Download Take-Home Test #3 v111213 The following chart is of batting

Take-Home Test #3 v111213
The following chart is of batting averages (scores) of 10 randomly selected baseball players:
Batting scores are determined by the number of times a player had a hit while at bat divided by the
number of times the player was a bat (whether a hit or not).
Attend to the 2012 Batting Averages (BA) and answer the following questions:
1. What is the average batting score for the 10 ball players?
2. What is the standard error of the average of the batting scores?
3. Assuming an 92% confidence in the true population average of baseball batting scores, what is
the correct statistical distribution (the test statistic) to use in determining the margin of error?
4. Assuming an 92% confidence in the true population average of baseball batting scores, what is
the correct value of the test statistic with which you would construct the total error?
5. What is the margin of error (E) if we were to establish a 92% confidence interval of the true
population average of the batting scores?
6. Assuming I want to have an allowable error of no more than +-.05 of the true population batting
score, what size sample will I need so to be this accurate?
7. The college president asks the statistics teacher to estimate the average age of the students at
their college. The statistics teacher would like to be 90% confident that the estimate should be
accurate within +-1 year. From a previous study, the standard deviation of the ages is known to
be 3 years How large should the sample size be?
8. A study of 51 English composition professors showed that they spent, on average, 12.6 minutes
correcting a student’s term paper.
a. Find the 95% confidence interval of the mean time for all composition papers when s is 2.5
minutes.
b. If a professor stated that he spent, on average, 30 minutes correcting a term paper, what
would be your reaction?
9. A sample of size n=100 produced the sample mean of X-bar=18. Assuming the population
standard deviation = 4, compute a 95% confidence interval for the population mean
.
10. Assuming the population standard deviation= 4, how large should a sample be to estimate the
population mean with a margin of error not exceeding 0.5?
11. We observed 40 successes in 70 independent Bernoulli trials. Compute a 90% confidence
interval for the population proportion P and state that confidence interval here in appropriate
format:
.
12. The operations manager of a large production plant would like to estimate the mean amount of
time a worker takes to assemble a new electronic component. Assume that the standard
deviation of this assembly time is 4.6 minutes.
a.
After observing 32 workers assembling similar devices, the manager noticed that their
average time was 15.2 minutes. Construct a 92% confidence interval for the mean assembly
time.
b. How many workers should be involved in this study in order to have the mean assembly
time estimated to within +- 15 seconds with 92% confidence?
13. An exit poll of 2000 randomly selected voters found that 1100 favored Candidate “A” over
Candidate “B.” Is the race too close to call or can you declare Candidate “A” a winner? In order
to win the race, a candidate would need the majority of votes. Answer this question by
performing an appropriate 99% confidence interval.
14. A sample of 64 observations is taken from a normal population with a population standard
deviation of 5. The sample mean is 30. Determine the 90 percent confidence interval for the
population mean.
15. A research firm conducted a survey to determine the mean amount steady smokers spend on
cigarettes during a week. They found the distribution of amounts spent per week followed the
normal distribution with a sample standard deviation of $5. A sample of 64 steady smokers
revealed that x-bar= $25.
a. What is the point estimate of the population mean and explain what it indicates.
b. Using the 95 percent level of confidence, determine the confidence interval for μ and
explain what it indicates.
16. Merrill Lynch Securities and Health Care Retirement, Inc., are two large employers in downtown
Toledo, Ohio. They are considering jointly offering child care for their employees. As a part of
the feasibility study, they wish to estimate the mean weekly child-care cost of their employees.
A sample of 10 employees who use child care reveals the following amounts spent last week.
$117
$82
$87
$85
$115
$111
$81
$99
$98
$104
Develop a 90 percent confidence interval for the population mean cost for child-care. Write it:
17. In the above problem (16) what is the margin of error?
18. What is the standard error for problem 16?
19. What is the critical value of the test statistic that you use here for problem 16 to develop the
total error?
20. What are the degrees of freedom for the test statistic that you use here for problem 16?
21. The owner of a popular chain of restaurants wishes to know if completed dishes are being
delivered to the customer’s table within one minute of being completed by the chef. A random
sample of 85 completed dishes found that 70 were delivered within one minute of completion.
Find the 95% confidence interval for the true population proportion of dishes that are delivered
within one minute of being completed by the chef.
22. The protective suits that the employees wear are designed to keep asbestos particles off the
employee’s body. The owner is interested in knowing the average amount of asbestos particles
left on the employee’s skin after a day’s work. Assume a normal distribution. A random sample
of 20 employees had skin tests after removing their protective suit. The average number of
particles found was .481 particles per square centimeter. Assuming that the population
standard deviation is 0.15 particles per square centimeter, calculate a 90% confidence interval
for the number of particles left on the employee's skin.
23. What is the margin of error in problem 22?
24. What is the standard error in problem 22?
25. What is the critical value of the test statistic you should use in problem 22?
26. What are the degrees of freedom (if any) in problem 22?
27. A researcher wishes to determine nationwide opinion about Obamacare acceptance in the
population. The researcher has no previous data but wishes to establish a 95% confidence
interval with an allowable error of +-3% for the true population proportion accepting
OBamacare. What sample size is required for this situation?
28. Have a look at this web page: http://www.wnd.com/2013/11/obamacare-sign-upsastonishingly-pathetic/
You can see there about 3% of the population had signed up for Obamacare whereas 50,000 had
apparently visited the Obamacare site – yes, that’s 3% of 50,000 or about 1500 people have actually
signed up.
Is Obamacare destined to fail or not? Why or why not? Supply as many reasons as possible to
support your answer using statistics and common sense. See here:
http://www.wsj.com/articles/obamacares-failure-contagion-1447116079
That’s all for this Take Home Test #3