Reference no: EM132555808

FAC 1014 Introduction to Statistics Assignment - UCSI College, Malaysia

Task - Answer all questions.

Q1. State and describe the two major types of statistics.

Q2. Indicate whether each of the following examples refers to a population or to a sample:

a) A group of 25 patients selected to test a new drug.

b) Total items produced on a machine for each year from 1995 to 2009.

c) Yearly expenditures on clothes for 50 persons.

d) Number of houses sold by each of the 10 employees of a real estate agency during 2009.

Q3. Sketch a chart to show types of variable and data.

Q4. Name any 5 different types of chart or graph. Categories those chart or graph among qualitative or quantitative variable.

Q5. Name 2 of the sampling methods that selected data in a more similar way. Describe the similarity and the difference between these 2 sampling methods.

Q6. An experiment compared the ability of three groups of participants to remember briefly-presented chess positions as shown in Figure 1 below. The data are shown below. The numbers represent the number of pieces correctly remembered from three chess positions. Create side-by-side box plots for these three groups. What can you say about the differences between these groups from the box plots?

Non-Players	Beginners	Tournament players
22.1	32.5	40.1
22.3	37.1	45.6
26.2	39.1	51.2
29.6	40.5	56.4
31.7	45.5	58.1
33.5	51.3	71.1
38.9	52.6	74.9
39.7	55.7	75.9
43.2	55.9	80.3
43.2	57.7	85.3
Figure1

Q7. Every year, Consumer Reports publishes a magazine titled New Car Ratings and Review that looks at vehicle profiles for the year's models as shown in Figure 2. It lets you see in one place how, within each category, the vehicles compare. One category of interest, especially when fuel prices are rising, is fuel economy, measured in miles per gallon (mpg). Following is a list of overall mpg for 14 different full-sized and compact pickups.

14	13	14	13	14	14	11
12	15	15	17	14	15	16
Figure 2

a) Find the rang of sample.

b) Find the standard deviation of the sample.

Q8. The following data give the number of hot dogs consumed by 10 participants in a hot dog-eating contest.

21

17

32

8

20

15

17

23

9

18

Calculate the range, variance, and standard deviation for these data.

Q9. Spot prices per barrel of crude oil reached their highest levels in history during June and July of 2008. The following data give the spot prices (in dollars) of a barrel of crude oil for 14 business days from June 30, 2008, through July 18, 2008 (Energy Information Administration, April 15, 2009).

139.96	141.06	143.74	145.31	141.38	136.06	135.88
141.47	144.96	145.16	138.68	134.63	129.43	128.94

a) Find the mean for these data.

b) Construct a frequency distribution table for these data using a class width of 3.00 and the lower boundary of the first class equal to 128.00.

c) Find the mean, mode and median of the grouped data of part b.

d) Compare your means from parts a and c. If the two means are not equal, explain why they differ.

Q10. Briefly explain the empirical rule. To what kind of distribution is it applied?

Q11. Nixon Corporation manufactures computer monitors. The following data give the numbers of computer monitors produced at the company for a sample of 30 days.

24	32	27	23	33	33	29	25	23	26
26	26	31	20	27	33	27	23	28	29
31	35	34	22	37	28	23	35	31	43

a) Calculate the values of the three quartiles and the interquartile range. Where does the value of 31 lie in relation to these quartiles?

b) Find the (approximate) value of the 65th percentile. Give a brief interpretation of this percentile.

c) For what percentage of the days was the number of computer monitors produced 32 or higher? Answer by finding the percentile rank of 32.

Q12. The mean monthly mortgage paid by all home owners in a town is $2365 with a standard deviation of $340.

a) Using Chebyshev's theorem, find at least what percentage of all home owners in this town pay a monthly mortgage of

i. $1685 to $3045

ii. $1345 to $3385

b) Using Chebyshev's theorem, find the interval that contains the monthly mortgage payments of at least 84% of all home owners.

Q13. Draw a tree diagram for three tosses of a coin. List all outcomes for this experiment.

Q14. According to Survey of Graduate Science Engineering Students and Postdoctorates, published by the U.S. National Science Foundation, the distribution of graduate science students in doctorate-granting institutions is as follows. Frequencies are in thousands.

Field	Frequency
Physical sciences	35.4
Environmental	10.7
Mathematical sciences	18.5
Computer sciences	44.3
Agricultural sciences	12.2
Biological sciences	64.4
Psychology	46.7
Social sciences	87.8

A graduate science student who is attending a doctorate-granting institution is selected at random. Determine the probability that the field of the student obtained is

a) psychology.

b) physical or social science.

c) not computer science.

Q15. The breakdown of the student ratio in a local high school according to race and ethnicity is 15% Malay, 27% Chinese, 11% Indian, 6% Kadazan, and 5% for all others. A student is randomly selected from this high school. (To select "randomly" means that every student has the same chance of being selected.) Find the probabilities of the following events:

a) The student is a Chinese,

b) The student is minority (that is, not Malay),

c) The student is not others.

Q16. A tutoring service specializes in preparing adults for high school equivalence tests. Among all the students seeking help from the services, 63% need help in mathematics, 34% need help in English, and 27% need help in both mathematics and English. What is the percentage of students who need help in either mathematics or English? (Student who needs help in a subject may need help in other subjects as well).

Q17. In the game of craps, a player rolls two balanced dice. Thirty-six equally likely outcomes are possible. Let

A = event the sum of the dice is 7,

B = event the sum of the dice is 11,

C = event the sum of the dice is 2,

D = event the sum of the dice is 3,

E = event the sum of the dice is 12,

F = event the sum of the dice is 8, and

G = event doubles are rolled.

a) Compute the probability of each of the seven events.

b) The player wins on the first roll if the sum of the dice is 7 or 11. Find the probability of that event by using the special addition rule and your answers from part (a).

c) The player loses on the first roll if the sum of the dice is 2, 3, or 12. Determine the probability of that event by using the special addition rule and your answers from part (a).

Q18. The U.S. Department of Agriculture publishes information about U.S. farms in Census of Agriculture. A joint frequency distribution for number of farms, by acreage and tenure of operator, is provided in the following contingency table. Frequencies are in thousands.

		Tenure of operator
		Full owner T1	Part owner T2	Tenant T3	Total
Acreage	Under 50 A1		64	41
	50-under 180 A2	487	131	41	659
	180-under 500 A3	203			389
	500-under 1000 A4	54	91	17	162
	1000 & over A5	46	112	18	176
	Total	1429	551

a) Fill in the six missing entries.

b) How many cells does this contingency table have?

c) How many farms have under 50 acres?

d) How many farms are tenant operated?

e) How many farms are operated by part owners and have between 500 and 1000 acres?

f) How many farms are not full-owner operated?

g) How many tenant-operated farms have 180 acres or more?

Q19. One card is selected at random from an ordinary deck of 52 playing cards. Let

A = event a face card is selected,

B = event a king is selected, and

C = event a heart is selected.

Find the following probabilities and express your results in words. Compute the conditional probabilities directly; do not use the conditional probability rule.

a) P(B)

b) P(B|A)

c) P(B|C)

d) P(B|(not A))

e) P(A)

f) P(A|B)

g) P(A|C)

h) P(A|(not B)

Q20. The probability that a randomly selected student from a college is a female is .55 and the probability that a student works for more than 10 hours per week is .62. If these two events are independent, find the probability that a randomly selected student is a

a) male and works for more than 10 hours per week

b) female or works for more than 10 hours per week

Q21. The National Center for Education Statistics publishes information on U.S. engineers and scientists in Digest of Education Statistics. The following table presents a joint probability distribution for engineers and scientists by highest degree obtained.

		Type		P(Di)
		Engineer T1	Scientist T2
Highest degree	Bachelor's D1	0.343	0.289	0.632
	Master's D2	0.098	0.146	0.244
	Doctorate D3	0.017	0.091	0.108
	Other D4	0.013	0.003	0.016
	P(Tj)	0.471	0.529	1.000

a) Determine P(T₂), P(D₃), and P(T₂ & D₃).

b) Are T₂ and D₃ independent events? Explain your answer.

Q22. When a balanced dime is tossed three times, eight equally likely outcomes are possible:

HHH	HTH	THH	TTH
HHT	HTT	THT	TTT

Let

A = event the first toss is heads,

B = event the third toss is tails, and

C = event the total number of heads is 1.

a) Compute P(A), P(B), and P(C).

b) Compute P(B | A).

c) Are A and B independent events? Explain your answer.

d) Compute P(C | A).

e) Are A and C independent events? Explain your answer.

Q23. In the United States, telephone numbers consist of a three-digit area code followed by a seven-digit local number. Suppose neither the first digit of an area code nor the first digit of a local number can be a zero but that all other choices are acceptable.

a) How many different area codes are possible?

b) For a given area code, how many local telephone numbers are possible?

c) How many telephone numbers are possible?

Q24. Determine the value of each quantity.

a) ₄P₃

b) ₁₅P₄

c) ₆P₂

d) ₁₀P₀

e) ₈P₈

Q25. Determine the value of each of the following quantities.

a) ₄C₃

b) ₁₅C₄

c) ₆C₂

d) ₁₀C₀

e) ₈C₈

Q26. A certain couple is equally likely to have either a boy or a girl. If the family has four children, let X denote the number of girls.

a) Identify the possible values of the random variable X.

b) Determine the probability distribution of X. (Hint: There are 16 possible equally likely outcomes. One is GBBB, meaning the first born is a girl and the next three born are boys.)

Use random-variable notation to represent each of the following events. Also use the special addition rule and the probability distribution obtained in part (b) to determine each event's probability. The couple has

c) exactly two girls.

d) at least two girls.

e) at most two girls.

f) between one and three girls, inclusive.

g) children all of the same gender.

Q27. The Federal Communications Commission publishes a semiannual report on providers and services for Internet access titled High Speed Services for Internet Access. The report published in March 2008 included the following information on the percentage of zip codes with a specified number of high-speed Internet lines in service. (Note: We have used "10" in place of "10 or more,")

Let X denote the number of high-speed lines in service for a randomly selected zip code.

a) Find the mean of X.

b) How many high-speed Internet lines would you expect to find in service for a randomly selected zip code?

c) Obtain and interpret the standard deviation of X.

Q28. An article titled "You're Eating That?", published in the New York Times, discussed consumer perception of food safety. The article cited research by the Food Marketing Institute, which indicates that 66% of consumers in the United States are confident that the food they buy is safe. Suppose that six consumers in the United States are randomly sampled and asked whether they are confident that the food they buy is safe.

Determine the probability that the number answering in the affirmative is

a) exactly two.

b) exactly four.

c) at least two.

d) Determine the probability distribution of the number of U.S. consumers in a sample of six who are confident that the food they buy is safe.

e) Strictly speaking, why is the probability distribution that you obtained in part (d) only approximately correct?

f) What is the exact distribution called?

Q29. Sickle cell anemia is an inherited blood disease that occurs primarily in blacks. In the United States, about 15 of every 10,000 black children have sickle cell anemia. The red blood cells of an affected person are abnormal; the result is severe chronic anemia (inability to carry the required amount of oxygen), which causes headaches, shortness of breath, jaundice, increased risk of pneumococcal pneumonia and gallstones, and other severe problems. Sickle cell anemia occurs in children who inherit an abnormal type of hemoglobin, called hemoglobin S, from both parents. If hemoglobin S is inherited from only one parent, the person is said to have sickle cell trait and is generally free from symptoms. There is a 50% chance that a person who has sickle cell trait will pass hemoglobin S to an offspring.

a) Obtain the probability that a child of two people who have sickle cell trait will have sickle cell anemia.

b) If two people who have sickle cell trait have five children, determine the probability that at least one of the children will have sickle cell anemia.

c) If two people who have sickle cell trait have five children, find the probability distribution of the number of those children who will have sickle cell anemia.

d) Construct a probability histogram for the probability distribution in part (c).

e) If two people who have sickle cell trait have five children, how many can they expect will have sickle cell anemia?

Q30. In the 1910 article "The Probability Variations in the Distribution of α Particles" (Philosophical Magazine, Series 6, No. 20, pp. 698-707), E. Rutherford and H. Geiger described the results of experiments with polonium. The experiments indicate that the number of α (alpha) particles that reach a small screen during an 8-minute interval has a Poisson distribution with parameter λ = 3.87. Determine the probability that, during an 8-minute interval, the number, Y, of α particles that reach the screen is

a) exactly four.

b) at most one.

c) between two and five, inclusive.

d) Construct a table of probabilities for the random variable Y. Compute the probabilities until they are zero to three decimal places.

e) Draw a histogram of the probabilities in part (d).

f) On average, how many alpha particles reach the screen during an 8-minute interval?

Q31. According to the National Health and Nutrition Examination Survey, published by the National Center for Health Statistics, the serum (noncellular portion of blood) total cholesterol level of U.S. females 20 years old or older is normally distributed with a mean of 206 mg/dL (milligrams per deciliter) and a standard deviation of 44.7 mg/dL.

Let x denote serum total cholesterol level for U.S. females 20 years old or older.

a) Sketch the distribution of the variable x.

b) Obtain the standardized version, z, of x.

c) Identify and sketch the distribution of z.

d) The percentage of U.S. females 20 years old or older who have a serum total cholesterol level between 150 mg/dL and 250 mg/dL is equal to the area under the standard normal curve between __________ and __________.

e) The percentage of U.S. females 20 years old or older who have a serum total cholesterol level below 220 mg/dL is equal to the area under the standard normal curve that lies to the __________ of __________.

Q32. The A. C. Nielsen Company reported in the Nielsen Report on Television that the mean weekly television viewing time for children aged 2-11 years is 24.50 hours. Assume that the weekly television viewing times of such children are normally distributed with a standard deviation of 6.23 hours and apply the 68.26-95.44-99.74 rule to fill in the blanks.

a) 68.26% of all such children watch between and hours of TV per week.

b) 95.44% of all such children watch between and hours of TV per week.

c) 99.74% of all such children watch between and hours of TV per week.

d) Sketch graph and interpret to portray your results.

Q33. An article titled "You're Eating That?", published November 26, 2007, online by the New York Times, discussed consumer perception of food safety. The article cited research by the Food Marketing Institute that indicates that 66% of consumers in the United States are confident that the food they buy is safe. Suppose that 200 consumers in the United States are randomly sampled and asked whether they are confident that the food they buy is safe. Determine the probability that the number answering in the affirmative is

a) exactly 66% of those sampled.

b) at most 66% of those sampled.

c) at least 66% of those sampled.

Q34. The winner of the 2008-2009 National Basketball Association (NBA) championship was the Los Angeles Lakers. One starting lineup for that team is shown in the following table.

Player	Position	Height (in.)
Trevor Ariza (T)	Forward	80
Kobe Bryant (K)	Guard	78
Andrew Bynum (A)	Center	84
Derek Fisher (D)	Guard	73
Pau Gasol (P)	Forward	84

a) Find the population mean height of the five players.

b) For samples of size 2, construct a table. Use the letter in parentheses after each player's name to represent each player.

c) Draw a dotplot for the sampling distribution of the sample mean for samples of size 2.

d) For a random sample of size 2, what is the chance that the sample mean will equal the population mean?

e) For a random sample of size 2, obtain the probability that the sampling error made in estimating the population mean by the sample mean will be 1 inch or less; that is, determine the probability that the mean, x will be within 1 inch of μ. Interpret your result in terms of percentages.

Q35. A brand of water-softener salt comes in packages marked "net weight 40 lb." The company that packages the salt claims that the bags contain an average of 40 lb of salt and that the standard deviation of the weights is 1.5 lb. Assume that the weights are normally distributed.

a) Obtain the probability that the weight of one randomly selected bag of water-softener salt will be 39 lb or less, if the company's claim is true.

b) Determine the probability that the mean weight of 10 randomly selected bags of water- softener salt will be 39 lb or less, if the company's claim is true.

c) If you bought one bag of water-softener salt and it weighed 39 lb, would you consider this evidence that the company's claim is incorrect? Explain your answer.

d) If you bought 10 bags of water-softener salt and their mean weight was 39 lb, would you consider this evidence that the company's claim is incorrect? Explain your answer.