Download /Users/heather/Desktop/Exam 2 Review.nb

1.
A new teacher is analyzing whether or not there is an association between scores earned by students on
their first exam in the course and the course grade earned by students at the end of the term. Exams are scored
using a 100 point scale (0 to 100 points) and course grades use a 100% scale (0% to 100%). There are 35
students in the course.
HaL Find the equation of the regression line y` = a + b x. The mean and standard deviation for the
Course Grade variable is 0.766 and 0.123 The mean and standard deviation for the Exam 1 Score
variable is 83.943 and 11.295 The correlation is 0.7845 Be very sensitive to roundoff errors.
HbL Predict the course grade for a student who scores a 91 on their first exam. Use the equation of the
regression line found in (b).
2.
A Gallup Poll asked "Do you think the United States needs to: change its current strategy in Iraq, keep
its current strategy, but change its tactics, or keep both its current strategy and tactics in Iraq? ... Nearly 6 in
10 Americans (59%) say the United States should change its strategy in Iraq." Gallup's report said "Results
for this panel study are based on telephone interviews with 1,001 national adults, aged 18 and older, conducted Oct. 23-26, 2006." Furthermore, the article included the statements "For results based on the total
sample of national adults, one can say with 95% confidence that the maximum margin of sampling error is ±3
percentage points. In addition to sampling error, question wording and practical difficulties in conducting
surveys can introduce error or bias into the findings of public opinion polls."
HaL
HbL
Describe in as much detail as possible given the excerpts from the article above the population.
How many members of the sample felt that the United States should change its strategy in Iraq?
HcL If the confidence level was changed from 95% to 99% would the maximum margin of sampling
error be (1) less than 3%, (2) greater than 3%, or (3) remain at 3%?
HdL Suppose that there are 240 million adults living in the US. How many members of the population
described by the article would you estimate feel that the United States should change its strategy in Iraq?
3.
Choose an adult aged 25 years or over at random. The probability is 0.151 that the person chosen did
not complete high school, 0.322 that the person has a high school diploma but no further education, and 0.289
that the person has at least a bachelor's degree.
HaL What must be the probability that a randomly chosen adult has some education beyond high school
but does not have a bachelor's degree?
HbL
4.
What is the probability that a randomly chosen young adult has at least a high school education?
The distribution of the weights of all bags of M&M candies measured in grams is NH48.5, 1.3L:
44.6 45.9 47.2 48.5 49.8 51.1 52.4
HaL If a single bag of M&M's was selected at random, what is the probability that the weight of the
bag would be between 48 grams and 48.5 grams?
HbL If a SRS of 40 bags of M&M's was selected and the average weight of the 40 bags was computed,
what is the probability that the average weight for the 40 bags would be between 48 grams and 48.5
grams?
Suppose a population is composed of uniformly distributed values ranging from 0 to 90 ( m = 45 and
5.
s = 25.98 ). The population distribution is shown below.
Uniformly Distributed Population
0
20
40
60
80
HaL What is the probability that a single value selected from the population would be greater than 40
and less than 45?
HbL What is the probability that a SRS of size 100 taken from this population would have a sample
mean greater than 40 and less than 45?
To estimate the mean height m of adult women in your city, you will measure an SRS of adult women.
6.
You know from government data that heights of adult women are approximately Normal with standard deviation 2.3 inches. How large an SRS do you need to collect so that the standard deviation of êê
x is 0.25?
7.
To estimate the mean weight of all bags of M&M candies you collect a SRS of 75 bags and find the
average weight of the 100 bags to be 48.95 grams. Give a 96% confidence interval for the mean weight of all
bags of M&M's. Assume s = 1.4 for the weights of all bags of M&M's.
8.
You would be satisfied to estimate the mean weight of all bags of M&M's to within ± 0.1 grams with
95% confidence. How many bags of M&M candies must be in your SRS? Assume s = 1.4 for the weights of
all bags of M&M's.
9.
The mean height of American women is about 64 inches, with standard deviation about 2.7 inches. The
mean height of American men is about 69 inches, with standard deviation about 2.8 inches. If the correlation
between the heights of husbands and wives is about r = 0.5, find the equation of the regression line that will
predict the height of the wife when given the height of the husband.
10. Use your answer from the previous problem to predict the height of the wife of a man who is 72 inches
tall. Would you consider this estimate to be an accurate one?
11. A study of children in elementary school shows a high positive correlation between the heights and
scores on a test of reading comprehension. Johnny, an exceptionally bright and tall fifth grader concludes that
he must have a high reading comprehension. Explain to Johnny what is wrong with his conclusion.
12. The following is a list of the 10 most popular boys names. Susy wants to name her newborn son one of
these names, but can't decide which one to use. Use line 108 of table B to find a SRS of size 3 of the names in
the list, so that Susy will only have three names to chose from.
AIDAN ETHAN
CADEN JADEN
CALEB DYLAN
JACOB CONNOR
LOGAN HAYDEN
13. A political scientist wants to know how college students feel about the Social Security program. The
scientist obtains a list of all the students at WWCC and mails a questionnaire to 200 of the students selected at
random. Based upon 98 returned surveys the scientist concludes that college students are dissatisfied with the
Social Security program. What are the population and sample of this study?
13. A political scientist wants to know how college students feel about the Social Security program. The
scientist obtains a list of all the students at WWCC and mails a questionnaire to 200 of the students selected at
random. Based upon 98 returned surveys the scientist concludes that college students are dissatisfied with the
Social Security program. What are the population and sample of this study?
14. Give an explanation for what is wrong with the conclusion of the study described in the previous
problem.
15.
Read the description for each of the following studies, then answer the question.
Study 1: A publishing company wants to measure the effectiveness of one of its textbooks. The company
tests a group of students for comprehension and then divides the students into two groups. One group uses the
book and one doesn't. The company then retests the students and compares the results.
Study 2: A political scientist wants to know how college students feel about the Social Security program.
The scientist obtains a list of all the students at WWCC and mails a questionnaire to 200 of the students
selected at random. Based upon 98 returned surveys the scientist concludes that college students are dissatisfied with the Social Security program.
For each study, determine whether it is an observational study or an experiment and give reasons for your
answers.
16. In a bag full of marbles there are three red marbles, five blue marbles, and seven yellow marbles. Give
the probability model for the act of drawing one marble at random from the bag (i.e. what is the sample space
and probability of each event).
17. What is the probability of drawing either a red marble or a blue marble? Explain your answer using the
appropriate probability rule.
18. Voter registration records in a small town in Washington show that 52% of all voters are Republican.
On Mayberry Ave., 50 people are polled and it is found that 49% of them are Republican. Which of these
numbers is a parameter and which is a statistic? Explain your answers.
19. The weight of the eggs produced by a certain breed of hen is Normally distributed with mean 65g and
standard deviation 5g. Think of cartons of such eggs as SRSs of size 12 from the population of all eggs.
What is the approximate distribution of the mean weight from each carton of eggs?
20. For the situation described in the previous problem, what is the probability that the weight of a carton
falls between 750g and 825g?
21. A class survey in a large class for first-year college students asked, "About how many minutes do you
study on a typical weeknight?" The mean response of the 200 students was 135 minutes. Suppose we know
that the study time of all first year students at this university follows a Normal distribution with standard
deviation s = 60 minutes. Find a 99% confidence interval for the mean study time of all first-year students.
22.
How large a sample is needed to cut the margin of error for the previous problem to 6?
23. If the distribution of the study time of all first year students at this university didn't follow a Normal
distribution but still had standard deviation s = 60, could you still find the same confidence interval asked for
above? Give a reason for your answer.
24. A manufacturer of small appliances wants to estimate retail sales of its hand mixers by gathering information from a sample of retail stores. This month an SRS of 75 stores finds that these stores sold an average of
24 mixers, with standard deviation 11. Give a 95% confidence interval for the mean number of mixers sold
by all stores.