Name:
Review: Final
College Statistics
Fall 2015
Chapter 15
– Make sure to check your conditions first!
– Know the sample distributions of means and proportions. (Central Limit Theorem)
1. It’s believed that 4% of children have a gene that may be linked to juvenile diabetes. Researchers
hoping to track 20 of these children for several years test 732 newborns for the presence of this gene.
What’s the probability that they find enough subjects for their study?
2. Statistics from Cornell’s NortheastRegional Climate Center indicate that Ithaca, New York, gets an
average of 35.4 inches of rain each year, with a standard deviation of 4.2 inches. Assume that a normala
model applies.
a. During what percentage of years does Ithaca get more than 40 inches of rain?
b. A Cornell Student is in Ithaca for 4 years. Let y represent the mean amount of rain for those 4 years.
Describe the sampling distribution model of this sample mean, y.
c. Whats the probability that those 4 years average less than 30 inches?
Chapter 16
– Remember how to do confidence intervals and figuring out standard error.
– Make sure to know the z values for 90% and 95% confidence intervals.
– Define clearly what these intervals mean.
3. First USA, a major credit card company, is planning a new o↵er for their current cardholders. The
o↵er will give double ariline miles on purchases for the next 6 months if the cardholder goes online and
registers for the o↵er. To test the e↵ectiveness of the campaign, First USA recently sent out o↵ers to
a random sample of 50,000 cardholders. Of those, 1184 registered.
a. Give a 95% CI for the true proportion of those cardholders who will register for the o↵er.
b. If the acceptance rate is only 2% or less, the campaign won’t be worth the expenses. Given the
confidence interval you found, what would you say?
4. Wildlife biologist inspect 153 deer taken by hunters and find 32 of them carrying ticks that test positive
for Lyme disease.
a. Create 90% CI for the percentage of deer that may carry such ticks.
b. Suppose we want to cut the margin of error in half, how many deer must they inspect?
Chapter 17
– Know how to do one-sided and two-sided alternative hypothesis testing.
– Make sure to check conditions first before testing.
5. During the 2010 season, the home team won 143 of the 246 regular-seaon National Football League
games. Is this strong evidence of a home field advantage in professional football? Test an appropriate
hypothesis and state your consclusion.
6. In 2009, a national vital statistics report indicated that about 3% of all births produced twins. Is
the rate of twin births the same among very young mothers? Data from a large city hospital found
that only 7 sets of twins were born to 469 tennage girls. Test appropiate hypothesis and state your
conlusion.
Chapter 18
– Know how to use one sample t-test and intervals for hypothesis testing.
– Check the conditions first.
– Make sure to know how to find a sample size to fit margin of error.
7. Looking at a mirex contamination in farmed salmon, we found our 95% CI for the mean concentration
to be between .0834 and .0992 parts per million. Later we rejected the null hypothesis that the mean
did not exceed the EPA’s recommended safe level of .08 ppm based on a P-value of .0027. Explain how
these two results are consistent. Your explanation should discuss the confidence level, the P-value, and
the decision.
8. Students investigating the packaging of potato chips purchased 6 bags of Lay’s Ru✏es maarked with
a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following
weights (in grams): 29.3, 28.2, 29.1, 28.7, 28.9, 28.5. Do a hypothesis test to determine if there is a
di↵erence in net weight.
Chapter 19
– Understand the meaning of a low and high P-value
– Understand Type I and Type II errors.
9. Production managers on an assembly line must monitor the output to be sure that the level of defective
products remains small. They periodically inspect a random sample of the items proudced. If they
find a significant increase in the proportion of items that must be rejected, they will halt the assembly
process until the problem can be identified and repaired.
a. In this context, what would be the Type I error? What would be the Type II error? Which would be
considered worse.
Chapter 20
– Know how to do a two sample z-test, the CIs, and the conditions you need in order to use test.
– Know how to do a two sample t-test, the CIs, and the conditions you need in order to use test.
– Know how to do a pooled t-test, the CIs, and the conditions you need in order to use test.
10. In October 2000, the U.S. Department of Commerce reported the results of a large-scale survey on
high school graduation. Researchers contacted more than 25,000 Americans aged 24 years to see if
they had finished high school; 84.9% of the 12,460 males and 88.1% of the 12,678 females indicated
that they had high school diplomas. Does this provide strong evidence that girls are more likely than
boys to complete high school? Create a 95% CI as well.
11. The study of the new CPMP Mathematics methodology also tested students abilities to solve word
problems. The table shows their scores. What do you conclude? (Df= 575)
Math Program
CPMP
Traditional
n
320
273
Mean
57.4
53.9
SD
32.1
28.5
