Two hundred students each take a random sample of $50$ households and record the sample proportion that own a dog. The $200$ proportions are graphed together. What does that graph show?

A teacher has $150$ classes each take a random sample of $30$ students and compute the sample mean homework time. The $150$ means are graphed. What distribution is being approximated?

Donations to a school fundraiser are strongly right-skewed with $\mu =18$ dollars and $\sigma =30$ dollars. Random samples of $10$ donations are taken. Why does the central limit theorem give little help?

Machine lifetimes are strongly right-skewed with mean $1200$ hours. Random samples of $64$ machines are taken. What does the central limit theorem say about the distribution of $\bar{x}$?

For samples of size $36$ from a population with $\sigma =12$ kilograms, the standard error of $\bar{x}$ is $2$ kilograms. What is the standard error for samples of size $144$ from the same population?

A population proportion is $p=0.40$. For random samples of $400$ people, what is the standard error of $\hat{p}$, rounded to three decimals?

Sixty percent of a large city recycles. In a random sample of $600$ people, what is the probability to three decimals that $\hat{p}$ is below $0.56$, given area below $z=2$ is $0.9772$?

A large program has completion rate $p=0.30$. In random samples of $400$ people, what is $P(\hat{p}>0.345)$ to three decimals, given area below $z=1.96$ is $0.9750$?

Clinic wait times have $\mu =24$ minutes and $\sigma =9$ minutes. For random samples of $81$ patients, use the empirical rule to find the probability that $\bar{x}$ falls between $23$ and $25$ minutes.

Cereal box masses have $\mu =500$ grams and $\sigma =16$ grams. For random samples of $64$ boxes, what is $P(\bar{x}>504)$ to three decimals, given area below $z=2$ is $0.9772$?

A biologist builds a $99\%$ confidence interval and a $95\%$ confidence interval for mean leaf length from the same sample. How does the $99\%$ interval differ?

A factory uses a method that makes $90\%$ confidence intervals for the mean bottle volume. What does the $90\%$ confidence level mean?

A $95\%$ confidence interval for a proportion from $600$ voters has margin of error $0.04$. Among lowering confidence to $90\%$, raising it to $99\%$, or using only $300$ voters, what makes the margin smaller?

A known population standard deviation is $10$ grams. For a $95\%$ confidence interval for a mean with $n=100$ and $z^{\ast }=1.96$, what is the margin of error to two decimals?

A $99\%$ confidence interval for mean seedling height has margin of error $3.4$ centimeters. Using the same data, how would a $95\%$ interval's margin of error compare?

A pollster takes a random sample of $50$ people from a town of $1200$ for a one-proportion z interval, and the sample has $4$ successes. What condition fails?

A random sample of $18$ fish is used for a t interval for mean length. The population has $500$ fish, and the histogram shows the sample lengths. What condition is most concerning?

A $95\%$ confidence interval for mean test score difference, new method minus old method, is $-1.2$ to $4.8$ points. What does the interval support?

A $95\%$ confidence interval for the proportion of voters supporting a school plan is $0.52$ to $0.60$. What does this interval support?

In a random sample of $900$ adults, $405$ exercise daily. With $z^{\ast }=1.96$, what is the margin of error for a $95\%$ confidence interval for the proportion, to four decimals?

A random sample of $200$ households has $124$ that recycle weekly. With $z^{\ast }=1.96$, what is the $95\%$ confidence interval for the proportion, rounded to three decimals?

A factory sample finds $48$ defective parts in $800$ parts. With $z^{\ast }=1.645$, what is the $90\%$ confidence interval for the defect proportion, rounded to three decimals?

A random sample of $36$ cartons has $\bar{x}=1.02$ liters and $s=0.06$ liters, with $t^{\ast }=2.030$. What is the $95\%$ confidence interval for the mean, to three decimals?

A random sample of $25$ plants has $\bar{x}=18.6$ centimeters and $s=4.0$ centimeters. With $t^{\ast }=2.064$, what is the $95\%$ confidence interval for the mean, to one decimal?

A researcher wants margin of error $2$ units at $95\%$ confidence for a population mean, with $\sigma =12$ units and $z^{\ast }=1.96$. What sample size is needed?

A poll wants a $95\%$ confidence interval for a proportion with margin of error at most $0.03$. With no prior estimate, use $p=0.50$ and $z^{\ast }=1.96$. What sample size is needed?

A chip maker claims at most $3\%$ of chips are defective, and a buyer suspects the true rate is higher. What hypotheses fit the buyer's test?

A school says the mean bus ride is $20$ minutes, and a parent thinks the true mean is less. What hypotheses fit the parent's test?

An app redesign is meant to change the proportion of users who finish signup from the old rate $0.70$, in either direction. What hypotheses fit this test?

A quality engineer must detect any drift in mean fill volume away from the $500$ milliliter target, whether high or low. What alternative hypothesis fits?

A farmer wants evidence that a new seed treatment increases germination above the old rate of $85\%$. What alternative hypothesis should be used?

A test of whether a coin is fair gives a p-value of $0.61$. What does that p-value say?

A test of whether a cafe's mean wait exceeds $5$ minutes gives p-value $0.032$. What is the correct interpretation?

A one-sample t test gives $t=2.68$ with $14$ df and p-value $0.018$, tested at $\alpha =0.01$. What is the decision?

A z test for a city proportion gives p-value $0.004$ at $\alpha =0.05$. What is the decision?

A chi-square test for a school survey gives p-value $0.087$ at $\alpha =0.10$. What is the decision?

A test of whether a water supply exceeds the lead limit fails to reject $H_0$ when the supply truly does exceed the limit. What error is this, and what is the cost?

A medical screen tests $H_0$: disease absent against $H_a$: disease present. The test rejects $H_0$ for a person who truly is not diseased. What error is this?

A factory tests $H_0:\mu =1000$ grams against $H_a:\mu <1000$ grams. It fails to reject $H_0$ when the true mean is $990$ grams. What error is this?

A two-sided test of $H_0:\mu =40$ minutes for mean delivery time gives p-value $0.004$ at $\alpha =0.05$. What conclusion is correct?

A one-sided test for whether a new fertilizer increases mean yield gives p-value $0.12$ at $\alpha =0.05$. What conclusion is correct?

A cable company claims $40\%$ of households subscribe. In a random sample of $500$ households, $180$ subscribe. What is the one-proportion z statistic, rounded to two decimals?

A clinic's goal is $90\%$ on-time appointments. In a random sample of $300$ appointments, $282$ are on time. What is the one-proportion z statistic for testing the goal, to two decimals?

A random sample of $25$ batteries gives $\bar{x}=9.4$ hours and $s=1.5$ hours, tested against claimed $\mu =10$ hours. What is the t statistic?

A sample of $16$ bottles has $\bar{x}=251$ milliliters and $s=4$ milliliters, tested against target $\mu =250$ milliliters. What is the t statistic?

A researcher measures each of $18$ patients' blood pressure before a four-week program and again after it. What inference procedure fits the data?

A scientist compares mean nitrate concentration from independent random samples of $12$ upstream sites and $14$ downstream sites. What inference procedure fits?

A $95\%$ confidence interval for $p_1-p_2$, the difference in approval between two cities, is $0.01$ to $0.11$. What does the interval support?

Clinic A has $84$ successes in $200$ trials, and Clinic B has $65$ successes in $250$ trials. Using the pooled proportion, what is the two-proportion z statistic for $p_A-p_B$, to two decimals?

Two fertilizers give ${\bar{x}}_1=32.4$ and ${\bar{x}}_2=29.8$ bushels per hectare, with standard error of the difference $1.3$ bushels. What is the t statistic?

Two classes have mean scores $78.4$ and $75.1$ points. The standard error for ${\bar{x}}_1-{\bar{x}}_2$ is $1.5$ points. What is the t statistic, to two decimals?

The calculator output gives a two-sample t test with p-value $0.0241$ for a difference in means. At $\alpha =0.05$, what is the decision?

The calculator output gives a two-proportion z test comparing two clinics, with p-value $0.2263$. At $\alpha =0.05$, what is the decision?

A chi-square test compares two treatments across three outcomes, so the observed-count table has $2$ rows and $3$ columns. How many degrees of freedom does the test use?

A chi-square test for independence has one expected count equal to $4.0$, while all other expected counts exceed $5$. What condition for the chi-square test fails?

A fair die is rolled $120$ times and the six faces occur $26,14,22,19,18,$ and $21$ times. Under the fair-die claim, what is the expected count for each face?

Four candy colors are expected equally in $100$ candies. The observed counts are $18,22,30,$ and $30$. What is the chi-square goodness-of-fit statistic?

A chi-square test for independence between commute mode and work shift gives chi-squared $=3.1$ with $3$ df and p-value $0.376$ at $\alpha =0.05$. What is the conclusion?

In a two-way table of $100$ students, the junior row total is $40$ and the bus-rider column total is $25$. For a chi-square independence test, what expected count goes in the junior-bus cell?

A chi-square test for independence between club type and grade level gives chi-squared $=7.82$ with $2$ df and p-value $0.020$ at $\alpha =0.05$. What conclusion is correct?