Expert answer:please see the files and do all thre part textbook questions and statistical investigation and every day statitics
1211111111.docx
housing_survey_data_fall_2014.xlsx
problem_set_8_econ_2100_fall_2017.docx
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1. 1 Nan Compos-Mentis, a technical consultant, claims that she can
increase average hourly productivity for the fabricators at Stryker
Manufacturing by more than 10 units per worker. To support her
claim, Nan plans to select a sample of workers, provide the workers in
the sample with special training, and then use results from the sample
in a hypothesis test designed to establish whether the training has had
the desired effect. What null and alternative hypotheses would you
recommend here?
3
In recent years the average time it takes audit teams from Trimble and
Martin to complete a company audit has been 55.8 hours. In monitoring
the performance of one of these audit teams recently, reviewers found
that the average time for a random sample of team audits differed by
nearly 6 hours from the company average. If you were to use the sample
average in a hypothesis test to determine if this team’s average
performance is different from the overall company average, what null and
alternative hypotheses would you recommend?
45. Suppose you are testing the following hypotheses:
H0: μ ≤ 1500
Ha: μ > 1500
Sample size is 25. The sample mean is 1545 and the sample standard
deviation is 75. The significance level is .05. Assume that the values in the
population are normally distributed.
a. Compute the sample test statistic, tstat.
b. With the help of a statistical calculator or a statistical software
package, determine the appropriate p-valuehere and use it to conduct
the test. (If you are using Excel, use the statistical function
T.DIST.RT to produce the appropriate p-value.)
c. Based on your work in parts a and b, should you reject the null
hypothesis? Explain.
d. 50. According to ePaynews.com, the average online retail transaction
is $187 (source: epaynews.com/.) Suppose you take a random sample
of 50 online transactions made through your company’s website and
find that the average transaction amount in the sample is $195. The
sample standard deviation is $36. Is the sample evidence sufficient to
reject the null hypothesis shown below? Use a significance level of
.05.
e. H0: μ = 187 (The average transaction amount for customers on your
company’s website is the same as the average for all retail transactions
on the Internet.)
f. Ha: μ ≠ 187 (The average transaction amount for customers on your
company’s website is not the same as the average for all retail
transactions on the Internet.)
g. 70. Your friend Fred claims that his average gym workout time
is at least 150 minutes per day. You pick a random sample of 10
days and observe that on the days in the sample, Fred’s average
workout time was 136 minutes. The standard deviation of
workout times in the sample was 28 minutes. You plan to use
the sample results to test Fred’s claim. Assume that Fred’s
workout times are normally distributed.
h. Set up an appropriate hypothesis test to test Fred’s claim. Use a
significance level of 5%. Should Fred’s claim be rejected?
Explain.
i. 71. Refer to Exercise 70. Suppose sample size was 50 days
rather than 10 days. Show the proper hypothesis test and report
your conclusion.
j. 76. You have set up a hypothesis test to determine if the
plywood sheets being produced by your mill meet company
standards. For each large batch of sheets, you select a sample of
six sheets and count the number of surface flaws in each. You
then compute the average number of flaws in the sample and
use the sample result to test the following hypotheses:
k. H0: μ ≤ 3.5 (The average number of flaws in the large batch of
plywood sheets is 3.5 or less.)
l. Ha: μ > 3.5 (The average number of flaws in the batch of
plywood sheets is greater than 3.5.)
m. Suppose a particular sample of six sheets yields the following
data:
Use a significance level of .05. Assume that the population
distribution of flaws in a sheet is normal. Determine the p-value for
the sample mean here and use it to decide whether you can reject the
null hypothesis. (If you are using Excel, use the statistical function
T.DIST.RT.)
77. From a recent production run of compact fluorescent (CF) bulbs,
you select a random sample of 10 bulbs. Using an accelerated bulb life
simulation, you find that the average life for the bulbs in the sample is
2440 hours, with a sample standard deviation of 60 hours. Use these
sample results to test, at the 5% significance level, the null hypothesis
that the average life for the full population—the entire production
run—of bulbs is precisely 2500 hours, no more and no less. Report
your conclusion and explain.
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ECON 2100
PROBLEM SET 8
Textbook questions
Chapter 9: 1, 3, 45, 50, 70, 71, 76, 77.
Statistical investigation
These questions again use data from a survey of Albers students conducted in Fall 2014,
regarding their housing situation. The data are found in the file “housing survey data fall 2014.”
Nationwide, the average household size in 2010 was determined to be 2.58 people
(www.census.gov). You would like to conduct a hypothesis test at a 5% significance level to
determine whether there is evidence that the household size for Albers students differs from the
national average.
a. State the null and alternative hypothesis for the test.
b. Calculate the appropriate test statistic (t-stat) for the test.
c. What is the critical value for the test?
d. Do you reject, or not reject, the null hypothesis? Explain your decision based on the critical
value.
e. Find the p-value for the hypothesis test (use Excel’s T.DIST.2T function).
f. Using the p-value, explain your decision regarding the null hypothesis (reject/not reject).
g. Summarize your conclusion in a sentence or two: what does the test show about household
size?
Everyday statistics
Please read the article “When Whites Get a Free Pass,” linked here and posted along with the
assignment. Also read “Everyday statistics: Smell Test” on page 349 of our textbook.
a. Briefly describe the study: what strategy was used to test for racial discrimination?
b. The fourth paragraph of the article includes the sentence, “the study uncovered substantial,
statistically significant race discrimination.” What does “statistically significant” mean here?
c. In the sentence, “the study uncovered substantial, statistically significant race discrimination,”
what evidence is provided to show that the racial discrimination was substantially (socially or
economically significant)?
d. This study is in the tradition of “audit testing,” in which randomized trials are used to test for
discrimination. What is particularly original about this “audit test”?
1
Opinion | Op-Ed Contributor
NYTimes
Research Shows White Privilege Is Real
By IAN AYRES, FEB. 24, 2015
Eddie Murphy before his “White Like Me” skit. Credit Frankie Ziths/Associated Press
NEW HAVEN — THE recent reunion show for the 40th anniversary of “Saturday Night Live”
re-aired a portion of Eddie Murphy’s 1984 classic “White Like Me” skit, in which he disguised
himself to appear Caucasian and quickly learned that “when white people are alone, they give
things to each other for free.”
The joke still has relevance. A field experiment about who gets free bus rides in Brisbane, a city
on the eastern coast of Australia, shows that even today, whites get special privileges,
particularly when other people aren’t around to notice.
As they describe in two working papers, Redzo Mujcic and Paul Frijters, economists at the
University of Queensland, trained and assigned 29 young adult testers (from both genders and
different ethnic groups) to board public buses in Brisbane and insert an empty fare card into the
bus scanner. After the scanner made a loud sound informing the driver that the card did not have
enough value, the testers said, “I do not have any money, but I need to get to” a station about 1.2
miles away. (The station varied according to where the testers boarded.)
With more than 1,500 observations, the study uncovered substantial, statistically significant race
discrimination. Bus drivers were twice as willing to let white testers ride free as black testers (72
percent versus 36 percent of the time). Bus drivers showed some relative favoritism toward
testers who shared their own race, but even black drivers still favored white testers over black
testers (allowing free rides 83 percent versus 68 percent of the time).
2
The study also found that racial disparities persisted when the testers wore business attire or
dressed in army uniforms. For example, testers wearing army uniforms were allowed to ride free
97 percent of the time if they were white, but only 77 percent of the time if they were black.
This elegant experiment follows in a tradition of audit testing, in which social scientists have sent
testers of different races to, for example, bargain over the price of new cars or old baseball cards.
But the Australian study is the first, to my knowledge, to focus on discretionary
accommodations. It’s less likely these days to find people in positions of authority, even at lower
levels of decision making, consciously denying minorities rights. But it is easier to imagine
decision makers, like the bus drivers, granting extra privileges and accommodations to
nonminorities. Discriminatory gifts are more likely than discriminatory denials.
A police officer is an out-and-out bigot if she targets innocent blacks for speeding tickets. But an
officer who is more likely to give a pass to white motorists who exceed the speed limit than to
black ones is also discriminating, even if with little or no conscious awareness. This is one
reason the Twitter hashtag #crimingwhilewhite is so powerful: It draws attention to the racially
biased exercise of discretion by police officers, prosecutors and judges, which results in whites
getting a pass for the kinds of offenses for which minorities are punished.
Racial discrimination is more likely in settings in which both decision makers and bystanders
cannot easily observe how comparable nonminorities are treated. A restaurant is unlikely to
charge Hispanics higher prices for a hamburger, because the victim could compare her bill to the
price listed on the menu. But one-off accommodations where the decision maker retains
substantial discretion don’t offer any easy point of comparison. My kids, who are white, have
never been turned down when I asked if they could use a bathroom designated for “employees
only.” After reading the Australian bus study, I wonder whether the same is true for minority
families.
The bus study underscores this point. Drivers were more likely to let testers ride free when there
were fewer people on the bus to observe the transaction. And the drivers themselves were
probably not aware that they were treating minorities differently. When drivers, in a
questionnaire conducted after the field test, were shown photographs of the testers and asked
how they would respond, hypothetically, to a free-ride request, they indicated no statistically
significant bias against minorities in the photos (86 percent said they would let the black
individual ride free).
Of course, unconscious bias might play out differently in the United States than in Australia. But
research in America, too, suggests that decision makers use discretion to bestow benefits in a
discriminatory fashion. For example, a recent study of 22 law firms by Arin N. Reeves, a lawyer
and sociologist, found that partners were less critical of a junior lawyer’s draft memo if they
were told the lawyer was white than if they were told the lawyer was black.
What does white privilege mean today? In part, it means to live in the world while being given
the benefit of the doubt. Have you ever been able to return a sweater without a receipt? Has an
employee ever let you into a store after closing time? Did a car dealership take a little extra off
the sticker price when you asked? When’s the last time you received service with a smile?
3
White privilege doesn’t (usually) operate as brazenly and audaciously as in the Eddie Murphy
joke, but it continues in the form of discretionary benefits, many of them unconscious ones.
These privileges are hard to eradicate, but essential to understand.
Ian Ayres is a law professor at Yale.
4
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