Unit Test — Unit test Answers

A grocery store shopper wants to estimate the mean weight of the eggs in a particular carton of extra-large eggs. She opens the carton of eggs, randomly selects three eggs, and weighs them on a food scale. Are the conditions for constructing a t confidence interval met?

An owner of a miniature golf course wants to know how many strokes it takes to get the ball in the last hole. The owner randomly selects 40 golfers and asks them how many strokes it took them. The owner then constructs a 90% confidence interval for the true mean number of strokes to get the ball in the hole. Which of the following would decrease the margin of error?

Nina would like to estimate the difference in the mean amount of time students spend on math homework at her public school versus her cousin Sharon’s private school. To do so, each girl selects a random sample of 30 students from their large schools and asks the selected students how much time they spent doing math homework the previous night. The 90% confidence interval for the true difference in the population means, for private – public, is 0.25 hours to 0.92 hours. Is it reasonable for the girls to claim that private school students tended to spend an additional 30 minutes on math homework the previous night?

The owner of a smart watch would like to estimate the mean number of steps they take per day. To do so, they select a random sample of 30 days from the previous year’s data and record the number of steps they took on each of those days. The mean number of steps taken per day was 8,575 with a standard deviation of 2,125 steps. What is the value of the standard error of the mean?

A medical study is conducted to determine which migraine treatment, A or B, provides faster relief. The study uses 10 volunteers who claim to suffer from migraines. Half of the volunteers are randomly assigned to use treatment A when they experience their first migraine. The other half are assigned to use treatment B. Then, after no treatment for one month, the treatments are reversed. The volunteers each record the amount of time it takes, in minutes, to experience relief from their migraine under each treatment. The data are displayed in the table.The conditions for inference are met. The 99% confidence interval for the mean difference (A – B) in the time it takes to experience relief is –8.37 minutes to 0.732 minutes. What is the correct interpretation of this interval?

The manager of an aquatic center is interested in the average number of fish people keep in their saltwater tanks. She randomly selects 38 people who own saltwater fish tanks and asks how many fish they have. The mean amount is 48.2 fish with a standard deviation of 22.1 fish.Which of the following correctly interprets the 99% confidence interval for the true mean number of fish in saltwater tanks?

A study seeks to estimate the difference in the mean fuel economy (measured in miles per gallon) for vehicles under two treatments: driving with underinflated tires versus driving with properly inflated tires. To quantify this difference, the manufacturer randomly selects 12 cars of the same make and model from the assembly line and then randomly assigns six of the cars to be driven 500 miles with underinflated tires and the other six cars to be driven 500 miles with properly inflated tires. Here are summary statistics and dotplots of the results:Group NamenmeanSDminQ1medQ3max1: Underinflated616.3330.75315.2515.7516.3751717.252: Properly inflated618.2921.49516.51718.12519.7520.2What is the correct 90% confidence interval for the true difference in the population means (underinflated – properly inflated)? Use the conservative df.Find the t-table here.

A cell phone manufacturer would like to estimate the mean difference in battery lifespan for a phone in full-power versus power-saver mode. They randomly select eight phones and determine the battery lifespan, in hours, for each phone using each power mode. The data are displayed in the table.What is the mean difference (low – full) and the standard deviation of the differences?

A researcher is 95% confident that the interval from 2.8 hours to 6.5 hours captures the true mean amount of time it takes for 1 square foot of fresh paint to dry.Is there evidence that the true mean number of hours for 1 square foot of this type of paint to dry is greater than 5?

A trainer would like to estimate the number of runs of the same length and same speed it takes for an individual’s body to adjust to the activity. To do this, the trainer selects a random sample of 30 adults who do not currently run and assigns them to run 1 mile at a 12-minute pace every day until they can do so easily. The trainer finds that the standard error of the mean is 2.2 days. What is the interpretation of the standard error of the mean?

A random sample of 50 pairs of parents and children is selected. The parent is asked to estimate how many hours their child spent watching TV yesterday. The child is asked many hours they spent watching TV yesterday. A 90% confidence interval for the mean difference (parent’s response – child’s response) in the amount of time spent watching TV is 0.25 hours to 2.5 hours. A newspaper columnist writes the headline "Parents overestimate how much time children spend watching TV.” Is this headline supported by the 90% confidence interval?

What critical value of t* should be used for a 80% confidence interval for the population mean based on a random sample of 38 observations?Find the t-table here.

Nina would like to estimate the difference in the mean amount of time students spend on math homework at her public school versus her cousin Sharon’s private school. To do so, each girl selects a random sample of 30 students from their large schools and asks the selected students how much time they spent doing math homework the previous night. Nina and Sharon would like to construct a 90% confidence interval for the true difference in the population means. Are the conditions for inference met?

A study seeks to estimate the difference in the mean fuel economy (measured in miles per gallon) for vehicles under two treatments: driving with underinflated tires versus driving with properly inflated tires. To quantify this difference, the manufacturer randomly selects 12 cars of the same make and model from the assembly line and then randomly assigns six of the cars to be driven 500 miles with underinflated tires and the other six cars to be driven 500 miles with properly inflated tires. A 95% confidence interval for the true difference in the mean fuel economy for cars of this make and model driven with underinflated tires versus properly inflated tires is –3.339 mpg to –0.585 mpg. Interpret this interval.

The manager of an aquatic center is interested in the average number of fish people keep in their saltwater tanks. She randomly selects 38 people who own saltwater fish tanks and asks how many fish they have. The mean number of fish is 48.2 with a standard deviation of 22.1 fish. Which of the following is the 99% confidence interval for the true mean number of fish in saltwater tanks?Find the t-table here.

Two students want to determine whose paper airplane model can fly the farthest. To put their models to the test, they recruit five friends to participate in a study. Because the friends have varying throwing abilities, the students decide to have each friend throw each model of airplane. To determine which paper airplane each friend throws first, a coin is tossed. The data are displayed in the table, which shows how far each airplane flies to the nearest inch.

What critical value of t* should be used for a 95% confidence interval for the population mean based on a random sample of 30 observations?Find the t-table here.

Two students want to determine whose paper airplane model can fly the farthest. To put their models to the test, they recruit five friends to participate in a study. Because the friends have varying throwing abilities, the students decide to have each friend throw each model of airplane. To determine which paper airplane each friend throws first, a coin is tossed. The data are displayed in the table, which shows how far each airplane flies to the nearest inch.

A government agency constructs a 95% confidence interval to estimate the mean amount of pollution in a city’s river. Assume that all conditions have been met. The one-sample t-interval is (1.26, 3.91).

Two students want to determine whose paper airplane model can fly the farthest. To put their models to the test, they recruit five friends to participate in a study. Because the friends have varying throwing abilities, the students decide to have each friend throw each model of airplane. To determine which paper airplane each friend throws first, a coin is tossed. The data are displayed in the table, which shows how far each airplane flies to the nearest inch.