A few comments on your homework...
- Remember, 2 and 3 both ask us to "estimate the percentage..." This means we need to create a confidence interval and do the 3 step process: Conditions, Math, Interpret the Interval
- Numbers 4 and 5 use an idea we have not discussed in class-finding sample size.
- First, think: what part of the confidence interval formula represents margin of error?
- Once you've figured that out, we want to set the ME = 0.05.
- So, set the margin of error part of the formula equal to 0.05\
- Substitute in z*, p-hat, and q-hat
- Then, do some algebra to solve for n
- Divide by z* on both sides
- Square both sides
- Multiply p-hat and q-hat to rewrite the numerator
- Cross multiply
- OR, check out the example on page 442, "Choosing Your Sample Size."
Enjoy! See you manana!
Classwork Examples: (Tonight's Homework)
1.)
In June 2004 Gallup/CNN/USA Today asked
909 registered voters if there was “Some chance they could vote for other
candidates” beside their first choice. Only 18% indicated a chance they may
switch votes. The resulting 95% confidence interval is shown below:
a. Show the work!
b.
What do we enter in our graphing calculator
to get this interval?
Based on your interval (above), which
statements below are correct? Incorrect?
a.
In the sample of 909 registered voters,
somewhere between 15.5% and 20.5% of them said there is a chance they might
switch votes.
b.
We’re 95% confident that 18% of all U.S.
registered voters had some chance of switching votes.
c.
We’re 95% confident that between 15.5% and 20.5%
of all U.S. registered voters had some chance of switching votes.
d.
We know that between 15.5% and 20.5% of all U.S.
registered voters had some chance of switching votes.
e.
95% of all U.S. registered voters had some
chance of switching votes.
2.)
College grads are more satisfied with their
jobs: College-educated Millennials are more likely to see
themselves on a career path, rather than just working at a job to get them by.
This is based on a Pew Research Center poll of 2,002 employed 25-32 year old
Americans. In the sample, 53% of employees say they are “very satisfied” with
their current job.
a.
Estimate the percentage of all employed 25-32
year old Americans with a bachelor’s degree who are “very satisfied” with their
current job.
b.
If we wanted to be 98% confident, would our confidence interval need to be wider
or narrower?
c.
Our margin of error was about 4%. If we wanted
to reduce it to 3%, would our level of
confidence be higher or lower?
d.
If the Pew organization had polled more people,
would the interval’s margin of error have
been larger or smaller?
3.)
Estimate the proportion of Americans who are or
who have been employed who say the sex of their coworkers doesn’t matter.
(p-hat = 0.77; n = 1,963)
4.)
It used to be more common for a husband to have
more education than his wife in America. But now, for the first time since Pew
Research has tracked this trend over the past 50 years, the share of couples in
which the wife is the one “marrying down” educationally is higher than those in
which the husband has more education.
Among married women in 2012, 21% had spouses who were less educated than
they were—a threefold increase from 1960, according to a new Pew Research
Center analysis of Census data.
How many people would we have to survey to estimate the proportion of
men who “married down” within 5%?
5.)
Let’s say we want a 3% margin of error with 95%
confidence…we’re polling voter support (2 candidates, each equally likely). How
many voters should we sample?
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