Confidence Intervals for Normal and T-Distributions

Why do we use a t-distribution instead of a z-distribution for means? 

• It reflects greater variability present in small samples.
• It allows us to decrease the margin of error without increasing our confidence level.
• It allows us to use the population standard deviation.
• None of these.

Which of the following is true about the t-distribution?

• Approaches a normal distribution as its degree of freedom increases.

• Assumes the population is normally distributed.

• It is more spread out than the normal standard distribution.

• All of these statements are true.

Which of the following does NOT have an affect on the width of a confidence interval?

• Sample mean

• t-score

• Sample standard deviation

• Sample size

Which of the following changes to a study would result in a narrower confidence interval?

• increasing the confidence level, increasing the sample size
• decreasing the confidence level, decreasing the sample size
• increasing the confidence level, decreasing the sample size
• decreasing the confidence level, increasing the sample size.

What is the degrees of freedom equal to?

• n
• n+1
• 1-n
• n-1

What is the t-score associated with 90% confidence and a sample size of 15?

• 1.341

• 1.345

• 1.761

• 1.753

Find the critical value (t-score) for a 99% confidence interval with a sample of 23 people.

• 1.714

• 1.711

• 2.064

• None of these.

The t-score that would be used to construct a 99% confidence interval for the mean with a sample of size n=17 would be ______.

• 2.921

• 2.583

• 2.567

• 2.898

You want to compute a 90% confidence interval for the mean of a population with unknown population standard deviation. The sample size is 30. The value of the t-score you would use for this interval is __________.

• 1.96

• 1.645

• 1..699

• 0.90

• 1.311

 For a sample of size 20 taken from a normally distributed population with standard deviation equal to 5, a 90% confidence interval for the population mean would require the use of ________________.