and the number of days the member attended the gym last week. The observational units are the individual gym members. Which classification is correct for the two recorded variables?
A public health official claims that more than 10% of adults in a county have received a flu shot this month. A random sample is used to compute an 80% confidence interval for the true proportion $p$ : $(0.09,\ 0.13)$ . Is the claim supported by the confidence interval?
Two medications are compared for the proportion of patients who report a certain side effect. A 95% confidence interval for the difference in proportions, defined as $p_{MedX} - p_{MedY}$ , is $(-0.02,\ 0.09)$ . A nurse claims, "MedX causes side effects in a higher proportion of patients than MedY." Is the claim supported by the confidence interval?
A cereal box label states the mean net weight is $\mu=18$ ounces. A quality-control analyst suspects the mean is less than stated. A random sample of 12 boxes is selected and a one-sample $t$ test is performed with $H_0:\mu=18$ versus $H_a:\mu<18$ at $\alpha=0.05$ . The p-value is 0.26. What conclusion is appropriate?
An environmental group wants to compare recycling behavior across three neighborhoods. Independent random samples of households are taken from Neighborhood A, B, and C. Each household is classified as Recycles regularly (Yes/No). Results are shown. Which test is appropriate, and what are the correct hypotheses?
A student claims to have randomly guessed answers (A–E) on a 30-question multiple-choice quiz. The recorded guesses show a very regular pattern: A, B, C, D, E, A, B, C, D, E, A, B, C, D, E, A, B, C, D, E, A, B, C, D, E, A, B, C, D, E. Under random behavior, you might see repeats and clusters, but a perfectly repeating 5-letter cycle is unusual. Is the pattern consistent with random behavior?
A hospital records one patient's status at a randomly chosen time today. Let event $A$ be "the patient is in the emergency department" and event $B$ be "the patient is in the operating room." Hospital policy states a patient can be in only one location at a time. Are the two events mutually exclusive?
A developer compares mean battery life (hours) of phones running Operating System P versus Operating System Q. Using independent random samples, a 95% confidence interval for $(\mu_P-\mu_Q)$ is $(0.0,\,1.8)$ . Which interpretation is correct?
A factory's historical defect rate is 2%. A quality inspector randomly checks 50 items from today's production, expecting about 1 defect, but finds 4 defects. Assuming the true defect rate is still 2% and items are independent, is the result unexpected due to random chance?
A discrete random variable $R$ represents the number of red lights a commuter hits on the way to work. The distribution of $R$ has mean $\mu_R=4.2$ and standard deviation $\sigma_R=1.1$ . Which interpretation of the mean is correct?
An ergonomics specialist compares mean typing speed (words per minute) between people using an ergonomic keyboard and a standard keyboard. Using independent random samples, a 90% confidence interval for $(\mu_{\text{ergo}}-\mu_{\text{standard}})$ is $(-3.5,\ 2.1)$ . Which interpretation is correct?
A new law is proposed in a state. The law will be enacted if it can be shown that the proportion of registered voters who support it is greater than 0.50. A politician plans to conduct a survey to gather evidence in favor of the law. Let $p$ be the true proportion of voters who support the law. Which hypotheses should the politician test?
An economist fits a regression model predicting household savings rate (percentage points) from annual income (in thousands of dollars) using a random sample of households. The economist claims: "Higher income is associated with a higher mean savings rate." A 95% confidence interval for the slope is $(0.10,\ 0.10)$ percentage points per thousand dollars. Is the claim supported by the confidence interval?

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