# Day 15

``` 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
You have a simple random sample
 Sample size is large

^
› np &lt; 10
^
› n(1-p) &lt; 10
Math symbol
𝑡𝛼
Def’n
Look up in table
Typically use 1.96 for
95% CI
2
confidence level
𝑋
se(𝑋)
How to find it
Estimated mean
Estimated standard
error
Degrees of freedom
Given to you
Math symbol
𝑡𝛼
Def’n
How to find it
T-distribution related Look up in table
to 𝛼
Typically use 1.96 for
95% CI
2
confidence level
𝛼
Given to you
Estimated mean
𝑋
se(𝑋)
df
^
Estimated standard
error
Degrees of freedom n-1
𝑥
𝑛
𝑠
𝑛

𝑋 - 𝑡𝛼 2 (𝑠𝑒(𝑋)) to 𝑋 + 𝑡𝛼 2 (𝑠𝑒(𝑋))
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)

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
```