Understanding Confidence Intervals and T-Distribution

What is the primary reason for using a T-distribution instead of a Z-distribution when constructing confidence intervals for the mean?

• The sample mean is always greater than the population mean.

• The data is not normally distributed.

• The population standard deviation is unknown.

• The sample size is always less than 30.

How is the T-score calculated when constructing a confidence interval?

• Sample mean divided by population mean.

• Sample mean minus population mean divided by sample standard deviation over the square root of sample size.

• Population mean minus sample mean divided by population standard deviation.

• Sample mean plus population mean divided by sample size.

What happens to the T-distribution as the degrees of freedom increase?

• It becomes identical to the Z-distribution.

• It becomes more skewed.

• It becomes wider.

• It becomes narrower.

When constructing a confidence interval, what is the formula for the margin of error?

• T-score times sample standard deviation divided by the square root of sample size.

• Sample mean plus T-score.

• Population mean minus T-score.

• T-score divided by sample size.

In the example problem, what is the sample mean temperature of the coffee?

• 165 degrees Fahrenheit

• 162 degrees Fahrenheit

• 167 degrees Fahrenheit

• 160 degrees Fahrenheit

What is the degrees of freedom used in the example problem with a sample size of 16?

• 16

• 15

• 17

• 14

What is the critical T-score for a 95% confidence level with 15 degrees of freedom?

• 2.228

• 2.131

• 2.000

• 2.145

What is the range of the 95% confidence interval for the coffee temperature in the example?

• 150.0 to 170.0 degrees Fahrenheit

• 156.7 to 167.3 degrees Fahrenheit

• 160.0 to 165.0 degrees Fahrenheit

• 155.0 to 168.0 degrees Fahrenheit

How do you find the sample mean from a given confidence interval?

• Subtract the lower bound from the upper bound.

• Add the lower and upper bounds and divide by two.

• Divide the upper bound by the lower bound.

• Multiply the lower bound by the upper bound.

What is the margin of error if the confidence interval is between 8.66 and 10.84?

• 1.50

• 1.09

• 2.18

• 0.50