# Answer the following questions and show work where appropriate

October 22, 2018

1. In the
presidential election of 2000, a number of events occurred between the initial
vote count of November 7 and the count as certified by the Florida Secretary of
State following counting of absentee ballots, a machine recount, and a Florida
Supreme Court decision to require some hand recounts. Table 2 shows results in
selected Florida counties indicating the initial count, the certified count,
and the change in votes for Gore.
a. Based
on this information, how strong is the relationship between the vote on
November 7 and the change (from November 7 to the certified totals)? Please
give both the name of the measure and its value.
b. Find
the regression equation to predict the change from the number of votes cast on
November 7.
c. Based
on this information, how large a change would you expect to see in a county
that recorded 250,000 votes for Gore on November 7?
d. How
much larger (or smaller) was the change in Duval County as compared to what you
would expect for the number of votes counted in Duval County on November 7,
based on this information?
e. How
much of the variability in certified totals is explained by the initial count
on November 7? Please give the name of the usual measure with its value.
f. Is
there a significant relationship between the vote on November 7 and the
certified total? Please give the result with justification.

TABLE 2 Votes for Albert Gore, Jr.

County

Nov 7

Certified

Change

Broward

386,518

387,760

1,242

Palm
Beach

268,945

269,754

809

328,702

328,867

165

Volusia

97,063

97,313

250

Orange

140,115

140,236

121

Duval

107,680

108,039

359

Hills.1em;”>o.1em;”>brough

169,529

169,576

47

1. Your
company is hoping to fill a key technical position and has advertised in hopes
of obtaining qualified applicants. Because of the demanding qualifications, the
pool of qualified people is limited and Table 1 below shows your subjective
probabilities for each outcome. a. Find the probability of obtaining at least
one applicant.
b. Find
the probability of obtaining two or more applicants.
c. Find
the mean number of applicants.
d. Find
the standard deviation of the number of applicants and write a sentence
interpreting its meaning.

Table 1
Probabilities for Qualified Technical Applicants

Number of
Applicants Probablity
0
0.30
1
0.55
2
0.10
3
0.05

2. Under
usual conditions, a distillation unit in a refinery can process a mean of
135,000 barrels per day of crude petroleum, with a standard deviation of 6,000
barrels per day. You may assume a normal distribution. a. Find the probability
that more than 130,000 barrels will be produced on a given day.
b.
Consider a random sample of 40 distilleries. Find the probability that the average
daily production will be more than 130,000 barrels.
c. Why are
the probabilities computed in a) and b) different?
d. Find
the probability that more than 150,000 barrels will be produced on a given day.

e. Find
the probability that less than 125,000 barrels will be produced on a given day.

3.You work
for a company that prepares and distributes frozen foods. The package claims a
net weight of 14.5 ounces. A random sample of today’s production was weighed,
producing the following data set:
14.43,
14.37, 14.38, 14.29, 14.60, 14.45, 14.16, 14.52, 14.19, 14.04, 14.31
A sample
was also selected from yesterday’s production. The average was 14.46 and the
standard deviation was 0.31.
a.
Estimate the mean weight you would have found had you been able to weigh all
packages produced today.
b. For a
typical individual package produced yesterday, approximately how different was
the actual weight from yesterday’s average?
c. Find
the 95% confidence interval for the mean weight for all packages produced
today.
d.
Identify the hypotheses you would work with to test whether or not your claimed
weight is correct, on average, today.
e. Is
there a significant difference between claimed and actual mean weight today?

Should We Keep or Get
Rid of This Supplier?You and your co-worker
B. W. Kellerman have been assigned the task of evaluating a new supplier of
parts that your firm uses to manufacture home and garden equipment. One
particular part is supposed to measure 8.5 centimeters, but in fact any
measurement between 8.4 and 8.6 cm is considered acceptable. Kellerman has
recently presented analysis of measurements of 99 recently delivered parts. The
executive summary of Kellerman’s rough draft of your report reads as follows:The quality of parts
delivered by HypoTech does not meet our needs. Although their prices are
attractively low and their deliveries meet our scheduling needs, the quality of
their production is not high enough. We recommend serious consideration of
alternative sources. Now it’ s your turn. In addition to reviewing Kellerman’s
figures and rough draft, you know you are expected to confirm (or reject) these
findings by your own independent analysis. It certainly looks as though the
conclusions are reasonable. The main argument is that while the mean is 8.494,
very close to the 8.5-cm standard, the standard deviation is so large, at
0.103, that defective parts occur about a third of the time. I fact, Kellerman
was obviously proud of having remembered a fact from statistics class long ago,
something about being within a standard deviation from the mean about a third
of the time. And defective parts might be tolerated 10% or even 20% of the time
for this particular application at these prices, but 30% or 33% is beyond
reasonable possibility. It looks so clear, and yet, just to be sure, you decide
t take a quick look at the data. Naturally, you expect it to confirm all this.
Here is the data set:8.503 8.503 8.500 8.496
8.500 8.503 8.497 8.504 8.503 8.5068.502 8.501 8.489 8.499
8.492 8.497 8.506 8.502 8.505 8.4898.505 8.499 8.489 8.505
8.504 8.499 8.499 8.506 8.493 8.4948.510 8.310 8.804 8.503
8.782 8.502 8.509 8.499 8.498 8.4938.346 8.499 8.505 8.509
8.499 8.503 8.494 8.511 8.501 8.4978.501 8.502 7.780 8.494
8.500 8.498 8.500 8.502 8.501 8.4918.511 8.494 8.374 8.492
8.497 8.150 8.496 8.501 8.489 8.5068.493 8.498 8.505 8.490
8.493 8.501 8.497 8.501 8.498 8.5038.508 8.501 8.499 8.504
8.505 8.461 8.497 8.495 8.504 8.5018.493 8.504 8.897 8.505
8.490 8.492 8.503 8.507 8.497Discussion Questions1.Are Kellerman’s
calculations correct? These are the first items to verify.2.Take a close look at
the data using appropriate statistical methods.3.Are Kellerman’s
conclusions correct? If so, why do you think so? If not, why not and what