Unit 1: Exploring One-Variable Data and Collecting Data

A city transit office wants to learn about bus travel in the city. Which of these is a statistical investigative question?

A researcher plans to randomly select 200 adults in Larkin County and record whether each has a library card. Which investigative question best fits this study?

A veterinary clinic records five things about each dog it sees: breed, weight in pounds, whether it is vaccinated, number of visits this year, and the owner's ZIP code. How many of these are quantitative variables?

A farm co-op weighs a random sample of 50 of the 4,000 apples in a delivery and finds a mean weight of 182 grams. Which statement is correct?

A bar chart shows the percent of customers satisfied with two phone plans: 81% for Plan A and 84% for Plan B. The vertical axis starts at 80%, so Plan B's bar looks four times as tall as Plan A's. What is the best description?

Which graph is appropriate for showing the distribution of one categorical variable?

The dotplot shows the wait times, in minutes, of 12 customers at a pharmacy counter. What is the median wait time?

The histogram shows the commute distances, in miles, of 40 employees. What proportion of these employees commute less than 20 miles?

A histogram of the prices of 300 homes sold in a town has a tall peak on the left and a long tail stretching to the right. Which statement is most likely true?

A student describes a distribution of 40 exam scores as: "Most students did well." Which addition would make this a complete description of the distribution?

A set of seven delivery times has mean 18.3 minutes and standard deviation 4.79 minutes. A traffic diversion adds exactly 5 minutes to every delivery. What are the new mean and standard deviation?

Daily high temperatures in a city for one month have mean 18°C and standard deviation 4°C. Converting to Fahrenheit uses F = 1.8C + 32. What is the standard deviation in °F?

The annual salaries, in thousands of dollars, of the 10 employees at a small firm are 38, 41, 42, 44, 45, 47, 48, 52, 55 and 210. Which pair of summaries best describes the center and variability of these salaries?

The five-number summary of the number of texts sent in a day by a group of students is: minimum 12, Q1 20, median 25, Q3 31, maximum 58. Using the 1.5 × IQR rule, which statement is true?

In a boxplot of battery life for 80 phones, measured to the nearest minute, the line from Q3 to the maximum is much longer than the line from the minimum to Q1. Which statement is the best interpretation?

Ana scored 82 on a biology test with mean 74 and standard deviation 5. Ben scored 88 on a history test with mean 80 and standard deviation 8. Relative to their own classes, who did better?

The boxplots compare the reaction times, in milliseconds, of two groups of drivers. Which comparison is supported by the boxplots?

The lengths of fish caught in a lake have mean 34 centimeters and standard deviation 4 centimeters. A fish has a z-score of −1.25. How long is it?

A small orchestra has 48 members. The manager asks every member which rehearsal night they prefer. What kind of data collection is this?

Researchers recorded the daily step counts of 500 adults who chose to use a standing desk at work and 500 who did not. Those with standing desks walked more. Which conclusion is justified?

A university has 6,000 undergraduates in four class years. To survey students about campus housing, the dean randomly selects 50 students from each class year. What sampling method is this?

A city wants to survey households about recycling. It randomly selects 12 of its 300 city blocks and surveys every household on those blocks. Why might a planner choose this cluster sample over a simple random sample of households?

A manager wants a simple random sample of 5 of the 80 employees. Which method gives one?

A county surveys residents about public transit by randomly selecting phone numbers from a list of landline numbers. Many younger residents have only cell phones. What is the main problem?

A magazine mails a long survey to a random sample of 2,000 subscribers; 240 return it. The editor says, "With 240 responses, our results are reliable." What is the best response?

A survey asks: "Given the rising cost of living, do you agree that the city should not raise bus fares this year?" What is the most likely effect of this wording?

A researcher has 60 volunteers to test whether a new pillow improves sleep. What is the main purpose of randomly assigning 30 volunteers to the new pillow and 30 to their usual pillow?

A farmer tests two fertilizers on 20 plots. Ten plots are on a hillside and ten are in a valley, and soil differs between the two places. Which design is best?

In an experiment on whether a supplement reduces muscle soreness, one group takes the supplement and one takes an identical-looking pill with no active ingredient. Neither the subjects nor the staff who rate soreness know who got which. Why use the identical-looking pill?

A student tests whether a plant food helps tomatoes grow. She gives plant food to one plant and none to another, measures each plant's height 10 times, and finds the fed plant taller. What is the main weakness?

A company randomly selected 400 of its 9,000 customers and randomly assigned 200 to receive a reminder email and 200 to receive none. More customers who got the email renewed. To whom does a cause-and-effect conclusion apply?

A study finds that towns with more ice cream shops have more swimming pool accidents. Which is the most likely confounding variable?