T Intervals for Means

A confidence interval is centered around...

• a parameter

• a statistic

• the sample size

• the population size

A sample of 20 cupcakes found the interval for calories to be (150, 350). Which is the correct interpretation of the 95% confidence interval?

• We are 95% confident that the true mean calorie content can be found with a sample of 150 to 350 cupcakes.

• We are 95% confident that the true mean calorie content in cupcakes is between 150 and 350 calories.

• We are 95% confident that a sample of 20 cupcakes will find 250 calories per cupcake.

• None of these are correct.

A sample of 30 women finds the mean height to be 62.3 in and the standard deviation to be 1.5 in. Find the margin of error of women's heights with a 95% CL.

• 699

• 0.56

• 0.537

• 19.325

A 90% confidence interval for the mean speed driven by cars on East Main St. is given by (21, 45). What was the sample mean of this study?

• 12

• 24

• 33

• None of these.

A 90% confidence interval for the mean speed driven by cars on East Main St. is given by (21, 45). What was the margin of error of this study?

• 12

• 24

• 33

• None of these.

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.

In a crash test of 15 troopers, collision repair costs are found to have a distribution that is approximately normal, with a mean of $1800 and a standard deviation of $950. Construct a 99% confidence interval for the repair cost. 

• (1070, 2530)

• (1273, 2326)

• (1799, 1801)

• None of these.

A local bank needs information concerning the savings account balances of its customers. A random sample of 13 accounts was checked. The mean balance was $686.75 with a sample standard deviation of $256.20. Find a 95% confidence interval for the true mean.

• ($513.14, $860.36)

• ($525.59, $847.91) 

• ($533.27, $840.23)

• ($531.92, $841.58)

Using the sample above, find a 95% confidence interval for the time students typically study for a quiz.

• (36.18, 51.83)

• (36.98, 51.02)

• (35.63, 52.37)

• (34.34, 53.66)

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

• 1.341

• 1.345

• 1.761

• 1.753