Confidence Intervals Mean Use Z or T?

I have sampled 100 students and found that the 95% confidence interval for the mean is:

(7.5, 8.5)

• There is a 95% chance that the true mean falls between 7.5 and 8.5

• We are 95% confident that the true mean falls between 7.5 and 8.5

• There is a 95% probability that my true mean is between 7.5 and 8.5

• My margin of error is 95% of the data

The z-score number used for calculating a 95% confidence interval is:

• 1.65

• 1.96

• 2.58

• 0.90

What is the confidence interval being calculated in the image to the left?

• 90% confidence interval

• 95% confidence interval

• 99% confidence interval

• 35% confidence interval

Which z-value is used for a 95% confidence interval?

• 1.65

• 1.96

• 2.58

• 2.33

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.

Which z-value is used for a 95% confidence interval?

• 2.58

• 1.66

• 1.96

• 2.33

Given a sample standard deviation "5", n=100, and a confidence interval "99%". Solve for the margin of error "E" for the t-distribution (σ unknown). Round your answer to the nearest hundredth.

• 1.31

• 0.85

• 0.99

• 1.21

Given a sample standard deviation "0.5", n=30, and a confidence interval "90%". Solve for the margin of error "E" for the t-distribution (σ unknown). Round your answer to the nearest hundredth.

• 0.16

• 1.18

• 0.19

• 1.06

Identify the confidence interval used in the figure below if each shaded area is equal to 0.05.

• 90%

• 95%

• 97%

• 99%

A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. Which of the following would result in the smallest margin of error in estimating the mean salt content μ?

• 90% confidence; n = 25

• 90% confidence; n = 50

• 95% confidence; n = 25

• 95% confidence; n = 50

• n=100 at any confidence level