Practice Test 82 - AP Statistics

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

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1. A principal wants to estimate the average number of hours of sleep per night for all students at the high school. She selects a sample by surveying students who arrive early to school to attend a 7:00 a.m. tutoring program, recording their reported sleep from the previous night. Which issue most threatens the validity of this sampling method?
2. A city claims that households with smart thermostats use less electricity per month on average than households without smart thermostats. A 95% confidence interval for $(\mu_{\text{smart}}-\mu_{\text{not smart}})$ is $( -42,\ -10)$ kWh. Is the claim supported by this interval?
3. An analyst studies the relationship between a stock's daily price change and the daily change in a major market index for a random sample of 60 trading days. The calculated slope of the least-squares regression line is $b = 0.02$. What is the main purpose of conducting a hypothesis test for the slope in this context?
4. A relative frequency table is given for the political affiliation of 500 voters in a district: Party A: 0.44, Party B: 0.38, Party C: 0.12, Independent: 0.06. A commentator states that Parties A and B together represent an overwhelming majority of voters. What is the combined frequency of voters for Party A and Party B?
5. A city planner recorded data for 15 neighborhoods on distance to the city center ($x$, in miles, from 0.5 to 12) and average monthly rent ($y$, in dollars, from 900 to 2400). The least-squares regression line predicting rent from distance is $\hat{y}=2350-85x.$ The purpose of this linear model is to describe the linear trend and predict typical rent for neighborhoods within the observed distances. Which interpretation of the model is correct?
6. A company tracks the number of minutes employees spend commuting. For all employees, the population mean commute time is $\mu=28$ minutes and the distribution is strongly right-skewed. An HR analyst repeatedly selects simple random samples of size $n=100$ employees and computes the sample mean commute time $\bar{x}$. Which statement about the sampling distribution of $\bar{x}$ is correct?​
7. A teacher models the relationship between number of absences ($x$) and final course average ($y$) for 28 students. A 90% confidence interval for the true slope is $( -4.1,\ -1.0)$ points per absence. Which interpretation is correct?
8. The manager's observation is an example of identifying an apparent pattern. What is the most appropriate next step from a statistical perspective?
9. A company estimates that 41% of customers choose express shipping. Many random samples of $n=20$ customers are taken and $\hat p$ is computed each time. Which statement about the sampling distribution is correct?
10. A company is testing whether a new training program changes mean time (in minutes) to complete a task compared with the old program. A random sample of 25 employees trained with the new program had a mean time of 14.2 minutes, and a random sample of 27 employees trained with the old program had a mean time of 15.0 minutes. The research claim is that the mean times are different. Which hypotheses are appropriate?
11. An ecologist measures fertilizer amount (x, in grams) and plant height after 4 weeks (y, in cm) for several pots. The scatterplot shows height increasing, then decreasing at higher fertilizer levels (an inverted U-shape). Which feature suggests a linear model is not appropriate for predicting height from fertilizer amount?
12. In a factory, let $X$ be the number of seconds it takes Machine A to seal a package and $Y$ be the number of seconds it takes Machine B to seal a package. Assume $X$ and $Y$ are independent, with $\mu_X=12$, $\sigma_X=3$, $\mu_Y=10$, and $\sigma_Y=2$. Define the combined variable $T=X+Y$, the total time to seal two packages (one on each machine). Which statement about $T$ is correct?
13. An online retailer claims that customers choose shipping speed in these proportions: Standard 0.55, Expedited 0.30, Overnight 0.15. A random sample of $n=200$ orders yields the counts below. A chi-square goodness-of-fit test returns p-value = 0.11. What conclusion is appropriate at the $\alpha=0.05$ level? Observed/Expected counts (with p-value):

    Shipping speed	Observed	Expected
    Standard	120	110
    Expedited	54	60
    Overnight	26	30

    p-value = 0.11
14. A restaurant chain wants to estimate the mean customer satisfaction rating (1–5) for all customers nationwide. The chain randomly selects 50 of its 500 locations using a random number generator. At each selected location, managers survey the first 20 customers who dine in on a Monday morning, for a total of about 1,000 surveys. Which statement best describes the sample representativeness?
15. A wildlife biologist studies the weights of a certain fish species. The population distribution of fish weights is not normal: it is left-skewed because of a minimum size limit and a few unusually light fish. A random sample of $n=100$ fish is taken, and the sample mean weight is calculated. Why is the sampling distribution of the sample mean approximately normal?
16. A political scientist wants to compare the proportion of voters who support a ballot measure between registered Democrats and registered Republicans. From a random sample, 120 of 300 Democrats support the measure and 98 of 280 Republicans support the measure. Which inference procedure is most appropriate to test whether the support proportions differ between the two parties?
17. A manufacturer advertises that at least $98\%$ of its light bulbs last 1,000 hours. A quality-control inspector tests a random sample of $n=200$ bulbs and finds $190$ last 1,000 hours (so $\hat{p}=0.95$). Which hypotheses are appropriate to test whether the advertisement is too optimistic?
18. A student uses a random number generator to pick integers from 1 to 6 (like a die). In 30 generated values, each number 1–6 appears exactly 5 times. Under random behavior, counts tend to be roughly equal but not usually perfectly equal in small samples; perfect balance can happen but is not required. Is this outcome consistent with random behavior?
19. An environmental scientist models ozone level (ppb) as a function of daily temperature (°F) using data from randomly selected summer days. The scientist claims: "Higher temperatures are associated with higher mean ozone levels." A 90% confidence interval for the slope is $(-0.4,\ 2.1)$ ppb per °F. Is the claim supported by the confidence interval?
20. A movie theater recorded 250 customers by whether they bought popcorn and whether they attended a matinee or evening show. If popcorn purchase and show time are independent, which expression calculates the expected count for the Popcorn & Evening cell?

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