Confidence Intervals: Master the Basics with Interactive Quizzes

Question 1

Which assumption is required for constructing a confidence interval for a population variance?

Accepted Answer

The population is normally distributed.

Answer

The sample is normally distributed.

Answer

The population standard deviation is known.

Question 2

How does increasing the sample size impact the width of a confidence interval constructed for a given confidence level?

Accepted Answer

The width of the confidence interval decreases.

Answer

The width of the confidence interval increases.

Answer

The width of the confidence interval stays the same.

Answer

The effect of sample size on confidence interval width is unpredictable.

Question 3

In constructing confidence intervals, what is the main purpose of the standard error?

Accepted Answer

To measure the variability within the sampling distribution.

Answer

To find the critical value for the calculation.

Answer

To determine the sample size for the study.

Answer

To represent the standard deviation of the population.

Question 4

In a confidence interval for a population variance, the distribution used to determine the critical values is the:

Accepted Answer

F-distribution

Answer

Normal distribution

Answer

Student's t-distribution

Answer

Chi-square distribution

Question 5

The margin of error for a confidence interval is calculated by:

Accepted Answer

Halving the width of the interval

Answer

Doubling the width of the interval

Answer

Taking the square root of the interval width

Answer

Inverting the interval width

Question 6

A confidence interval provides a range within which there is a specified likelihood of capturing the unknown population parameter.

Accepted Answer

True

Answer

False

Answer

Only true for large sample sizes

Answer

Only true for small sample sizes

Question 7

Confidence intervals are useful for making inferences about:

Accepted Answer

Population parameters based on sample data.

Answer

Population means

Answer

Population proportions

Answer

Sample parameters

Question 8

A confidence interval is described as unbiased if:

Accepted Answer

The expected value of the interval estimate equals the true population parameter.

Answer

The interval is symmetric about the true population parameter.

Answer

The interval contains the true population parameter with probability 1.

Question 9

Which of the following is NOT a benefit of using confidence intervals?

Accepted Answer

They provide a precise estimate of the population parameter.

Answer

They quantify uncertainty in estimation.

Answer

They can be used for hypothesis testing.

Question 10

Which of the following is a requirement for constructing a confidence interval for a proportion?

Accepted Answer

The sample size must be large enough (at least 30 successes and 30 failures).

Answer

The population standard deviation must be known.

Answer

The population mean must be known.

Question 11

What does the confidence level in a confidence interval represent?

Accepted Answer

The probability that the confidence interval contains the true population parameter.

Answer

The percentage of the population that is covered by the confidence interval.

Answer

The precision of the confidence interval.

Question 12

What does it mean to reject the null hypothesis when performing a hypothesis test using a confidence interval?

Accepted Answer

The confidence interval does not contain the hypothesized population parameter.

Answer

The confidence interval contains the hypothesized population parameter.

Answer

The sample mean is significantly different from the hypothesized population mean.

Question 13

A researcher wants to estimate the average height of students in a university. Which type of confidence interval would be most appropriate?

Accepted Answer

Confidence interval for a mean

Answer

Confidence interval for a proportion

Answer

Confidence interval for a standard deviation

Answer

Confidence interval for a variance

Question 14

A 95% confidence interval for the mean height of adult women is calculated to be (63.5 inches, 65.1 inches). What is the most accurate interpretation of this interval?

Accepted Answer

We are 95% confident that the true mean height of adult women lies between 63.5 inches and 65.1 inches.

Answer

95% of adult women have heights between 63.5 inches and 65.1 inches.

Answer

There is a 95% probability that the true mean height of adult women falls within this interval.

Answer

The sample mean height of adult women is guaranteed to be between 63.5 inches and 65.1 inches.

Question 15

How does increasing the sample size affect the width of a confidence interval?

Accepted Answer

The width of the confidence interval decreases.

Answer

The width of the confidence interval increases.

Answer

The effect on the width depends on the population mean.

Answer

The width of the confidence interval remains the same.

Question 16

A company wants to determine the average lifespan of a specific type of battery. A sample of 25 batteries is tested, yielding a sample mean lifespan of 100 hours and a standard deviation of 10 hours. Construct a 99% confidence interval for the true mean lifespan of the batteries.

Accepted Answer

96.5 to 103.5

Answer

95.0 to 105.0

Answer

97.5 to 102.5

Answer

98.0 to 102.0

Question 17

What is the critical value for a two-tailed 90% confidence interval for a population mean, assuming a standard normal distribution?

Accepted Answer

1.645

Answer

2.576

Answer

1.96

Answer

1.282

Question 18

A researcher wants to estimate the average GPA of students at a university. She collects data from a random sample of 50 students, finding a sample mean GPA of 3.2 with a standard deviation of 0.4.  To construct a 95% confidence interval for the true mean GPA, what is the margin of error?

Accepted Answer

0.11

Answer

0.08

Answer

0.22

Answer

0.05

Question 19

How does increasing the confidence level affect the width of a confidence interval?

Accepted Answer

As the confidence level increases, the confidence interval width increases.

Answer

As the confidence level increases, the confidence interval width decreases.

Answer

The confidence level and confidence interval width are independent.

Question 20

A company wants to estimate the variability in the weight of its products. A sample of 16 products is taken, resulting in a sample standard deviation of 2 grams. Calculate the 90% confidence interval for the population variance.

Accepted Answer

1.7 to 4.3

Answer

2.0 to 3.0

Answer

1.5 to 4.5

Answer

1.0 to 5.0

Question 21

What assumption is necessary when constructing a confidence interval for a population mean using the t-distribution?

Accepted Answer

The population must be normally distributed, or the sample size must be large enough for the Central Limit Theorem to apply.

Answer

The sample size must be greater than 30.

Answer

The population must have a known standard deviation.

Question 22

A researcher wants to estimate the average time it takes to complete a certain task. She knows the population standard deviation is 5 minutes.  What sample size should she use to ensure a 99% confidence interval for the mean has a margin of error no greater than 1 minute?

Accepted Answer

96

Answer

49

Answer

25

Answer

64

Question 23

A 90% confidence interval for the proportion of voters who support a particular candidate is (0.45, 0.55). Which of the following statements is TRUE?

Accepted Answer

We are 90% confident that the true proportion of voters who support the candidate lies between 0.45 and 0.55.

Answer

The sample proportion of voters who support the candidate is guaranteed to be between 0.45 and 0.55.

Answer

There is a 90% chance that the candidate will win the election.

Answer

90% of voters in the population support the candidate.

Question 24

A confidence interval for the population variance is constructed using the _____________ distribution.

Accepted Answer

Chi-square

Answer

F

Answer

t

Answer

Normal

Question 25

A study is conducted to estimate the average weight of newborn babies in a hospital. The sample mean weight is 3.2 kg. The 95% confidence interval for the population mean weight is (3.0 kg, 3.4 kg). What is the margin of error?

Accepted Answer

0.2 kg

Answer

0.3 kg

Answer

0.1 kg

Answer

0.4 kg

Question 26

The width of a confidence interval is directly proportional to the _____________ of the confidence level.

Accepted Answer

Square root

Answer

Logarithm

Answer

Inverse

Answer

Exponent

Question 27

A researcher wants to construct a 90% confidence interval for the mean weight of a certain species of fish. The sample mean weight is 1.5 kg, and the sample standard deviation is 0.2 kg. What is the critical value for this confidence interval?

Accepted Answer

1.645

Answer

0.82

Answer

1.96

Answer

2.576

Question 28

A company claims that the average lifespan of its batteries is 100 hours. A consumer group tests a random sample of 25 batteries and finds that the sample mean lifespan is 95 hours with a sample standard deviation of 10 hours. At a 5% significance level, what can we conclude about the company's claim?

Accepted Answer

There is sufficient evidence to reject the company's claim.

Answer

The company's claim is definitely false.

Answer

There is not sufficient evidence to reject the company's claim.