buisness stats final

Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with σ = 2.4%. A random sample of 15 Australian bank stocks has a sample mean of x = 6.83%. For the entire Australian stock market, the mean dividend yield is μ = 6.9%. Do these data indicate that the dividend yield of all Australian bank stocks is higher than 6.9%? Use α = 0.05. What is the value of the test statistic?

-0.113

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 king and a 5 in either order. Round your answer to the nearest thousandth.

0.012

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. x:1303623312526 -13 -13 -23 y:8 -2 2616241716 -2 -3 -8

92

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. 1617171718191919202020202021212121212222232323232324242424252525252525262626272727282830303131333437 Illinois has a bachelor's degree percentage rate of about 16%. Into what quartile does this rate fall? ​

first quartile

The Grand Canyon and the Colorado River are beautiful, rugged, and sometimes dangerous. Assume there is a physician at the park clinic in Grand Canyon Village. Suppose the physician has recorded (for a 5-year period) the number of visitor injuries at different landing points for commercial boat trips down the Colorado River in both the Upper and Lower Grand Canyon. Compute a 5% trimmed mean for Upper Canyon and Lower Canyon. Round your answer to the nearest thousandth. Upper Canyon: Number of injuries per Landing Point BetweenNorth Canyon and Phantom Ranch23113469313 ​ Lower Canyon: Number of injuries per Landing Point BetweenBright Angel and Lava Falls8110672113011021

The 5% trimmed mean for Lower Canyon is 3.500 and for Upper Canyon is 2.889.

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 = 215 numerical entries from the file and r = 57 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 = 0.01. Are the data statistically significant at the significance level? Based on your answers, will you reject or fail to reject the null hypothesis?

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

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

nominal

Find the technique for gathering data in the study below. A study of all league football scores attained through touchdowns and field goals was conduced by the National Football League to determine whether field goals account for more scoring events than touchdowns (USA Today).

census

Identify the variable in the information below. USA Today reported that 44.9% of those surveyed (1261 adults) ate in a fast-food restaurant from one to three times each week.

response regarding frequency of at restaurants

Assume that the U.S Open Golf Tournament was played at Congressional Country club, with prizes ranging from $465,000 for first place to $5000. Par for the course is 70. The tournament consists of four rounds played on different days. Suppose the scores for each round of the 32 players who placed in the money (more than $17,000) were given on a web site. The scores for the first round were as follows: ​ 6965707374737171747368657571727166717171747566757166717272737167 ​ The scores for the fourth round for these players were as follows: ​ 7269747472727071717075687372717172727071727474727268697069717374 ​ Compare the two distributions.

scores are lower in the first round

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 = 308 numerical entries from the file and r = 90 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. What is the level of significance?

0.100

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. Less Than 1 Year 1 - 2 Years 3 - 4 Years 5 - 9 Years 10 - 14 Years 15 or More Years Row Total East 32 54 59 112 77 118 452 Midwest 31 68 68 120 63 173 523 South 53 92 93 158 106 158 660 West 41 56 67 78 45 86 373 Column Total 157 270 287 468 291 535 2008 What is the probability that a customer chosen at random has been loyal from 1 to 2 years? Round your answer to the nearest thousandth.

0.134

In a random sample of 41 professional actors, it was found that 15 were extroverts. Find a 99% confidence interval for p.

0.163 to 0.569

Diagnostic tests of medical conditions have several results. The test 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 131 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. Condition Present Condition Absent Row Total Test Result + 111 20 131 Test Result - 20 60 80 Column Total 131 80 211 Assume that the sample is representative of the entire population. For a person selected at random, find P(getting test result - and condition absent). Round your answer to the nearest hundredth.

0.28

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. Less Than 1 Year 1 - 2 Years 3 - 4 Years 5 - 9 Years 10 - 14 Years 15 or More Years Row Total East 32 54 59 112 77 118 452 Midwest 31 68 68 120 63 173 523 South 53 92 93 158 106 158 660 West 41 56 67 78 45 86 373 Column Total 157 270 287 468 291 535 2008 What is the probability that a customer chosen at random is from the South given that he or she has been loyal 10 to 14 years? Round your answer to the nearest thousandth.

0.364

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: 57% of all Wing Foot stores show a profit the first year; 74% 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) = 0.57, P(B) = 0.74, and P(B|A) = 0.80. Round your answer to the nearest hundredth.

0.46

John runs a computer software store. He counted 120 people who walked by his store in a day, 53 of whom came into the store. Of the 53, only 26 bought something in the store. Estimate the probability that a person who walks into the store will buy something. Round your answer to the nearest hundredth.

0.49

In a random sample of 50 professional actors, it was found that 36 were extroverts. Let p represent the proportion of all actors who are extroverts. Find a point estimate for p.

0.720

A person's level of blood glucose and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 85 and standard deviation of σ = 28. What is the probability that, for an adult after a 12-hour fast, x is more than 65?

0.762

Suppose the method of tree ring dating gave the following dates A.D. for an archaeological excavation site. 1,247 1,254 1,224 1,207 1,151 1,280 1,271 1,283 1,233 Find a0 95% confidence interval for the mean of all tree ring dates from this archaeological site.

1,206.7 to 1,271.1

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: x 5.75 6.00 7.00 8.00 9.00 y 8 10 58 53 76 At an archaeological site with elevation 8.25 (thousand feet), what does the least-squares equation forecast for the percentage of culturally unidentified artifacts?

63.8%

Find z such that 74.3% of the standard normal curve lies between -z and z. ​

1.132

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 (°F) 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. 147 152 166 171 188 179 187 188 179 179 166 ​165 152 143

168.5

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: x 5.75 6.25 7.25 8.25 9.25 y 22 18 78 67 95 What percentage of the variation in y cannot be explained by the corresponding variation in x and the least-squares line?

18.2%

A professional employee in a large corporation receives an average of μ = 41.3 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 37 employees showed that they were receiving an average of x = 34 e-mails per day. The computer server through which the e-mails are routed showed that σ = 16.2. 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?

2.741

Find the sample variance s2 for the following sample data. Round your answer to the nearest hundredth. x: 22 20 15 33 25

44.50

Assuming that the heights of college women are normally distributed with mean 62 inches and standard deviation 2.5 inches, what percentage of women are taller than 62 inches?

50%

A random sample of 356 medical doctors showed that 175 had a solo practice. As a news writer, how would you report the survey results regarding the percentage of medical doctors in solo practice? What is the margin of error based on a 90% confidence interval?

A recent study shows that about 49% of medical doctors have a solo practice with a margin of error of 4.4 percentage points.

At Westgate Community College, a survey was done to determine when students are available for class. A questionnaire was given to a random sample of students. The instructions were to mark each of the time categories in which they could take classes. Many students marked more than one category. Responses from the students in the sample indicated that 52 would take early morning classes, 85 would take mid-morning classes, 41 would take afternoon classes and 37 would take evening classes. Would a circle graph be appropriate for this data? Give a reason for your answer.

No. Since there were multiple responses from some students this data does not represent parts of a whole.

Identify the sampling technique used in the following information. An important part of employee compensation is a benefits package that might include health insurance, life insurance, child care, vacation days, retirement plan, parental leave, bonuses, etc. Suppose you want to conduct a survey of benefits packages available in private businesses in Hawaii. You want a sample size of 100. Sampling technique used to get the sample size of 100 is described below. Assign each business in the Island Business Directory a number, and then use a random-number table to select the business to be included in the sample.

Simple random sample

A professional employee in a large corporation receives an average of μ = 44.1 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 33 employees showed that they were receiving an average of x = 35.8 e-mails per day. The computer server through which the e-mails are routed showed that σ = 15.1 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 is the level of significance?

α = 0.01