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## Statistics and maths essay assignment

Statistics and maths essay assignment

1. Identify the variable in the information here.

The archeological site of Tara is more than 4000 years old. Tradition states that Tara was the seat of the high kings of Ireland. Because of its archeological importance, Tara has received extensive study (Reference: Tara: An Archeological survey by Conor Newman, Royal Irish Academy, Dublin). Suppose an archeologist wants to estimate the density of ferromagnetic artifacts in the Tara region. For this purpose, a random sample of 55 plots, each of size 100 square meters, is used. The number of ferromagnetic artifacts for each plot is determined.

(Points: 4)

number of plots

size of the plots

the density of artifacts

number of ferromagnetic artifacts per 100 square meters

number of plots as well as size of the plots

2. Use the list of random numbers given below to simulate the outcomes of tossing a quarter 11 times. Assume that the quarter is balanced (i.e., fair) and an even digit is assigned to the outcome heads (H) and an odd digit to the outcome tails (T).

9 1 9 7 2 3 9 8 0 0 4

(Points: 4)

T T T T H T H H H H H

T T T T H T T H H H H

T T T T H H T H H H H

T T T T H T T H H H T

T T T T H T T H H T H

3. Finish times (to the nearest hour) for 59 dogsled teams are shown below. Draw a histogram. Use five classes. 261

269

236

244

280

296

284

297

290

290

247

256

338

360

341

333

261

267

287

296

313

311

309

309

299

303

277

283

304

305

286

290

286

287

297

299

332

330

309

326

309

326

285

291

295

298

306

315

310

318

318

320

333

321

323

324

327

239

358

The frequency table for the above data is given below.

Class Limits

Boundaries

Midpoint

Freq.

Relative Freq.

Cumulative Freq.

236 260

235.5 260.5

248

5

0.08

5

261 285

260.5 285.5

273

9

0.15

14

286 310

285.5 310.5

298

25

0.42

39

311 335

310.5 335.5

323

16

0.27

55

336 360

335.5 360.5

348

4

0.07

59

(Points: 4)

4. Finish times (to the nearest hour) for 57 dogsled teams are shown below. Use five classes. Categorize the basic distribution shape as uniform, mound-shaped symmetric, bimodal, skewed left, or skewed right.

The relative frequency histogram of the above data is given below.

(Points: 4)

approximately skewed left

approximately bimodal

approximately uniform or rectangular

approximately mound-shaped symmetric

approximately skewed right

5. Pyramid Lake, Nevada, is described as the pride of the Paiute Indian Nation. It is a beautiful desert lake famous for very large trout. The elevation of the lake surface (feet above sea level) varies according to the annual flow of the Truckee River from Lake Tahoe. Assume that the U.S. Geological Survey provided the following data:

Year

1986

1987

1988

1989

1990

1991

1992

1993

Elevation

3812

3815

3817

3803

3798

3808

3795

3797

Year

1994

1995

1996

1997

1998

1999

2000

Elevation

3811

3797

3802

3811

3819

3820

3812

Make a time series graph.

(Points: 4)

6. Use the data given in the following table to make a stem-and-leaf display for milligrams of nicotine per cigarette smoked. In this case, truncate the measurements at the tenths position and use two lines per stem.

Brand

Brand

Alpine

0.82

Multifilter

0.78

Benson & Hedges

1.07

Newport Lights

0.69

Bull Durham

2.06

Now

0.19

Camel Lights

0.67

Old Gold

1.26

Carlton

0.34

Pall Mall Lights

1.08

Chesterfield

1.04

Raleigh

0.95

Golden Lights

0.76

Salem Ultra

0.42

Kent

0.95

Tareyton

1.01

Kool

1.29

True

0.62

L&M

1.02

Viceroy Rich Light

0.69

Lark Lights

1.01

Virginia Slim

1.02

Marlboro

0.90

Winston Lights

0.82

Merit

0.57

(Points: 4)

0

1 = 0.1 milligram

0

1 3 4

0

6 6 6 7 7 8 8 9 9 9

1

0 0 0 0 0 1 1 2 2 3 3

2

0

0

1 = 0.1 milligram

0

2 3 4

0

6 6 6 6 7 8 8 9 9 9

1

0 0 0 0 0 0 1 1 2 2 2

2

0

0

1 = 0.1 milligram

0

1 3 4

0

6 6 6 6 7 7 8 9 9 9

1

0 0 0 1 1 2 2 2 2 2 3

2

0

0

1 = 0.1 milligram

0

2 3 4

0

6 6 7 7 7 8 8 8 9 9

1

0 0 0 0 0 0 0 1 1 3 3

2

1

0

1 = 0.1 milligram

0

2 3 4

0

6 6 6 7 7 8 8 9 9 9

1

0 0 0 0 0 0 1 1 2 2 3

2

2

7. In your biology class, your final grade is based on several things: a lab score, score on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 25% of your total grade, each major test is worth 22.5%, and the final exam is worth 30%. Compute the weighted average for the following scores: 92 on the lab, 83 on the first major test, 94 on the second major test, and 84 on the final exam. Round your answer to the nearest hundredth. (Points: 4)

86.02

88.42

88.02

85.55

90.42

8. Suppose automobile insurance companies gave annual premiums for top-rated companies in several states. The figure below shows box plots for the annual premium for urban customers in three states.

Which state has the smallest range of premiums?

(Points: 4)

California has the smallest range of premiums.

Pennsylvania has the smallest range of premiums.

Texas has the smallest range of premiums.

Texas as well as Pennsylvania have the smallest ranges.

Texas has the largest range of premiums.

Statistics and maths

9. Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let y be the depth (in kilometers) of the quake below the surface at the epicenter. Suppose a random sample of earthquakes gave the following information.

As x increases, does the value of r imply that y should tend to increase, decrease, or remain the same? Explain.

(Points: 4)

Since r is zero, as x increases, y decreases.

Since r is negative, as x increases, y remains the same.

Since r is negative, as x increases, y decreases.

Since r is positive, as x increases, y increases.

Since r is positive, as x increases, y remains the same.

10. It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico:

Given that:

what percentage of the variation in y cannot be explained by the corresponding variation in x and the least-squares line?

(Points: 4)

2.1%

7.2%

26.9%

73.1%

85.5%

11. John runs a computer software store. He counted 124 people who walked by his store in a day, 55 of whom came into the store. Of the 55, only 21 bought something in the store. Estimate the probability that a person who walks by the store will come in and buy something. Round your answer to the nearest hundredth. (Points: 4)

0.17

0.38

0.12

0.61

0.25

Statistics and maths

12. You draw two cards from a standard deck of 52 cards and replace the first one before drawing the second. Find the probability of drawing a 9 and a king in either order. Round your answer to the nearest thousandth. (Points: 4)

0.078

0.012

0.037

0.311

0.024

13. There are three nursing positions to be filled at Lilly Hospital. Position 1 is the day nursing supervisor, position 2 is the night nursing supervisor; and position 3 is the nursing coordinator position. There are 19 candidates qualified for 3 of the positions. Determine the number of different ways that 3 positions can be filled by these applicants. (Points: 4)

5814

969

19

57

437

14. Jim has a 5-year-old car in reasonably good condition. He wants to take out a $30,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows:

x = age

5

6

7

8

9

P (accident)

0.01191

0.01292

0.01396

0.01503

0.01613

Jim is applying to a car insurance company for his car insurance policy. If the car insurance company wants to make a profit of $900 above the expected total losses, how much should it charge for the policy? Round your answer to the nearest dollar.

Statistics and maths

(Points: 4)

$2997

$2999

$3001

$2994

$2992

15. Suppose that about 20% of those called will find an excuse (work, poor health, travel out of town, etc.) to avoid jury duty. If 14 people are called for jury duty, what is the probability that all 14 will be available to serve on the jury? Round your answer to three decimal places. (Points: 4)

**Statistics and maths**

0.035

0.044

0.000

0.055

1.000

16. At a certain excavation site, archaeological studies have used the method of tree-ring dating in an effort to determine when people lived in there. Wood from several excavations gave a mean of (year) 1332 with a standard deviation of 24 years. The distribution of dates was more or less mound-shaped and symmetrical about the mean. Use the empirical rule to estimate a range of years centered about the mean in which about 99.7% of the data (tree-ring dates) will be found. (Points: 4)

from 1284 to 1356

from 1284 to 1332

from 1332 to 1356

from 1260 to 1284

from 1260 to 1404

17. Let z be a random variable with a standard normal distribution. Find the indicated probability below.

(Points: 4)

0.029

0.953

0.982

0.471

0.579

18. Find z such that 20.3% of the standard normal curve lies to the right of z. (Points: 4)

0.831

0.533

-0.533

-0.257

0.257

Statistics and maths

19. How do frequency tables, relative frequencies, and histograms showing relative frequencies help us understand sampling distributions? (Points: 4)

They help us to measure or estimate of the likelihood of a certain statistic falling within the class bounds.

They help us visualize the probability distribution through tables and graphs that approximately represent the random sampling distribution.

They help us visualize the probability distribution through tables and graphs that approximately represent the population distribution.

They help us visualize the sampling distribution through tables and graphs that approximately represent the sampling distribution.

They help us visualize the statistic through tables and graphs that approximately represent the sampling distribution.

20. Assume that about 45% of all U.S. adults try to pad their insurance claims. Suppose that you are the director of an insurance adjustment office. Your office has just received 110 insurance claims to be processed in the next few days. What is the probability that fewer than 45 of the claims have been padded? (Points: 4)

0.778

0.831

0.194

0.806

0.169

21. Total plasma volume is important in determining the required plasma component in blood replacement theory for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that sample of 50 male firefighters are tested and that they have a plasma volume sample mean of ml/kg (milliliters of plasma per kilogram body weight). Assume that ml/kg for the distribution of blood plasma. Find the 95% confidence interval of the population mean blood plasma volume in male firefighters. Round your answer to two decimal places. (Points: 4)

37.47 ml/kg to 39.53 ml/kg

36.87 ml/kg to 35.87 ml/kg

36.37 ml/kg to 40.63 ml/kg

38.20 ml/kg to 38.80 ml/kg

38.13 ml/kg to 38.87 ml/kg

22. A random sample of medical files is used to estimate the proportion p of all people who have blood type B. If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 85% sure that the point estimate will be within a distance of 0.1 from p? (Points: 4)

208

8

4

104

52

23. Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 7.6 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is different from 7.6 seconds. What would you use for the alternative hypothesis? (Points: 4)

seconds

seconds

seconds

seconds

seconds

**Statistics and maths**

24. Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with A random sample of 17 Australian bank stocks has a sample mean of For the entire Australian stock market, the mean dividend yield is Do these data indicate that the dividend yield of all Australian bank stocks is higher than 6.7%? Use Are the data statistically significant at the given level of significance? Based on your answers, will you reject or fail to reject the null hypothesis? (Points: 4)

The P-value is less than the level of significance and so the data are not statistically significant. Thus, we fail to reject the null hypothesis.

The P-value is less than the level of significance and so the data are statistically significant. Thus, we fail to reject the null hypothesis.

The P-value is greater than the level of significance and so the data are statistically significant. Thus, we fail to reject the null hypothesis.

The P-value is greater than the level of significance and so the data are not statistically significant. Thus, we fail to reject the null hypothesis.

The P-value is less than the level of significance and so the data are statistically significant. Thus, we reject the null hypothesis.

**Statistics and maths**

25. A professional employee in a large corporation receives an average of e-mails per day. Most of these e-mails are from other employees in the company. Because of the large number of e-mails, employees find themselves distracted and are unable to concentrate when they return to their tasks. In an effort to reduce distraction caused by such interruptions, one company established a priority list that all employees were to use before sending an e-mail. One month after the new priority list was put into place, a random sample of 38 employees showed that they were receiving an average of e-mails per day. The computer server through which the e-mails are routed showed that Has the new policy had any effect. Use a 1% level of significance to test the claim that there has been a change (either way) in the average number of e-mails received per day per employee. What are the critical values? (Points: 4)

2.58

-2.33 and 2.33

-0.842 and 0.842

1.28

-2.58 and 2.58