AP Statistics Full-length practice exam 2

A large school district conducts a two-sample $z$-test and finds a statistically significant difference in graduation rates between two schools ($p$-value = 0.002). The school with the lower rate has ${\hat{p}}_1=0.91$ vs. ${\hat{p}}_2=0.93$. What is the most important caveat when reporting these results?

A researcher conducts a one-sample $t$-test with $n=12$, $\bar{x}=55$, $s=8$, testing $H_0:\mu =50$ vs. $H_a:\mu \ne 50$. Compute the $t$ test statistic.

Regression of hours of TV watched per day on sleep hours gives the following computer output:

$n=25$, $r^2=0.24$

Which of the following best describes the result of the test of the slope?

Events $A$ and $B$ satisfy $P(A)=0.4$, $P(B)=0.5$, and $P(A\cap B)=0.2$. Are $A$ and $B$ independent?

Two sampling distributions are described: (I) $n=25$ samples from a symmetric, bell-shaped population; (II) $n=100$ samples from a heavily skewed population. Which is more likely to be approximately normal?

A data set of 12 exam scores has a mean of 78 and a median of 82. Which of the following best describes the shape of the distribution?

Which of the following correctly identifies an outlier using the 1.5 × IQR rule? A data set has Q1 = 20, Q3 = 50, and contains the value 95.

In a standard deck of 52 cards, two cards are drawn without replacement. Given that the first card drawn is an ace, what is the probability that the second card is also an ace?

A stemplot of hourly wages (in dollars) for 10 part-time workers is shown below. What is the median wage?

An experiment randomly assigns participants to one of three diets. After 8 weeks, mean weight loss is compared across groups. Which principle of experimental design ensures that unmeasured variables (like initial metabolism) are evenly distributed among the groups?

In an experiment on plant growth, a researcher uses 24 plants from 6 different species (4 of each). She randomly assigns 2 plants of each species to receive fertilizer and 2 to a control group. What design is this?

A study finds a statistically significant difference between two teaching methods at $\alpha =0.05$. The mean score difference is 2 points on a 100-point exam. What is the most important follow-up consideration?

In a goodness-of-fit test with $k=4$ categories, the expected frequencies are each 25 and the observed frequencies are 20, 30, 22, 28. Compute ${\chi }^2$.

A researcher wants to estimate the proportion of adults who exercise regularly. She samples 400 adults and finds 160 exercise regularly. What is the 95% confidence interval for the true proportion?

A $t$-test for the mean produces $t=2.45$ with $df=14$. For $H_a:\mu >50$, the $p$-value is between 0.01 and 0.025. At $\alpha =0.05$, what conclusion should be drawn?

A chi-square test for independence is conducted on a $3\times 4$ contingency table. What are the degrees of freedom?

A geometric random variable $X$ counts the number of trials until the first success, where $p=0.25$. What is $P(X=3)$?

A researcher removes one influential point from a scatterplot. After removing it, $r$ increases from 0.60 to 0.91. What type of point was removed?

A sample proportion $\hat{p}=0.55$ is calculated from a sample of $n=200$. The population proportion is claimed to be $p=0.50$. What is the approximate $z$-score for $\hat{p}$?

A study finds that towns with more fast-food restaurants have higher rates of obesity. A researcher concludes that fast food causes obesity. Which of the following is the strongest critique of this conclusion?

A biology class recorded the number of seeds that germinated out of 20 seeds for each of 30 students. The data are roughly bell-shaped with mean $\bar{x}=14.2$ and $s=2.1$. Using the normal model, approximately what proportion of students had fewer than 10 seeds germinate?

A population has mean $\mu =50$ and standard deviation $\sigma =10$. A simple random sample of size $n=25$ is taken. What is the standard deviation of the sampling distribution of $\bar{x}$?

A 3×2 contingency table (3 education levels × 2 voting outcomes) shows the following row totals and column totals:

The expected count for the High school/Voted cell is $E_{11}$. Compute ${\chi }^2$ for this cell if the observed count is 40.

A chi-square test of independence produces ${\chi }^2=9.2$ with $df=3$. The critical value at $\alpha =0.05$ is 7.815. What is the correct conclusion?

A scatterplot of hours studied ($x$) versus exam score ($y$) for 20 students shows a positive linear association with no obvious outliers. The correlation coefficient is $r=0.83$. What does this value tell us?

A 95% confidence interval for the difference in mean scores ${\mu }_1-{\mu }_2$ between two schools is $(-3,11)$. What can you conclude at $\alpha =0.05$?

A researcher increases the confidence level from 90% to 99% while keeping the sample size constant. What happens to the confidence interval?

A poll finds that 54 of 200 surveyed voters support a ballot measure. A reporter states: "We are 95% confident that between 20.5% and 33.5% of all voters support the measure." How should this interval be correctly interpreted?

A two-sample $t$-test compares mean test scores for two independent classes (Class A: $n_1=25$, Class B: $n_2=30$). Assuming unequal variances, what are the degrees of freedom? (Use the conservative formula: $df=\min (n_1-1,n_2-1)$.)

Two independent random samples are taken from two populations. Group 1: $n_1=20$, ${\bar{x}}_1=45$, $s_1=6$. Group 2: $n_2=20$, ${\bar{x}}_2=41$, $s_2=7$. What is the test statistic for testing $H_0:{\mu }_1={\mu }_2$?

A researcher wants to estimate a population proportion to within ±0.04 with 95% confidence, but has no prior estimate of $p$. What minimum sample size is needed?

The regression equation for predicting a city's high temperature in July ($y$, °F) from its latitude ($x$, degrees north) is $\hat{y}=115-1.1x$. Interpret the $y$-intercept in context.

A teacher wants to determine whether students improved from a pre-test to a post-test. Each of 15 students took both tests. What is the appropriate procedure?

A set of exam scores has mean 70 and standard deviation 10. Each score is multiplied by 1.05 (a 5% curve), then 3 points are added. What are the new mean and standard deviation?

A least-squares regression line is fit to data on advertising spending ($x$, thousands of dollars) and sales ($y$, thousands of units). The residual for one observation is $+12$. What does this mean?

A dot plot shows the ages (in years) of 9 trees: 3, 5, 5, 7, 8, 9, 10, 12, 40. Which measure of center best represents the typical age, and why?

A school wants to estimate the proportion of students who bike to school. They survey every 10th student on the enrollment list. What type of sampling method is this?

A researcher collects a random sample of 20 measurements and wants to construct a confidence interval for the population mean. The population standard deviation is unknown. Which distribution should be used?

A student claims that because $P(A)=0.5$ and $P(B)=0.4$, events $A$ and $B$ cannot both occur since $P(A)+P(B)=0.9<1$. Is this reasoning valid?

A die is rolled 60 times and the observed frequencies for each face are recorded. A chi-square goodness-of-fit test is used to check if the die is fair. What are the degrees of freedom?