Confidence Intervals Warmup You are wanting to find

Confidence Intervals

Warm-up � You are wanting to find the average number of siblings a student at Iowa State has. Instead of taking a census, you decide to obtain a sample and use that sample to estimate the true average. • Voluntary Response • Convenience Sample • Systematic Sample

Conditions � You have a simple random sample � Sample size is large ^ › np < 10 ^ › n(1 -p) < 10

Confidence interval Math symbol Def’n How to find it Look up in table Typically use 1. 96 for 95% CI confidence level Estimated mean Estimated standard error Degrees of freedom Given to you

Confidence interval Math symbol Def’n How to find it Look up in table Typically use 1. 96 for 95% CI confidence level Given to you Estimated mean ^ df Estimated standard error Degrees of freedom n-1

A package of light bulbs promises an average life of more than 750 hours per bulb. A consumer group did not believe the claim and tested a sample of 40 bulbs. The average lifetime of these 40 bulbs was 740 hours with s=30 hours. � Find the consumers groups 95% confidence interval � Based on this, what conclusions would you make about the promise of 750 hours. � If the manufacturer follows the same estimate of s, what is their 95% confidence interval � Based on this, what might their response be if the consumer group complains they lie.

� Create a generic sentence that can apply to any confidence interval in any situation. (Leave blanks where you would specify when given context)

Interpret � I am 95% confident that the mean _______ lies between _____ and _____. � 95% of the confidence intervals made this way would contain the true population mean

� A catalog sales company promises to deliver orders placed on the Internet within 3 days. Follow-up calls to randomly selected customers show that a 95% confidence interval for the proportion of all orders that arrive on time is 88% +/- 6%. What does this mean? Which of these are correct a) Between 82% and 94% of all orders arrive on time b) 95% of all random samples of customers will show that 88% of orders arrived on time c) 95% of all random samples of customers will show that 82% to 94% of orders arrived on time. d) We are 95% sure that between 82% and 94% of the orders placed by the customers in this sample arrived on time e) On a randomly chosen day, we can be 95% confident that between 82% and 94% of the large volume of orders will arrive on time

� A catalog sales company promises to deliver orders placed on the Internet within 3 days. Follow-up calls to randomly selected customers show that a 95% confidence interval for the proportion of all orders that arrive on time is 88% +/- 6%. What does this mean? Which of these are correct a) Between 82% and 94% of all orders arrive on time b) 95% of all random samples of customers will show that 88% of orders arrived on time c) 95% of all random samples of customers will show that 82% to 94% of orders arrived on time. d) We are 95% sure that between 82% and 94% of the orders placed by the customers in this sample arrived on time e) On a randomly chosen day, we can be 95% confident that between 82% and 94% of the large volume of orders will arrive on time