Quiz on Confidence Intervals

What is a confidence interval used for in statistics?

• To measure the exact value of a population parameter

• To estimate a range within which the population parameter lies

• To measure the significance of sample results

• To find the mean of the sample

In a confidence interval calculation, what does the "margin of error" represent?

• The range within which the population parameter lies

• The number of errors allowed in a study

• The probability that a null hypothesis is true

• The difference between the highest and lowest sample value

For a 95% confidence interval, what is the commonly used alpha (α) level?

• 0.05

• 0.1

• 0.01

• 0.025

If the sample mean is 100, the sample standard deviation is 10, and the sample size is 25, what is the margin of error for a 95% confidence level? (Use Z = 1.96 for 95% confidence)

• 2

• 3.92

• 1.96

• 5

How does increasing the sample size affect the margin of error, assuming the confidence level remains the same?

• Increases the margin of error

• Decreases the margin of error

• Has no effect on the margin of error

• Changes the confidence level

Which of the following statements is NOT true about a 99% confidence interval compared to a 95% confidence interval?

• It has a smaller margin of error

• It has a larger margin of error

• It requires a smaller sample size

• It has a lower alpha value than a 95% confidence interval

If a researcher wants to reduce the width of a confidence interval without changing the confidence level, which of the following actions can they take?

• Increase the alpha level

• Decrease the sample size

• Increase the sample size

• Use a higher Z-score

The Z-score for a 90% confidence level is approximately:

• 1.96

• 2.58

• 1.645

• 1.282

Which statement is correct about alpha (α) in relation to confidence intervals?

• Alpha represents the width of the confidence interval

• Alpha is the probability that the confidence interval contains the true population parameter

• Alpha represents the probability of rejecting a true null hypothesis

• Alpha increases as the confidence level increases

A 95% confidence interval for a population mean is found to be (15, 25). Which of the following interpretations is correct?

• There is a 95% probability that the sample mean is between 15 and 25

• There is a 95% probability that the true population mean is between 15 and 25

• The true population mean is definitely between 15 and 25

• There is a 5% probability that the true population mean is 15 or 25