QUESTION 1

Suppose the American Medical Association Center for Health Policy Research included data, by state, on the number of community hospitals and the average patient stay (in days) in its publication. The data (by state) are shown in the table.
Which two states have an unusually high number of hospitals?

4 points   

QUESTION 2

In one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was 2.0. Suppose you are going to dig up and examine 40 liters of sediment at this site. Let  r = 0, 1, 2, 3,… be a random variable that represents the number of prehistoric artifacts found in your 40 liters of sediment. Find the probability that you will find 1 or more artifacts in the 40 liters of sediment. Round your answer to the nearest ten thousandth.

4 points   

QUESTION 3

Compute the population standard deviation σ for the following sample data, assuming the sample comprises the entire population. Round your answer to the nearest hundredth.

4 points   

QUESTION 4

What is a sampling distribution?

4 points   

QUESTION 5

To compare two elementary schools regarding teaching of reading skills, 12 sets of identical twins were used. In each case, one child was selected at random and sent to school A, and his or her twin was sent to school B. Near the end of fifth grade, an achievement test was given to each child. The results follow:

Suppose a sign test for matched pairs with a 5% level of significance is used to test the hypothesis that the schools have the same effectiveness in teaching reading skills against the alternate hypothesis that the schools have different levels of effectiveness in teaching reading skills. Let p denote portion of positive signs when the scores of school B are subtracted from the corresponding scores of school A. Calculate the P-value. Round your answer to four decimal places.

4 points   

QUESTION 6

A data processing company has a training program for new salespeople. After completing the training program, each trainee is ranked by his or her instructor. After a year of sales, the same class of trainees is again ranked by a company supervisor according to net value of the contracts they have acquired for the company. The results for a random sample of 11 salespeople trained in the last year follow, where x is rank in training class and y is rank in sales after 1 year. Lower ranks mean higher standing in class and higher net sales.

Using a 10% level of significance, test the claim that the relation between x and y is monotone (either increasing or decreasing). What is the level of significance α?

4 points   

QUESTION 7

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute the sample mean for x and for y. Round your answer to the nearest tenth.

4 points   

QUESTION 8

Benford’s Law claims that numbers chosen from very large data files tend to have “1” as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with “1” as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 247 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.1. Are the data statistically significant at the significance level? Based on your answers, will you reject or fail to reject the null hypothesis?

4 points   

QUESTION 9

Suppose the age distribution of the Canadian population and the age distribution of a random sample of 528 residents in the Indian community of Red Lake are shown below.

Use a = 0.05 to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village. Given a value of 9.673 for x², find (or estimate) the P-value of the sample test statistic.

4 points   

QUESTION 10

Identify the level of measurement corresponding to the data “Cost of rod and reel” associated with fishing.

4 points   

QUESTION 11

Data may be classified by one of the four levels of measurement. What is the name of the lowest level?

4 points   

QUESTION 12

Compute the expected age μ of a British nurse in 1851. Assume that the table below shows the age distribution of nurses in Great Britain in 1851. Round your answer to nearest hundredth.

4 points   

QUESTION 13

Wetlands offer a diversity of benefits. They provide habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years the United States has lost more than half its wetlands. Suppose Environmental Almanac gives the percentage of wet lands lost in each state in the last 200 years. Assume that for the lower 48 states, the percentage loss of wetlands per state is as follows:

The distribution is approximately mound shaped.

4 points   

QUESTION 14

1.      Wing Foot is a shoe franchise commonly found in shopping centers across the United States. Wing Foot knows that its stores will not show a profit unless they gross over $940,000 per year. Let A be the event that a new Wing Foot store grosses over $940,000 its first year. Let B be the event that a store grosses over $940,000 its second year. Wing Foot has an administrative policy of closing a new store if it does not show a profit in either of the first two years. Assume that the accounting office at Wing Foot provided the following information: 56% of all Wing Foot stores show a profit the first year; 75% of all Wing Foot store show a profit the second year (this includes stores that did not show a profit the first year); however, 80% of Wing Foot stores that showed a profit the first year also showed a profit the second year. Compute P(A and B), if P(A) = 0.56, P(B) = 0.75 and P(B|A) = 0.80. Round your answer to the nearest hundredth.

4 points   

QUESTION 15

1.      How hot does it get in Death Valley? Assume that the following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures^oF  were taken from May to November in the vicinity of Furnace Creek. Compute the median for these ground temperatures. Round your answer to the nearest tenth.

4 points   

QUESTION 16
Assume that the following data represent baseball batting averages (multiplied by 1000) for a random sample of National League players near the end of the baseball season. The frequency table showing class limits, class boundaries, midpoints and frequency is given below. Draw a histogram.

		Boundaries	Midpoint		Frequency

4 points   

QUESTION 17

1.      There are 4 radar stations and the probability of a single radar station detecting an enemy plane is 0.55. Make a histogram for the probability distribution.

4 points   

QUESTION 18

1.      Richard has been given a 9-question multiple-choice quiz in his history class. Each question has three answers, of which only one is correct. Since Richard has not attended the class recently, he doesn’t know any of the answers. What is the value of p? (p is the value of success) Round your answer to the nearest tenth.

4 points   

QUESTION 19

In baseball, is there a linear correlation between batting average and home run  percentage? Let x represent the batting average of a professional baseball player. Let y represent the home run percentage (number of home runs per 100 times at bat). Suppose a random sample of baseball players gave the following information.

Make a scatter diagram for the data. Draw the line that best fits the data.

4 points   

QUESTION 20

Sand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded.

Convert this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median gives ABABABABAABB. The number of runs is 10. What is the lower critical number c₁?

4 points   

QUESTION 21

The probability of a single radar station detecting an enemy plane is 0.75 and the probability of not detecting an enemy plane is 0.25. How many such stations are required to be 98% certain that an enemy plane flying over will be detected by at least one station?

4 points   

QUESTION 22

A professional employee in a large corporation receives an average of μ = 42.7 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 x = 35.3 e-mails per day. The computer server through which the e-mails are routed showed that σ = 19.6. Has the new policy had any effect? Use a 5% 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 is the value of the test statistic?

4 points   

QUESTION 23

What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following information (based on data from classic text Notes on Nursing, by Florence Nightingale). Note: In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants. Find the probability that a British nurse selected at random in 1851 would be 70 years of age or older. Round your answer to nearest thousandth.

4 points   

QUESTION 24

Independent random samples from two regions in the same area gave the following chemical measurements (ppm). Assume the population distributions of the chemical are mound-shaped and symmetric for these two regions.
Region I: ;
981 726 686 496 657 627 815 504 950 605 570 520
Region II: ;

1024 830 526 502 539 373 888 685 868 1093 1132 792 1081 722 1092 844
Let  be the population mean and  be the population standard deviation for . Let  be the population mean and  be the population standard deviation for . Determine and examine the 90% confidence interval for . Does the interval consist of numbers that are all positive? all negative? or different signs? At the 90% level of confidence, is one region more interesting that the other from a geochemical perspective?

4 points   

QUESTION 25

When do creative people get their good ideas? Assume that the survey of 963 inventors gives the following information:

Assuming that the time interval includes the left limit and all the times up to but not including the right limit, estimate the probability that an inventor has a good idea during the time interval from 6 A.M. to 12 noon. Write your answer as a fraction in simplest form.

4 points   

QUESTION 26

The systolic blood pressure of individuals is thought to be related to both age and weight. Let the systolic blood pressure, age, and weight be represented by the variables x₁, x₂, and x₃, respectively. Suppose that Minitab was used to generate the following descriptive statistics, correlations, and regression analysis for a random sample of 15 individuals.

Regression Analysis

The regression equation is
x₁ = 0.703 + 1.388x₂ + 0.907x₃ 

Test the coefficient of  in the regression equation to determine if it is zero or not zero. Use a level of significance of 5%.  Do you accept or reject the null hypothesis that the coefficient should equal zero?

4 points   

QUESTION 27

How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let y be the average weight of the pony (in kilograms). Suppose a random sample of ponies gave the following information.

Make a scatter diagram for the data.4 points   

QUESTION 28

Draw a tree diagram to display all the possible head-tail sequences that can occur when you flip a coin foour times.

4 points   

QUESTION 29

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 highest median premium?

4 points   

QUESTION 30

1.      Assume that the table below shows the age distribution of nurses in Great Britain in 1851. Make a histogram for the probability distribution.

4 points   

QUESTION 31

The systolic blood pressure of individuals is thought to be related to both age and weight. Let the systolic blood pressure, age, and weight be represented by the variables x₁, x₂, and x₃, respectively. Suppose that Minitab was used to generate the following descriptive statistics, correlations, and regression analysis for a random sample of 15 individuals.

Regression Analysis

The regression equation is
x₁ = 0.804 + 1.308x₂ + 0.966x₃ 

Relative to its mean, which variable has the smallest spread of data values?

a.       X₁

b.      X₂

c.       X₃

4 points   

QUESTION 32

Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. Suppose for a random sample of years, one plot gave the following annual wheat production (in pounds):

For this plot, the sample variance is . Another random sample of years for a second plot gave the following annual wheat production (in pounds):

For this plot, the sample variance is . Test the claim using  that the population variance of annual wheat production for the first plot is larger than that for the second plot.
What are the degrees of freedom?

4 points   

QUESTION 33

A random sample of  communities in western Kansas gave the following information for people under 25 years of age.

: Rate of hay fever per 1000 population for people under 25

A random sample of   regions in western Kansas gave the following information for people over 50 years old.

: Rate of hay fever per 1000 population for people over 50

Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use a = 0.05 State the null and alternate hypotheses.

4 points   

QUESTION 34

Are customers more loyal in the East or in the West? The following table is based on information from Trends in the United Sates, published by the food marketing Institute, Washington, D.C. The columns represent loyalty (in years) at a primary supermarket. The rows represent regions of the United States.

What is the probability that a customer chosen at random has been loyal 5 or more years given that he or she is from the South? Round your answer to the nearest thousandth.

4 points   

QUESTION 35

Assume that about 30% 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 140 insurance claims to be processed in the next few days. What is the probability that from 45 to 47 of the claims have been padded?

4 points   

QUESTION 36

What percentage of the general U.S. population have bachelor’s degrees? Suppose that the Statistical Abstract of the United States, 120th Edition, gives the following percentage of bachelor’s degrees by state. For convenience, the data are sorted in increasing order.

Illinois has a bachelor’s degree percentage rate of about 18%. Into what quartile does this rate fall?

4 points   

QUESTION 37

Wing Foot is a shoe franchise commonly found in shopping centers across the United States. Wing Foot knows that its stores will not show a profit unless they gross over $940,000 per year. Let A be the event that a new Wing Foot store grosses over $940,000 its first year. Let B be the event that a store grosses over $940,000 its second year. Wing Foot has an administrative policy of closing a new store if it does not show a profit in either of the first two years. Assume that the accounting office at Wing Foot provided the following information: 61% of all Wing Foot stores show a profit the first year; 72% of all Wing Foot store show a profit the second year (this includes stores that did not show a profit the first year); however, 87% of Wing Foot stores that showed a profit the first year also showed a profit the second year. Compute  if , , and . Round your answer to the nearest hundredth.

4 points   

QUESTION 38

How long did real cowboys live? One answer may be found in the book The Last Cowboys by Connie Brooks (University of New Mexico Press). This delightful book presents a thoughtful sociological study of cowboys in West Texas and Southeastern New Mexico around the year 1890. Assume that a sample of 32 cowboys gave the following years of longevity:

Make a stem-and-leaf display for these data.

4 points   

QUESTION 39

Wind Mountain is an archaeological study area located in southwestern New Mexico. Potsherds are broken pieces of prehistoric Native American clay vessels. One type of painted ceramic vessel is called Mimbres classic black-on-white. At three different sites the number of such sherds was counted in local dwelling excavations.

Shall we reject or not reject the claim that there is no difference in population mean Mimbres classic black-on-white sherd counts for the three sites? Test given a = 0.01.
Find (or estimate) the P-value of the sample test statistic.

4 points   

QUESTION 40

Jim has a 5-year-old car in reasonably good condition. He wants to take out a $50,000 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:

Jim is applying to a car insurance company for his car insurance policy. Using the probabilities that the car will have an accident in its 5th, 6th, 7th, 8th, or 9th year, and the $50,000 accident benefit, what is the expected loss to Car Insurance Company for the respective years? Round your answers to the nearest dollar.

4 points   

QUESTION 41

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.

4 points   

QUESTION 42

Does talking while walking slow you down? Suppose a study considered mean cadence (steps per minute) for subjects using no walking device, a standard walker, and a rolling walker. In addition, the cadence was measured when the subjects had to perform dual tasks. The second task was to respond vocally to a signal or respond to an interview question while walking. Cadence was measured for subjects who were just walking (using no walking device, a standard walker, or a rolling walker), for subjects required to respond to a signal, and for subjects required to respond to an interview question while walking. How many cells are there in the data table?

4 points   

QUESTION 43

John runs a computer software store. He counted 125 people who walked by his store in a day, 51 of whom came into the store. Of the 51, only 23 bought something in the store. Estimate the probability that a person who comes into the store will buy nothing. Round your answer to the nearest hundredth.

4 points   

QUESTION 44

Diagnostic tests of medical conditions have several results. The rest result can be positive or negative. A positive test (+) indicates the patient has the condition. A negative test (–) indicates the patient does not have the condition. Remember, a positive test does not prove the patient has the condition. Additional medical work may be required. Consider a random sample of 137 patients, some of whom have a medical condition and some of whom do not. Results of a new diagnostic test for the condition are shown.

Assume that the sample is representative of the entire population. For a person selected at random, find P(getting test result – or condition present). Round your answer to the nearest hundredth.

4 points   

QUESTION 45

1.      Suppose a certain species bird has an average weight of x = 3.80 grams. Based on previous studies, we can assume that the weights of these birds have a normal distribution with o = 0.37 grams. For a small group of 10 birds, find the margin of error for a 70% confidence interval for the average weights of these birds.

4 points   

QUESTION 46

Finish times (to the nearest hour) for 57 dogsled teams are shown below. Draw a relative – frequency histogram. Use five classes.

4 points   

QUESTION 47

In one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was . Suppose you are going to dig up and examine  liters of sediment at this site. Let  0, 1, 2, 3,… be a random variable that represents the number of prehistoric artifacts found in your  liters of sediment. Find the probability that you will find fewer than  prehistoric artifacts in the  liters of sediment. Round your answer to the nearest ten thousandth.

4 points   

QUESTION 48

1.      A coin is to be tossed 1000 times. What is the probability that the 785th toss is heads?

4 points   

QUESTION 49

1.      If event A is certain to occur, what is P(A)?

4 points   

QUESTION 50

1.      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:

2.
Find a for the equation of the least-squares line y = a + bx.