Week 1 Assignment

 

1. Determine which of the following statements is descriptive in nature and which is inferential. Refer to the data below in How Old is My Fish?

How Old is My Fish
Average age by length of largemouth bass in new York State
Length	8	9	10	11	12	13	14
Age	2	3	3	4	4	5	5

a. All 9-inch largemouth bass in New York State are an average of 3 years old.

b. Of the largemouth bass used in the sample to make up th NYS DEC Freshwater Fishing Guide, the average age of 9-inch largemouth bass was 3 years.

In your answer also describe and explain the difference between descriptive statistics and inferential statistics.

Question 2

2. Since 1981, Fortune magazine has been tracking what they judge to be the best 100 companies to work for. The companies must be at least ten years old and employ no less than 500 people. Below are the top 25 from the list compiled in 1998, together with each company’s percentage of females, percentage of job growth over a 2 year span, and number of hours of professional training required each year by the employer.

Company Name	Women (%)	Job Growth (%)	Training (hr/yr)
Southwest Airlines	55	26	15
Kingston Technology	48	54	100
SAS Institute	53	34	32
FEL-Pro	36	10	60
TDIndustries	10	31	40
MBNA	58	48	48
W.L.Gore	43	26	27
Microsoft	29	22	8
Merck	52	24	40
Hewlett-Packard	37	10	0
Synovus Financial	65	23	13
Goldman Sachs	40	13	20
MOOG	19	17	25
DeLoitte&Touche	45	23	70
Corning	38	9	80
Wegmans Food Products	54	3	30
Harley-Davidson	22	15	50
Federal Express	32	11	40
Proctor & Gamble	40	1	25
Peoplesoft	44	122	0
First Tennessee Bank	70	1	60
J.M. Smucker	48	1	24
Granite Rock	17	29	43
Petagonia	52	5	62
Cisco Systems	25	189	80

a. Find the mean, range, variance, and standard deviation for each of the three variables shown in the list. Present your results in a table.

b. Using your results from (a), compare the distributions for job growth percentage and percentage of women employed. What can you conclude?

Grading Criteria Assignments	Maximum Points
Meets or exceeds established assignment criteria	40
Demonstrates an understanding of lesson concepts	20
Clearly present well-reasoned ideas and concepts	30
Mechanics, punctuation, sentence structure, spelling that affects clarity, and citation of sources as needed	10
Total	100

 

 

Week2 Assignment

Assignment Week 2

Question 1

1. Baseball stadiums vary in age, style, size, and in many other ways. Fans might think of the size of the stadium in terms of the number of seats; while the player might measure the size of the stadium by the distance from the homeplate to the centerfield fence. Note: CF = distance from homeplate to centerfield fence.

Using the Excell add-in construct your scatter diagram with the data set provide below.

Seats		CF
38805		420
41118		400
56000		400
45030		400
34077		400
40793		400
56144		408
50516		400
40615		400
48190		406
36331		434
43405		405
48911		400
50449		415
50091		400
43772		404
49033		407
47447		405
40120		422
41503		404
40950		435
38496		400
41900		400
42271		404
43647		401
42600		396
46200		400
41222		403
52355		408
45000		408

 

Is there a relationship between these two measurements for the size of the 30 Major League Baseball stadiums?

a. Before you run your scatter diagram answer the following: What do you think you will find? Bigger fields have more seats? Smaller fields have more seats? No relationship exists between field size and number of seats? A strong relationship exists between field size and number of seats? Explain.

b. Construct a scatter diagram and include it in your answer.

c. Describe what the scatter diagram tells you, including a reaction to your answer in (a).

Question 2

2. Place a pair of dice in a cup, shake and dump them out. Observe the sum of dots. Record 2, 3, 4, _ , 12. Repeat the process 25 times. Using your results, find the relative frequency for each of the values: 2, 3, 4, 5, _ , 12.

Grading Criteria Assignments	Maximum Points
Meets or exceeds established assignment criteria	40
Demonstrates an understanding of lesson concepts	20
Clearly present well-reasoned ideas and concepts	30
Mechanics, punctuation, sentence structure, spelling that affects clarity, and citation of sources as needed	10
Total	100

Assignment Week 3

Question 1

If you could stop time and live forever in good health, what age would you pick? Answers to this question were reported in a USA Today Snapshot. The average ideal age for each age group is listed in the following table; the average ideal age for all adults was found to be 41. Interestingly, those younger than 30 years want to be older, whereas those older than 30 years want to be younger.

Age Group	Ideal Age
18 – 24	27
25 – 29	31
30 – 39	37
40 – 49	40
50 – 64	44
65 +	59

Age is used as a variable twice in this application.

1. The age of the person being interviewed is not the random variable in this situation. Explain why and describe how age is used with regard to age group.
2. What is the random variable involved in this study? Describe its role in this situation.
3. Is the random variable discrete or continuous?

Question 2

Find the area under the normal curve that lies to the left of the following z-values.

1. Z=-1.30
2. Z=-3.20
3. Z=-2.56
4. Z=-0.64

Grading Criteria Assignments	Maximum Points
Meets or exceeds established assignment criteria	40
Demonstrates an understanding of lesson concepts	20
Clearly present well-reasoned ideas and concepts	30
Mechanics, punctuation, sentence structure, spelling that affects clarity, and citation of sources as needed	10
Total	100

 

 

Assignment Week 5

Question 1

Using the telephone numbers listed in your local directory as your population, randomly obtain 20 samples of size 3. From each telephone number identified as a source, take the fourth, fifth, and sixth digits.

1. Calculate the mean of the 20 samples
2. Draw a histogram showing the 20 sample means. (Use classes -0.5 to 0.5, 0.5 to 1.5, 1.5 to 2.5 and so on).
3. Describe the distribution of the x-bars that you see in part b (shape of distribution, center, and the amount of dispersion).
4. Draw 20 more samples and add the 20 new x-bars to the histogram in part b. Describe the distribution that seems to be developing.

Use the empirical rule to test for normality. See the sampling distribution of sample means and the central limit theorem develop from your own data!

Question 2

Consider a population with μ = 43 and σ = 5.2.

1. Calculate the z-score for an xÌ… of 46.5 from a sample of size 35.
2. Could this z-score be used in calculating probabilities using Table 3 in Appendix B? Why or why not?

Question 3

State the null and alternative hypotheses for each of the following:

1. You want to show an increase in buying and selling of single-family homes this year when compared with last year’s rate.
2. You are testing a new recipe for low-fat cheesecake and expect to find that its taste is not as good as traditional cheesecake.
3. You are trying to show that music lessons have a positive effect on a child’s self-esteem.
4. You are investigating the relationship between a person’s gender and the automobile he or she drives—specifically you want to show that more males than females drive truck-type vehicles.

Grading Criteria Assignments	Maximum Points
Meets or exceeds established assignment criteria	40
Demonstrates an understanding of lesson concepts	20
Clearly present well-reasoned ideas and concepts	30
Mechanics, punctuation, sentence structure, spelling that affects clarity, and citation of sources as needed	10
Total	100

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Assignment Week 6

Question 1

Based on a survey of 1,000 adults by Greenfield Online and reported in a May 2009 USA Today Snapshot, adults 24 years of age and under spend a weekly average of $35 on fast food. If 200 of the adults surveyed were in the age category of 24 and under and they provided a standard deviation of $14.50, construct a 95% confidence interval for the weekly average expenditure on fast food for adults 24 years of age and under. Assume fast food weekly expenditures are normally distributed.

Question 2

An experiment was designed to estimate the mean difference in weight gain for pigs fed ration A as compared with those fed ration B. Eight pairs of pigs were used. The pigs within each pair were littermates. The rations were assigned at random to the two animals within each pair. The gains (in pounds) after 45 days are shown below:

RationA	RationB
65	58
37	39
40	31
47	45
49	47
65	55
53	59
59	51

Assuming weight gain is normal, find the 95% confidence interval estimate for the mean of the differences μ_d where d= ration A – ration B.

Assignment Week 7

Question 1

To compare commuting times in various locations, independent random samples were obtained from the six cities presented in the Longest Commute to Work graphic on page 255 in your textbook. The samples were from workers who commute to work during the 8:00 a.m. rush hour. One-way Travel to Work in Minutes

Atlanta	Boston	Dallas	Philadelphia	Seattle	St. Louis
29	18	42	29	30	15
21	37	25	20	23	24
20	27	26	33	31	42
15	25	32	37	39	23
37	32	20	42	14	33
26	34	26			18
	48	35

1. Construct a graphic representation of the data using six side-by-side dotplots.
2. Visually estimate the mean commute time for each city and locate it with an X.
3. Does it appear that different cities have different effects on the average amount of time spent by workers who commute to work during the 8:00 a.m. rush hour? Explain.
4. Does it visually appear that different cities have different effects on the variation in the amount of time spent by workers who commute to work during the 8:00 a.m. rush hour? Explain.

Part 2

1. Calculate the mean commute time for each city depicted.
2. Does there seem to be a difference among the mean one-way commute times for these six cities?
3. Calculate the standard deviation for each city’s commute time.
4. Does there seem to be a difference among the standard deviations between the one-way commute times for these six cities?

Part 3

1. Construct the 95% confidence interval for the mean commute time for Atlanta and Boston.
2. Based on the confidence intervals found does it appear that the mean commute time is the same or different for these two cities (Atlanta and Boston). Explain
3. Construct the 95% confidence interval for the mean commute time for Dallas.
4. Based on the confidence intervals found in (Atlanta and Boston) and Dallas does it appear that the mean commute time is the same or different for Boston and Dallas? Explain.
5. Based on the confidence levels found in (Atlanta and Boston) and (Dallas) does it appear that the mean commute time is the same or different for the set of three cities, Atlanta, Boston, and Dallas? Explain
6. How does your confidence intervals compare to the intervals given for Atlanta, Boston, and Dallas in Longest Commute to Work on page 255?

Question 2

Interstate 90 is the longest of the east-west U.S. interstate highways with its 3,112 miles stretching from Boston, MA at I-93 on the eastern end to Seattle WA at the Kingdome on the western end. It travels across 13 northern states; the number of miles and number of intersections in each of those states is listed below.

State	No. of Inter	Miles
WA	57	298
ID	15	73
MT	83	558
WY	23	207
SD	61	412
MN	52	275
WI	40	188
IL	19	103
IN	21	157
OH	40	244
PA	14	47
NY	48	391
MA	18	159

1. Construct a scatter diagram of the data.
2. Find the equation for the line of best fit using x= miles and y=intersections.
3. Using the equation found in part (b), estimate the average number of intersections per mile along I-90.
4. Find a 95% confidence interval for β₁.
5. Explain the meaning of the interval found in part d.

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