Question 1

A researcher reports a 95% confidence interval for the mean number of hours college students study per week as (13, 17). Which of the following is the correct interpretation of this interval?

Accepted Answer

We are 95% confident that the mean hours per week spent studying by college students is between 13 and 17 hours.

Question 2

A random sample of 120 dorm rooms at a university found that 70% had been cleaned properly. What is the standard error of the sample proportion $$\hat{p}$$?

Accepted Answer

$$0.042$$

Question 3

Which of the following statements about confidence intervals is correct?

Accepted Answer

A confidence interval gives a range in which we are confident the population mean lies, based on our sample.

Question 4

Suppose a 90% confidence interval for the mean birthweight of babies is (3364.0, 3633.4) grams. Which of the following is a correct interpretation?

Accepted Answer

We are 90% confident that the mean birthweight is between 3364.0 and 3633.4 grams.

Question 5

Which of the following is NOT an appropriate condition to check before constructing a confidence interval for a mean?

Accepted Answer

The sample mean is equal to the population mean.

Question 6

A 95% confidence interval for the mean age of all NHL players is 25 to 29. Which interpretation below is correct?

Accepted Answer

I am 95% confident that the mean age for all NHL players is between 25 and 29.

Question 7

Which of the following is a common mistake when interpreting a confidence interval for a mean?

Accepted Answer

Stating that the interval is about the mean of the sample.

Question 8

If a histogram of your data is strongly skewed, which of the following is the best course of action before constructing a confidence interval for the mean?

Accepted Answer

Consider re-expressing the data or using a larger sample.

Question 9

Why is it important to check for outliers before constructing a confidence interval for the mean?

Accepted Answer

Outliers can violate the Nearly Normal Condition and distort the interval.

Question 10

Which of the following best describes the meaning of a 95% confidence level?

Accepted Answer

95% of all possible samples will produce intervals that contain the true mean.

Question 11

A student claims: 'I am 95% sure that all NHL players are between 25 and 29 years old.' What is wrong with this statement?

Accepted Answer

It incorrectly applies the confidence interval to individual values rather than the mean.

Question 12

Which of the following is a correct technical statement about a 90% confidence interval for a mean?

Accepted Answer

90% of all random samples will produce intervals that cover the true value.

Question 13

Which of the following is NOT a reason to be cautious when constructing a confidence interval for a mean?

Accepted Answer

The sample mean is close to the population mean.

Question 14

If the Central Limit Theorem (CLT) does not apply, which of the following is most likely to be true?

Accepted Answer

The sample size is too small or the data are not from a normal population.

Question 15

Which of the following is a correct formula for the standard error of a sample proportion $$\hat{p}$$?

Accepted Answer

$$\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 16

A confidence interval for the mean is constructed from a sample. What does the interval estimate?

Accepted Answer

The range in which the true population mean is likely to fall.

Question 17

Which of the following is a violation of the independence assumption when constructing a confidence interval?

Accepted Answer

Sampling students from the same classroom where they influence each other.

Question 18

If a sample is taken from a population with outliers, what should you do before constructing a confidence interval for the mean?

Accepted Answer

Analyze the data with and without the outliers and discuss their impact.

Question 19

Which of the following is a correct statement about the population mean in the context of confidence intervals?

Accepted Answer

The population mean is fixed but usually unknown.

Confidence Intervals for Means: Interpretation and Common Pitfalls

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