Constructing Confidence Intervals

When constructing a confidence interval for a t-distribution (σ unknown), the data must be normally distributed, or n ≥ 30

• True

• False

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

Given a sample standard deviation "2", n=100, and a confidence interval "95%". What is the degree of freedom?

• 100

• 99

• 98

• 95

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 "99%". what is the critical value for the t-distribution (σ unknown). Round your answer to the nearest hundredth.

• 2.626

• 2.756

• 2.750

• 2.763

x̄= 50, s = 5.02, n = 16, CI=95%

Find the critical value (t) for the t-distribution (σ unknown)

• 2.120

• 2.131

• 1.676

• 1.677

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

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

• We are 95% confident that the interval (150, 350) captures the true average caloric content.

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

• None of these are correct.

A large sample has mean of 7.1 and Standard Error of 2.3.

Construct a 90% Confidence Interval for the population mean µ (to two decimal places).

• (3.32, 10.88)

• (3.8, 7.1)

• (3.3, 10.9)

• (3.3165, 10.8835)

A survey of 800 women shoppers found that 17% of them shop on impulse.  What is the 98% confidence interval for the true proportion of women shoppers who shop on impulse? 

• 0.148 < p < 0.192

• 0.136 < p < 0.204

• 0.144 < p < 0.196

• 0.139 < p < 0.201

When constructing a confidence interval for a proportion, we want to make sure our sample data and sample statistics are unbiased. The best way to ensure this is to:

• randomly select the sample

• ask a very large number of people

• not ask very personal questions

• ask the first 100 people you see.