Finding Confidence Intervals Using T Distribution

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)

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

• 1.341

• 1.345

• 1.761

• 1.753

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

• Sample mean

• t*

• Sample standard deviation

• Sample 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 quality control specialist at a glass factory must estimate the mean clarity rating for a new batch of glass using a sample of 18 glass sheets from the batch. Past investigations show that clarity ratings are normally distributed. The specialist decides to use a t-distribution rather than a z-distribution because ...

• The sample size is too small for a z-distribution

• Clarity ratings for the entire bacth are normally distributed.  

• The t-distribution will create a narrower interval than z.

• The standard deviation for the batch is unknown.

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 t* you would use for this interval is

• 1.96

• 1.645

• 1.699

• 0.90

• 1.311

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

• 1.683

• 1.234

• 1.437

• 1.761

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

• Because the population standard deviation is UNKNOWN and it accounts for a 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.

• Because the population standard deviation is KNOWN and it accounts for a greater variability present in LARGE samples.

Find the t* value for a 99% confidence interval with a sample of 23 people.

• 1.714

• 1.711

• 2.064

• None of these.

A quality control specialist at a glass factory must estimate the mean clarity rating for a new batch of glass using a sample of 18 glass sheets from the batch. Past investigations show that clarity ratings are normally distributed. The specialist decides to use a t-distribution rather than a z-distribution because ...

• The t distribution is more accurate than a z distribution.

• Clarity ratings for the entire bacth are normally distributed.

• The t-distribution will create a narrower interval than z.

• The standard deviation for the population is unknown.