Statistics Final Exam
Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with σ =2.1%. A random sample of 17 Australian bank stocks has a sample mean of . For the entire Australian stock market, the mean dividend yield is μ =8.6%. Do these data indicate that the dividend yield of all Australian bank stocks is higher than 8.6%? Use α = 0.05. Find (or estimate) the P-value.
0.021
Let z be a random variable with a standard normal distribution. Find the indicated probability below. P(z ≤ 1.6)
0.945
Let z be a random variable with a standard normal distribution. Find the indicated probability below. P(-2.1 ≤ z ≤ 2.2)
0.968
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 99% sure that the point estimate will be within a distance of 0.04 from p?
1,041
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
Suppose that more than a decade ago high levels of lead in the blood put 82% of children at risk. A concerted effort was made to remove lead from the environment. Suppose, according to a survey, only 9% of children in the United States are at risk of high blood-lead levels. In a random sample of 100 children taken more than a decade ago, what is the probability that 70 or more had high blood-lead levels?
1.000
Suppose that x has a distribution with μ = 23 and σ = 7. If a random sample is taken of size n = 39, find .
1.12
Find z such that 74.3% of the standard normal curve lies between -z and z.
1.132
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: 15 0 38 24 31 26 27 -15 -15 -24 y: 10 -3 27 18 25 18 18 -3 -4 -10
2,560
Compute the population variance σ2 for the following sample data, assuming the sample comprises the entire population. Round your answer to the nearest hundredth. x: 21 18 12 35 25
58.96
What is a parameter?
A numerical descriptive measure of a population
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
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 = 391 numerical entries from the file and r = 101 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. What does the area of the sampling distribution corresponding to your P-value look like?
The area in the left tail of the standard normal curve.
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: 46 37 36 42 81 20 73 59 35 50 87 52 24 27 38 56 39 74 56 31 27 91 46 9 54 52 30 33 28 35 35 23 90 72 85 42 59 50 49 48 38 60 46 87 50 89 49 67 The distribution is approximately mound shaped.
True
Data may be classified by one of the four levels of measurement. What is the name of the lowest level?
nominal
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
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. Make a frequency table showing class limits, class boundaries, midpoints and frequency. Use five classes. (Round your answer for boundaries and midpoints to the nearest tenth.) 196 257 150 293 147 297 199 252 183 125 107 259 306 306 273 289 316 254 215 252 249 259 265 184 115 204
Class Limits Boundaries Midpoint Frequency 107-149 106.5-149.5 128.0 4 150 - 192 149.5 - 192.5 171.0 3 193 - 235 192.5 - 235.5 214.0 4 236 - 278 235.5 - 278.5 257.0 9 279-321 278.5-321.5 300.0 6
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
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
A certain company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a battery is normally distributed, with a mean of 57 months and a standard deviation of 8 months. If the company does not want to make refunds for more than 10% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries (to the nearest month)?
46 months
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: 11 0 37 25 32 27 28 -11 -11 -25 y: 8 -3 27 14 26 17 14 -3 -4 -8
5519
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 5.00 6.00 6.50 7.25 7.50 y 25 44 63 69 87 Find y.
57.60
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 5.00 6.00 6.50 7.25 7.50 y 25 44 63 69 87 Find y.
57.60
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: 69 65 70 73 74 73 71 71 74 73 68 65 75 71 72 71 66 71 71 71 74 75 66 75 71 66 71 72 72 73 71 67 The scores for the fourth round for these players were as follows: 72 69 74 74 72 72 70 71 71 70 75 68 73 72 71 71 72 72 70 71 72 74 74 72 72 68 69 70 69 71 73 74 Compare the two distributions.
Scores are lower in the first round.
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. x 2.5 4 3.4 4.4 2.4 y 5.2 10.3 10.8 10.3 8.3 As x increases, does the value of r imply that y should tend to increase, decrease, or remain the same? Explain.
Since r is positive, as x increases, y increases.
Identify the implied population in the information below. Government agencies carefully monitor water quality and its effect on wetlands (Reference: Environment Protection Agency Wetland Report EPA 832-R-93-005). Of particular concern is the concentration of nitrogen in water draining from fertilized lands. Too much nitrogen can kill fish and wildlife. Twenty-eight samples of water were taken at random from a lake. The nitrogen concentration (milligrams of nitrogen per liter of water) was determined for each sample. The variable in this information is nitrogen concentration (mg nitrogen/l water).
nitrogen concentration (mg nitrogen/l water) in the entire lake
Identify the level of measurement corresponding to the data "Salesperson's performance: below average, average, above average" associated with robotics.
ordinal
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 = 58 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. What is the value of the test statistic?
-2.268
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
Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. Suppose for healthy females, x has an approximately normal distribution with mean μ = 4.8 and standard deviation σ = 0.8 Convert the following x interval from a laboratory test to a z interval. 2.4 > x
-3 > z
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 0.83 Multifilter 0.78 Benson & Hedges 1.06 Newport Lights 0.73 Bull Durham 2.08 Now 0.21 Camel Lights 0.67 Old Gold 1.26 Carlton 0.38 Pall Mall Lights 1.08 Chesterfield 1.04 Raleigh 0.91 Golden Lights 0.76 Salem Ultra 0.42 Kent 0.95 Tareyton 1.01 Kool 1.24 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
0 2 = 0.2 milligram 0 2 3 4 0 5 6 6 6 7 7 7 8 8 9 9 9 1 0 0 0 0 0 0 0 2 2 2 0
0 Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a percentage of claims. Suppose a random sample of employees gave the following information. x 2 8 14 32 73 y 50 45 35 28 16 Compute r.
0 Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a percentage of claims. Suppose a random sample of employees gave the following information. x 2 8 14 32 73 y 50 45 35 28 16 Compute r.
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
A professional employee in a large corporation receives an average of μ = 39.9 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 45 employees showed that they were receiving an average of x = 33.6 e-mails per day. The computer server through which the e-mails are routed showed that σ = 17.3. 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. Find (or estimate) the P-value.
0.015
Suppose a certain species bird has an average weight of = 3.10 grams. Based on previous studies, we can assume that the weights of these birds have a normal distribution with σ = 0.21 grams. For a small group of 13 birds, find the margin of error for a 70% confidence interval for the average weights of these birds.
0.06 grams
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 given that he or she is from the Midwest? Round your answer to the nearest thousandth.
0.130
Assume that x has a normal distribution, with the specified mean and standard deviation. Find the indicated probabilities. P(x ≥ 6); μ = 17; σ = 5
0.986
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
Find the area under the standard normal curve over the interval specified below. Between z = -2 and -1
0.136
Assume that x has a normal distribution, with the specified mean and standard deviation. Find the indicated probabilities. P(1 ≤ x ≤ 8); μ = 11; σ = 3
0.158
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
Assume that about 35% 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 fewer than 44 of the claims have been padded?
0.165
Suppose that about 55% of the people who are murdered actually knew the person who committed the murder. Suppose that a detective file in Boston has 51 current unsolved murders. What is the probability that fewer than 21 victims did not know their murderer?
0.245
Find the area under the standard normal curve over the interval specified below. To the right of z = -3
0.999
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
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 = 84 and standard deviation of σ = 26 What is the probability that, for an adult after a 12-hour fast, x is less than 81?
0.454
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
John runs a computer software store. He counted 121 people who walked by his store in a day, 51 of whom came into the store. Of the 51, only 20 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.
0.61
Find z such that 26.5% of the standard normal curve lies to the right of z.
0.628
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 6.00 6.50 6.75 7.50 8.50 y 28 20 17 30 85 Find the value of the coefficient of determination r2.
0.703
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
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 132 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.2 Condition Present Condition Absent Row Total Test Result + 112 20 132 Test Result - 20 57 77 Column Total 132 77 209 Assume that the sample is representative of the entire population. For a person selected at random, find P(condition absent | getting test result -). Round your answer to the nearest hundredth.
0.74
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 6.00 6.25 7.25 7.75 8.50 y 44 52 43 53 91 Calculate the sample correlation coefficient r.
0.749
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 100 insurance claims to be processed in the next few days. What is the probability that more than 51 of the claims are not padded?
0.759
A coin is to be tossed 1000 times. What is the probability that the 785th toss is heads?
1/2
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%
At Center Hospital there is some concern about the high turnover of nurses. A survey was done to determine how long (in months) nurses had been in their current positions. The responses (in months) of 20 nurses were 23 2 5 14 25 36 27 42 12 8 7 23 29 26 28 11 20 31 8 36 A box-and-whisker plot of the data is shown below. Find the interquartile range.
19.0
Finish times (to the nearest hour) for 10 dogsled teams are shown below. Find the class width. Use five classes. (Round your answer to the nearest integer.) 252 314 315 284 255 245 292 335 244 342
20
Find the range for the following sample data. x: 21 18 12 35 25
23
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%
Suppose a certain species bird has an average weight of = 3.85 grams. Based on previous studies, we can assume that the weights of these birds have a normal distribution with σ = 0.31 grams. Find the sample size necessary for a 98% confidence level with a maximal error of estimate E = 0.09 for the mean weights of the hummingbirds.
65
Find the sample standard deviation s for the following sample data. Round your answer to the nearest hundredth. x: 22 17 15 33 26
7.23
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 5.50 6.50 7.25 8.00 8.75 y 10 41 53 89 89 What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line?
94.8%
What is a statistic?
A numerical descriptive measure of a sample
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.
Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 7.1 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is less than 7.1 seconds. What would you use for the alternative hypothesis?
H1 : μ < 7.1 seconds
Suppose twenty-two communities have an average of = 139.6 reported cases of larceny per year. Assume that σ is known to be 45.4 cases per year. Find a 90%, 95%, and 98% confidence interval for the population mean annual number of reported larceny cases in such communities. Compare the margins of error. As the confidence level increase, do the margins of error increase?
The 90% confidence level has a margin of error of 15.9; the 95% confidence level has a margin of error of 19.0; and the 98% confidence level has a margin of error of 22.6. As the confidence level increases, the margins of error increase.
Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with σ = 2.8%. A random sample of 15 Australian bank stocks has a sample mean of x = 8.47%. For the entire Australian stock market, the mean dividend yield is μ = 9.6%. Do these data indicate that the dividend yield of all Australian bank stocks is higher than 9.6%? Use α = 0.05. 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?
The P-value is greater than than the level of significance and so the data are not statistically significant. Thus, we fail to reject the null hypothesis.
A professional employee in a large corporation receives an average of μ = 41.9 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 = 34.1 e-mails per day. The computer server through which the e-mails are routed showed that σ = 17.7. Has the new policy had any effect? Use a 10% 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. Are the data statistically significant at level α? Based on your answers, will you reject or fail to reject the null hypothesis?
The P-value is less than than the level of significance and so the data are statistically significant. Thus, we reject the null hypothesis.
You draw two cards from a standard deck of 52 cards and do not replace the first one before drawing the second. State whether the following statement is true or false. The outcomes for the two cards are independent.
false
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
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 a 75% Chebyshev interval around the mean for x-values and also for y-values. Round your answers to the nearest hundredth. x: 13 0 36 25 34 27 28 -13 -13 -25 y: 10 -5 28 16 26 17 16 -5 -6 -10
for x-values: -33.36 to 55.76 and for y-values: -19.50 to 36.90
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 coefficient of variation for each fund. Round your answers to the nearest tenth. x: 11 0 36 24 35 26 27 -11 -11 -24 y: 9 -4 28 14 25 17 14 -4 -5 -9
for x-values: 190.4%, and for y-values: 156.2%
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. x: 12 0 38 23 34 25 26 -12 -12 -23 y: 10 -3 27 15 24 18 15 -3 -4 -10 The sample means for x and y are 11.10 and 8.90, respectively. Compute the coefficient of variation for each fund. Round your answers to the nearest tenth.
for x-values: 193.7%, and for y-values: 146.1%
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. x 0.251 0.259 0.29 0.265 0.269 y 1.3 3.7 5.8 3.9 3.7 Would you say the correlation is low, moderate, or strong? Positive or negative? If necessary, draw a scatter diagram of the given data.
strong and positive
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 5.50 6.25 6.75 7.00 7.75 y 57 86 73 82 81 Find the equation of the least squares line .
y= 17+9x
Assuming that the heights of college women are normally distributed with mean 63 inches and standard deviation 3 inches, what percentage of women are between 57 inches and 66 inches?
81.9%
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 6.00 6.50 7.00 8.00 8.50 y 50 46 61 96 90
-81.093
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 6.00 6.50 7.00 8.00 8.50 y 50 46 61 96 90 Find a for the equation of the least-squares line .
-81.093
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 Midwest given that he or she has been loyal 5 to 9 years? Round your answer to the nearest thousandth.
0.256
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
Suppose that about 23% of ice cream sales are vanilla and that about 11% of ice cream sales are chocolate. A customer who buys ice cream is not limited to one container or one flavor. What is the probability that someone who is buying ice cream will buy chocolate or vanilla? [Hint: Use the probability of success.]
0.315
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 122 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 + 97 25 122 Test Result - 25 48 73 Column Total 122 73 195 Assume that the sample is representative of the entire population. For a person selected at random, find P(getting test result - or condition absent). Round your answer to the nearest hundredth.
0.50
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: 65% of all Wing Foot stores show a profit the first year; 70% of all Wing Foot store show a profit the second year (this includes stores that did not show a profit the first year); however, 83% of Wing Foot stores that showed a profit the first year also showed a profit the second year. Compute P(A or B) if P(A) = 0.65, P(B) = 0.70, and P(B|A) = 0.83. Round your answer to the nearest hundredth.
0.81
Use a random-number table to get a list of 4 random numbers between 100 and 150 beginning at row 5, block 2. 65321 85623 10204 50218 20321 22315 98532 91972 39800 45670 20510 10451 92012 59826 35456 79289 91483 29754 45652 98653 45863 36963 15326 78952 45678 10100 91251 37041 13712 14672
101 0 125 0 137 0 121 0 0 0
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: 11 0 38 24 31 26 27 -11 -11 -24 y: 6 -2 29 14 25 16 14 -2 -3 -6
111
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? State Hospitals State Hospitals State Hospitals Alabama 119 Colorado 78 Georgia 163 Alaska 16 Connecticut 35 Hawaii 19 Arizona 61 Delaware 8 Idaho 41 Arkansas 88 Dist. of Columbia 11 Illinois 209 California 440 Florida 227 Indiana 113 Iowa 123 Nebraska 90 Rhode Island 12 Kansas 133 Nebraska 21 S.Carolina 68 Kentucky 109 New Hampshire 21 S.Dakota 52 Louisiana 136 New Jersey 96 Tennessee 122 Maine 38 New Mexico 37 Texas 421 Maryland 51 New York 231 Utah 42 Mass. 101 N.Caroline 117 Vermont 15 Michigan 175 N.Dakota 47 Virginia 98 Minnesota 148 Ohio 193 Washington 92 Mississippi 102 Oklahoma 113 W.Virginia 59 Missouri 133 Oregon 66 Wisconsin 129 Montana 53 Pennsylvania 239 Wyoming 27
California and Texas
Finish times (to the nearest hour) for 10 dogsled teams are shown below. Make a frequency table showing class limits, class boundaries, midpoints, frequency, relative frequencies, and cumulative frequencies. Use three classes. The class size of the given data is 24. (Round your answer for relative frequency to the nearest hundredth and for midpoint to the nearest tenth.) 236 310 262 301 272 299 282 295 287 246
Class Limits Boundaries Midpoint Freq. Relative Freq. Cumulative Freq. 236-260 235.5-260.5 248.0 2 0.20 3 261-285 260.5-285.5 273.0 3 0.30 5 286-310 285.5-310.5 298.0 5 0.50 10
A professional employee in a large corporation receives an average of μ = 39.8 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 47 employees showed that they were receiving an average of x = 29.9 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 are the null and alternate hypotheses?
H0 : μ = 39.8 e-mails; H1 : μ ≠ 39.8 e-mails
A severe storm has an average peak wave height of 16.4 feet for waves hitting the shore. Suppose that a storm is in progress with a severe storm class rating. Let us say that we want to set up a statistical test to see if the wave action (i.e., height) is dying down or getting worse. If you wanted to test the hypothesis that the storm is getting worse, what would you use for the alternate hypothesis? Is the P-value area on the left, right, or on both sides of the mean?
H1 : μ is greater than 16.4 feet; the P-value area is on the right of the mean
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. 16 17 17 17 18 19 19 19 20 20 20 20 20 21 21 21 21 21 22 22 23 23 23 23 23 24 24 24 24 25 25 25 25 25 25 26 26 26 27 27 27 28 28 30 30 31 31 33 34 37 Illinois has a bachelor's degree percentage rate of about 16%. Into what quartile does this rate fall?
first quartile
Identify whether the variable in the information below is qualitative or quantitative. 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.
quantitative
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
