You are wanting to find the average number of siblings a student at Iowa State has. Instead of...
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Transcript of You are wanting to find the average number of siblings a student at Iowa State has. Instead of...
![Page 1: 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.](https://reader036.fdocuments.in/reader036/viewer/2022072008/56649d6e5503460f94a4f333/html5/thumbnails/1.jpg)
Confidence Intervals
![Page 2: 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.](https://reader036.fdocuments.in/reader036/viewer/2022072008/56649d6e5503460f94a4f333/html5/thumbnails/2.jpg)
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
![Page 3: 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.](https://reader036.fdocuments.in/reader036/viewer/2022072008/56649d6e5503460f94a4f333/html5/thumbnails/3.jpg)
Conditions
You have a simple random sample
Sample size is large› np < 10› n(1-p) < 10
^
^
![Page 4: 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.](https://reader036.fdocuments.in/reader036/viewer/2022072008/56649d6e5503460f94a4f333/html5/thumbnails/4.jpg)
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
![Page 5: 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.](https://reader036.fdocuments.in/reader036/viewer/2022072008/56649d6e5503460f94a4f333/html5/thumbnails/5.jpg)
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
![Page 6: 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.](https://reader036.fdocuments.in/reader036/viewer/2022072008/56649d6e5503460f94a4f333/html5/thumbnails/6.jpg)
- to
![Page 7: 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.](https://reader036.fdocuments.in/reader036/viewer/2022072008/56649d6e5503460f94a4f333/html5/thumbnails/7.jpg)
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.
![Page 8: 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.](https://reader036.fdocuments.in/reader036/viewer/2022072008/56649d6e5503460f94a4f333/html5/thumbnails/8.jpg)
Create a generic sentence that can apply to any confidence interval in any situation. (Leave blanks where you would specify when given context)
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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
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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
![Page 11: 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.](https://reader036.fdocuments.in/reader036/viewer/2022072008/56649d6e5503460f94a4f333/html5/thumbnails/11.jpg)
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