What a Confidence Interval Means

Question 1

A polling firm makes 95 percent confidence intervals for p, the proportion of state voters who support a bond measure. What does the confidence level describe?

Accepted Answer

The 95 percent level means that about 95 percent of intervals made by this method would capture p, the true proportion.

Answer

The 95 percent level means that about 95 percent of state voters have opinions inside this interval.

Answer

The 95 percent level means that there is a 95 percent probability that p lies inside this one interval.

Answer

The 95 percent level means that about 95 percent of sampled voters gave the same answer as p-hat.

Question 2

A clinic reports a 95 percent confidence interval for mu, the mean wait time in minutes for all patient visits. What is the correct interpretation of that interval?

Accepted Answer

We are 95 percent confident that mu, the true mean wait time for all patient visits, lies in the interval.

Answer

We are 95 percent confident that 95 percent of patient visits have wait times in the interval.

Answer

We are 95 percent confident that the next patient visit will have a wait time in the interval.

Answer

We are 95 percent confident that x-bar, the sample mean wait time, lies in the interval.

Question 3

A school newsletter says a 95 percent confidence interval for the mean backpack mass shows 95 percent of students have backpack masses in the interval. What is the error?

Accepted Answer

The error is that it treats an interval for a population mean as a claim about individual students.

Answer

The error is that it treats the confidence level as if it were a sample size.

Answer

The error is that it treats the margin of error as if it were the point estimate.

Answer

The error is that it uses a sample instead of measuring every student in the population.

Question 4

A 95 percent confidence interval for p, the proportion of city residents who recycle weekly, is computed from one random sample of 600 residents. What can be said about that one interval?

Accepted Answer

This one interval either contains p or it does not; 95 percent describes the method used to make intervals.

Answer

This one interval has a 95 percent chance that p moved inside it after the sample was selected.

Answer

This one interval contains exactly 95 percent of the 600 sampled residents' recycling responses.

Answer

This one interval will contain p-hat from the next random sample 95 percent of the time.

Question 5

A factory repeatedly samples jars and builds 95 percent confidence intervals for mu, the mean fill volume in milliliters. What does the 95 percent confidence level describe?

Accepted Answer

It describes the long-run percent of such intervals that would contain the true mean fill volume mu.

Answer

It describes the percent of jars whose fill volumes would fall inside any one interval.

Answer

It describes the chance that the true mean fill volume changes to fit this one interval.

Answer

It describes the percent of sample means x-bar that must equal the true mean fill volume.

Question 6

An agriculture study gives a 95 percent confidence interval for p, the proportion of tomato plants in a greenhouse with blossom rot. How should the interval be interpreted?

Accepted Answer

We are 95 percent confident that p, the true proportion of greenhouse tomato plants with blossom rot, is in the interval.

Answer

We are 95 percent confident that 95 percent of greenhouse tomato plants have blossom rot values in the interval.

Answer

We are 95 percent confident that the next tomato plant checked will have blossom rot if it is in the interval.

Answer

We are 95 percent confident that p-hat, the sample proportion with blossom rot, is in the interval.

Question 7

A report states that a 95 percent confidence interval for mean caffeine content proves the next bottle tested will have caffeine content in that interval. What is the error?

Accepted Answer

The error is that it treats an interval for a population mean as a prediction about one future bottle.

Answer

The error is that it treats the population mean as if it were measured in milliliters.

Answer

The error is that it treats the confidence level as if it were the margin of error.

Answer

The error is that it reports an interval instead of a single point estimate.

Question 8

A 95 percent confidence interval for mu, the mean height in centimeters of all seedlings in a nursery, is based on one random sample of 80 seedlings. What is true about this one interval?

Accepted Answer

The interval either captures mu or misses mu; the 95 percent level describes repeated use of the method.

Answer

The interval gives a 95 percent chance that mu is randomly located inside it.

Answer

The interval contains 95 percent of the 80 sampled seedling heights.

Answer

The interval will contain x-bar from every future sample of 80 seedlings.

Question 9

A district repeatedly surveys random samples and makes 95 percent confidence intervals for p, the proportion of families favoring a later start time. What does 95 percent confidence mean?

Accepted Answer

It means about 95 percent of intervals from this repeated survey method would include the true proportion p.

Answer

It means about 95 percent of all district families favor a later start time.

Answer

It means this single interval has a 95 percent probability of containing the sample proportion p-hat.

Answer

It means about 95 percent of future individual survey answers will match the interval.

Question 10

A transportation planner reports a 95 percent confidence interval for mu, the mean daily bicycle count on a trail. Give the correct meaning of the interval.

Accepted Answer

We are 95 percent confident that mu, the true mean daily bicycle count on the trail, lies in the interval.

Answer

We are 95 percent confident that 95 percent of days have bicycle counts inside the interval.

Answer

We are 95 percent confident that tomorrow's bicycle count will lie inside the interval.

Answer

We are 95 percent confident that x-bar, the sample mean daily count, lies in the interval.

Question 11

A website says a 95 percent confidence interval for the proportion of teens with library cards means p has a 95 percent chance of being in this exact interval. What is the error?

Accepted Answer

The error is that it treats the fixed population proportion as random after the interval has been computed.

Answer

The error is that it treats a proportion as if it had to be measured in centimeters.

Answer

The error is that it treats the sample size as if it were the confidence level.

Answer

The error is that it uses random sampling, which is not allowed for confidence intervals.

Question 12

A 95 percent confidence interval for p, the proportion of a university's students who commute by bus, is made from one random sample of 500 students. What can that interval do?

Accepted Answer

It can be one of the intervals that captures p, but only repeated intervals have a 95 percent capture rate.

Answer

It can make p have a 95 percent probability of being inside it after it is reported.

Answer

It can include exactly 95 percent of all university students who commute by bus.

Answer

It can guarantee that p-hat from the sample equals p for the full university population.

Question 13

A quality team would use the same random sampling plan many times to make 95 percent confidence intervals for mu, the mean aluminum cap mass in grams. What does the level mean?

Accepted Answer

The level means about 95 percent of those intervals would contain mu, the true mean cap mass.

Answer

The level means about 95 percent of aluminum caps would have masses in each interval.

Answer

The level means there is a 95 percent probability that x-bar equals mu in this sample.

Answer

The level means the margin of error is 95 percent of the point estimate.

Question 14

A biologist gives a 95 percent confidence interval for mu, the mean dissolved oxygen level in milligrams per liter for a lake. What does the interval say?

Accepted Answer

We are 95 percent confident that mu, the true mean dissolved oxygen level for the lake, is in the interval.

Answer

We are 95 percent confident that 95 percent of water samples from the lake are in the interval.

Answer

We are 95 percent confident that the next water sample's oxygen level is in the interval.

Answer

We are 95 percent confident that the sample mean oxygen level x-bar is in the interval.

Question 15

A news story says a 95 percent confidence interval for mean screen time shows that 95 percent of sampled teens are represented by the interval. What is the error?

Accepted Answer

The error is that it treats a confidence interval for mu as a statement about sampled individuals.

Answer

The error is that it treats the confidence level as a unit of time.

Answer

The error is that it treats screen time as a categorical variable.

Answer

The error is that it uses a sample statistic to estimate a population parameter.

Question 16

A 95 percent confidence interval for mu, the mean reaction time in seconds for all drivers in a study population, has already been computed. What statement is correct?

Accepted Answer

The interval is fixed now, so it either contains mu or it does not contain mu.

Answer

The interval is fixed now, so mu has a 95 percent chance of being randomly placed inside it.

Answer

The interval is fixed now, so it contains 95 percent of all individual driver reaction times.

Answer

The interval is fixed now, so x-bar from the original sample must equal mu.

Question 17

In repeated random samples, a researcher builds 95 percent confidence intervals for p, the proportion of households with fiber internet. What does the confidence level describe?

Accepted Answer

The confidence level describes how often intervals from that process would capture p in the long run.

Answer

The confidence level describes how often households in the population have fiber internet.

Answer

The confidence level describes the probability that p-hat is the true population proportion.

Answer

The confidence level describes how often a future household's internet status falls inside the interval.

Question 18

A researcher reports a 95 percent confidence interval for p, the proportion of adult patients who prefer text reminders. How should the interval be read?

Accepted Answer

We are 95 percent confident that p, the true proportion of adult patients who prefer text reminders, lies in the interval.

Answer

We are 95 percent confident that 95 percent of adult patients prefer text reminders.

Answer

We are 95 percent confident that the next adult patient asked will prefer text reminders.

Answer

We are 95 percent confident that p-hat, the sample proportion, lies in the interval.

Question 19

A lab summary says a 95 percent confidence interval for mean tablet mass gives the range where the sample mean x-bar has a 95 percent chance to fall. What is the error?

Accepted Answer

The error is that it treats the interval for mu as a probability statement about the sample statistic x-bar.

Answer

The error is that it treats tablet mass as though grams were not a metric unit.

Answer

The error is that it treats the confidence interval as though it required a random sample.

Answer

The error is that it treats the population mean mu as the value being estimated.

Question 20

A 95 percent confidence interval for p, the proportion of registered voters who support a tax change, is calculated from one random poll. What is correct about this interval?

Accepted Answer

The interval's success is already determined; the 95 percent level belongs to the polling method.

Answer

The interval's success is uncertain because p will be randomly selected after the poll.

Answer

The interval's success means 95 percent of voters in the sample supported the tax change.

Answer

The interval's success means the next poll's p-hat must fall inside this interval.

Question 21

A museum uses many random visitor samples to build 95 percent confidence intervals for p, the proportion of visitors who buy audio guides. What does 95 percent confidence describe?

Accepted Answer

It describes the approximate long-run share of those intervals that would include the true visitor proportion p.

Answer

It describes the approximate share of visitors in the museum who buy audio guides.

Answer

It describes the probability that this sample's p-hat is equal to the true visitor proportion p.

Answer

It describes the probability that the next visitor will buy an audio guide.

Question 22

A 95 percent confidence interval is reported for mu, the mean strength in newtons of a type of recycled plastic strip. What is the correct interpretation?

Accepted Answer

We are 95 percent confident that mu, the true mean strength of all such strips, lies in the interval.

Answer

We are 95 percent confident that 95 percent of all such strips have strengths in the interval.

Answer

We are 95 percent confident that the next strip tested will have strength in the interval.

Answer

We are 95 percent confident that x-bar, the sample mean strip strength, lies in the interval.

Question 23

A city report says a 95 percent confidence interval for the proportion of buses arriving late means 95 percent of future buses will arrive within the interval. What is the error?

Accepted Answer

The error is that it treats an interval for a population proportion as a prediction about future individual buses.

Answer

The error is that it treats a bus arrival outcome as a categorical variable.

Answer

The error is that it treats a confidence interval as an estimate of an unknown parameter.

Answer

The error is that it treats a sample proportion as information from the sample.

Question 24

An orchard manager repeatedly samples apples and builds 95 percent confidence intervals for mu, the mean apple mass in grams for the orchard. What does the 95 percent confidence level describe?

Accepted Answer

The proportion of all such intervals from repeated sampling that would capture mu.

Answer

The probability that mu, the true mean apple mass, lies inside this one interval.

Answer

The proportion of the sampled apples whose mass lies inside the interval.

Answer

The proportion of sampled apples whose mass agrees with the sample mean.

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What a Confidence Interval Means

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Top Corner

What a Confidence Interval Means

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner