Use your 90% box plots for the following

1.  Suppose that Pentel gave each of 20 randomly selected students their newest mechanical pencil to try.  At the end of one week 14 students preferred the new pencil to the previous model.  Find the confidence interval for all students to prefer the new model.

2a.  Of the 20 students in question 1, suppose that 11 chose the old model as the best.  What is the 90% confidence interval for the percentage of all students who prefer the old model to all other models.

b.  Can you be fairly confident that at least half of all students prefer the old model?  Why or why not?

3. A random sample of size 20 contains 10 yeses.  Find the 90% confidence interval for the percentage of yeses in the population.  What is the sampling error?

4.  A random sample of size 40 contains 20 yeses.  Find the 90% confidence interval for the percentage of yeses in the population.  What is the sampling error?

5.  A random sample of size 60 contains 30 yeses.  Find the 90% confidence interval for the percentage of yeses in the population.  What is the sampling error?

6.  A random sample of size 80 contains 40 yeses.  Find the 90% confidence interval for the percentage of yeses in the population.  What is the sampling error?

7.  A random sample of size 100 contains 50 yeses.  Find the 90% confidence interval for the percentage of yeses in the population.  What is the sampling error?

8.  What is happening to the size of the confidence interval in the questions above?  What is happening to the sampling error?

9.  True or False: With larger sample sizes, the sample proportion is more likely to be close to the population percentage.

10.  To decrease the length of the confidence interval, must a pollster increase or decrease the sample size?

11.  If Harris Polls sent out 180 pollsters for a poll on educational practices of high school teachers, and each pollster sampled 100 people to try to find a 90% confidence interval.  How many of the  confidence intervals did not contain the real population percentage?

For 95% confidence intervals use the formula   Sampling Error = 1.96(pq/n)^1/2

^{12.  In a sample of 400 people, 320 said yes.  What is the sample error?}

^{13.  In a sample of 1600 people, 1280 said no.  What is the sample error?}

^{14.  In a sample of 200 taxpayers, 76 cheated on their income tax (shame!!)  Find the 95% confidence interval for the percentage of taxpayers who cheat.}

^{15.  In a study of 500 children, ages three to seven, 68% didn't know their home phone number.  Find the 95% confidence interval for the population percentage.}

^{16.  If p=.5, what sample size gives a sampling error of
a.  1%?
b.  2%?
c.  3%?
d.  4%?
e.  5%?
f.  6%?
g.  7%?
h.  8%?}

^{16.  A study of 300 mathematically gifted children found that 20% were left-handed.
a.  Find the 95% confidence interval for the percentage of mathematically gifted children who are left-handed.
b.  About 8% of the whole student population is left-handed.  Do you think the proportion of left-handers is greater among mathematically talented students than among students in general?  Why?}

^{17.  In a toss of 1000 dice, there were 211 sixes.  At the 95% confidence level is this a likely occurance?}