# Answer the following questions and show work where appropriate

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

Dade

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?

Justify your answer.

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

should be done instead?

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