Understanding Confidence Intervals and the T Distribution

What distribution is used to calculate confidence intervals for means when the population standard deviation is unknown?

• Normal distribution

• Student T distribution

• Chi-square distribution

• F distribution

Which of the following is a property of the T distribution?

• It is skewed to the right

• It has a mean of 1

• It is symmetrical around zero

• It has thinner tails than the normal distribution

What happens to the T distribution as the sample size increases?

• It becomes more like the normal distribution

• It becomes more skewed

• It becomes less symmetrical

• It becomes wider

How is the degrees of freedom calculated for a T distribution?

• Sample size divided by two

• Sample size times two

• Sample size minus one

• Sample size plus one

What is the first step in calculating a confidence interval using the T distribution?

• Calculate the Z critical value

• Calculate the T critical value

• Find the sample mean

• Determine the population mean

How is the T critical value calculated?

• Using the sample mean

• Using the Z critical value

• Using the inverse T function

• Using the population standard deviation

What is the purpose of dividing the confidence level by two when calculating the T critical value?

• To find the area under the curve

• To find the area in both tails

• To find the area in one tail

• To find the area in the center

Which tool can be used to find the T critical value besides a table?

• Calculator

• Inverse T function

• Z table

• Normal distribution chart

What is the T critical value for a 95% confidence level with 14 degrees of freedom?

• 1.761

• 1.960

• 2.145

• 1.645

What is the final step in calculating a confidence interval using the T distribution?

• Multiply the margin of error by the sample mean

• Both add and subtract the margin of error from the sample mean

• Add the margin of error to the sample mean

• Subtract the margin of error from the sample mean