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

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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

se()Estimated standard error

Degrees of freedom

Confidence interval

^

Math symbol Def’n How to find it

T-distribution related to

Look up in tableTypically use 1.96 for 95% CI

confidence level Given to you

Estimated mean

se()Estimated standard error

df Degrees of freedom

n-1

- to

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 timeb) 95% of all random samples of customers will show that 88%

of orders arrived on timec) 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 timee) 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 timeb) 95% of all random samples of customers will show that 88%

of orders arrived on timec) 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 timee) 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