Practice Test 19 - AP Statistics

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

A researcher wants to compare whether three different neighborhoods (North, Central, South) have the same distribution of primary commuting method (Car, Public transit, Bike/Walk). She takes separate random samples of adults from each neighborhood and records each person's commuting method. The results are shown in the two-way table. Which chi-square test is appropriate, and what are the correct hypotheses? Note: This study uses multiple groups (neighborhoods) and compares a single categorical response.
A candy company claims that the colors in its assorted bag occur in the following distribution: 30% red, 25% blue, 20% green, 15% yellow, and 10% orange. A student randomly samples 200 candies from recent bags and records the observed counts below. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the company's claim?
A fitness app company sampled 30 users and recorded average daily steps ( $x$ ) and resting heart rate ( $y$ ). A least-squares regression of $y$ on $x$ was computed. The slope test used $H_0: \beta_1=0$ vs. $H_a: \beta_1\ne 0$ and gave a p-value of 0.078 with an estimated negative slope. At the $\alpha=0.05$ level, the company failed to reject $H_0$ . What conclusion is appropriate?
A game uses a fair six-sided die. A player wins if the sum of 3 rolls is at least 14. To estimate the probability of winning, a student simulates 1000 trials: each trial consists of generating 3 random integers 1–6, summing them, and recording whether the sum is at least 14. The student gets 216 wins. Which interpretation of the simulation results is correct?
A wildlife researcher is estimating the mean wingspan (in cm) of adult birds of a certain species in a large preserve. Two independent random samples of 35 adult birds are captured, measured, and released during the same month. Sample X has a mean wingspan of 18.4 cm; Sample Y has a mean wingspan of 19.1 cm. Why might the sample results differ?
To estimate the mean amount of time (in seconds) it takes a website to load for all users, a random sample of 60 load times was collected. A 99% confidence interval for the population mean load time was $(2.10, 2.55)$ seconds. Which interpretation is correct?
A bookstore compares spending by two independent customers. Let $X$ be the amount (in dollars) spent by Customer A with $\mu_X=35$ and $\sigma_X=12$ . Let $Y$ be the amount (in dollars) spent by Customer B with $\mu_Y=28$ and $\sigma_Y=9$ . Define $W=X-Y$ , the difference in spending (A minus B). Which statement about the combined variable is correct?
Which statement correctly compares the two distributions?
Researchers compare mean resting heart rate (beats per minute) for people who drink coffee daily versus those who do not. Independent random samples were taken, and a 95% confidence interval for $(\mu_{\text{coffee}}-\mu_{\text{no coffee}})$ is $(1.2,\,5.6)$ . Which interpretation is correct?
A company measures the time (in minutes) to complete a task using two different software interfaces. In each repetition, an independent random sample of $n_1=25$ workers uses Interface 1 and an independent random sample of $n_2=100$ workers uses Interface 2. The population standard deviations are $\sigma_1=8$ and $\sigma_2=8$ . The statistic is $\bar{x}_1-\bar{x}_2$ . Which statement is correct about how the sampling distribution of $\bar{x}_1-\bar{x}_2$ would change if the company instead used $n_1=100$ and $n_2=25$ (swapping the sample sizes)?
A university wants to estimate the proportion of all undergraduates who have taken at least one online course. A simple random sample of 200 undergraduates finds that 78 have taken at least one online course. Which inference procedure is most appropriate to estimate the population proportion?
A city surveys residents about support for a new recycling program in Neighborhood A and Neighborhood B. A 90% confidence interval for the difference in support proportions, defined as $p_A - p_B$ , is $(-0.12, 0.03)$ . A council member claims, "Neighborhood A has a higher support rate than Neighborhood B." Is the claim supported by the confidence interval?
A coffee shop chain wants to estimate the mean time (in seconds) customers wait in line on weekday mornings at one location. A random sample of 40 customers last Tuesday had a mean wait of 92 seconds, while a different random sample of 40 customers last Thursday had a mean wait of 105 seconds. Both samples were taken from the same location between 7:00–9:00 AM. Why might the sample results differ?
A nutritionist compares mean daily sodium intake (mg) for adults who follow Diet A versus Diet B. From independent random samples, a 99% confidence interval for $(\mu_{A}-\mu_{B})$ is $(-420,\ -110)$ . Which interpretation is correct?
A student flips a coin repeatedly until it lands heads for the first time. A success is "heads" and a failure is "tails." The student records the number of flips needed to get the first head. Does this meet binomial conditions for modeling the number of successes in the process?
A county wants to estimate the proportion of registered voters in the county who plan to vote in the next election. The county has a list of all registered voters and uses a random number generator to select 1,000 voters from the list to contact. Only 420 of the selected voters respond. The county reports results based only on the 420 respondents. Which statement best describes the sample representativeness?
A wildlife biologist claims that a certain species of bird builds nests in three types of trees in the following proportions: 50% oak, 30% pine, and 20% maple. The biologist observes 120 nests and records the tree type for each nest; results are shown in a table. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the biologist's claim?
For a binomial distribution with mean 12 and variance 3, what is n?
A botanist measured the heights (in centimeters) of 50 sunflower plants of the same variety grown under similar conditions. The summaries were: mean $=152.1$ cm, median $=152$ cm, SD $=4.8$ cm, five-number summary $(141,\ 149,\ 152,\ 155,\ 161)$ , and IQR $=6$ cm. Which interpretation is correct?
A nutrition label claims a certain cereal has a mean of 210 calories per serving. A random sample of 30 servings is measured, and a one-sample $t$ test is performed with $H_0: \mu = 210$ calories and $H_a: \mu < 210$ calories at $\alpha=0.05$ . The p-value from the test is 0.51. What conclusion is appropriate?

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