Stats final
midwest-1 to 2 years
0.130
midwest loyal 5-9years
0.256
find y
5
Given the sample data below, use the defining formula to compute the sample standard deviation. 21 17 32 12 22 12
7.53
x
California and Texas
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
Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 6.8 seconds. Suppose that you want to set up a statistical test to challenge the claim of 6.8 seconds. What would you use for the null hypothesis?
H0 : μ = 6.8 seconds
x
T T H T T T T H H T T T T T H T H H T H
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 Ranch2 3 1 1 3 4 6 9 3 1 3 Lower Canyon: Number of injuries per Landing Point BetweenBright Angel and Lava Falls8 1 1 0 6 7 2 11 3 0 1 10 2 1
The 5% trimmed mean for Lower Canyon is 3.500 and for Upper Canyon is 2.889.
coefficient of variation
for x-values: 190.4%, and for y-values: 156.2%
x
for x-values: 193.7%, and for y-values: 146.1%
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
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
A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 80 months and a standard deviation of 6.1 month. When this computer-relay microchip malfunctions, the entire satellite is useless. A large London insurance company is going to insure the satellite for 60 million dollars. Assume that the only part of the satellite in question is the microchip. All other components will work indefinitely. If the satellite is insured for 73 months, what is the expected loss to the insurance company? Round to the nearest ten-thousand dollars.
$7.53 million
x
-81.093
0.681
0.681
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
Let z be a random variable with a standard normal distribution. Find the indicated probability below. P(z ≤ 1.6)
0.945
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
find b in y=a +bx
20.195
California has the highest median premium. 0 0
California has the highest median premium. 0 0
x
Scores are lower in the first round.
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?
a = 0.01
Data may be classified by one of the four levels of measurement. What is the name of the lowest level?
nominal
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
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
Find the technique for gathering data in the study below. The Colorado Division of Wildlife netted and released 774 fish at Quincy Reservoir. There were 219 perch, 315 blue gill, 83 pike, and 157 rainbow trout.
observational study
Finish times (to the nearest hour) for 57 dogsled teams are shown below. Use five classes. Categorize the basic distribution shape as uniform or rectangular, mound-shaped symmetric, bimodal, skewed left, or skewed right. 261 271 236 244 279 296 284 299 288 288 247 256 338 360 341 333 261 266 287 296 313 311 307 307 299 303 277 283 304 305 288 290 288 289 297 299 332 330 309 328 307 328 285 291 295 298 306 315 310 318 318 320 333 321 323 324 327
approximately mound-shaped symmetric
Let z be a random variable with a standard normal distribution. Find the indicated probability below. P(-2.1 ≤ z ≤ 2.2)
0.968
P (getting test result and condition absent)
0.28
p(condition absent | getting result -)
0.74
lowest vs highest premium
California has the lowest premium and Pennsylvania has the highest.
find y=a +bx
y= 17+ 9x
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.
-0.949
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
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 y=a +bx.
-81.093
stem and leaf
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
You draw two cards from a standard deck of 52 cards and do not replace the first one before drawing the second. Find the probability of drawing a 5 for the first card and a 4 for the second card. Round your answer to the nearest thousandth.
0.006
Let x be a random variable representing dividend yield of Australian bank stocks. We may assume that x has a normal distribution with σ = 2.2%. A random sample of 16 Australian bank stocks has a mean x = 6.03%. For the entire Australian stock market, the mean dividend yield is μ = 5.8%. Do these data indicate that the dividend yield of all Australian bank stocks is higher than 5.8%? Use α = 0.01. What is the level of significance?
0.010
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
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 = 74 and standard deviation of σ = 23. What is the probability that, for an adult after a 12-hour fast, x is between 94 and 103?
0.089
Assuming that the heights of college women are normally distributed with mean 64 inches and standard deviation 1.5 inches, what percentage of women are shorter than 59.5 inches?
0.1%
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
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
Assume that 56% of all customers will take free samples. Furthermore, of those who take the free samples, assume that about 30% will buy what they have sampled. Suppose that you set up a counter in a supermarket offering free samples of a new product and that the day you were offering free samples, 284 customers passed by your counter. What is the probability that a customer will take a free sample and buy the product? [Hint: Use the multiplication rule for dependent events. Notice we are given the conditional probability P(buy, given sample) = 0.3, while P(sample) = 0.56.]
0.168
John runs a computer software store. He counted 120 people who walked by his store in a day, 50 of whom came into the store. Of the 50, only 21 bought something in the store. Estimate the probability that a person who walks by the store will come in and buy something. Round your answer to the nearest hundredth.
0.18
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
south and 10-14 years
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
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
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
Coefficient of variation r squared
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
If the probability that an event will happen is 0.27, what is the probability that the event won't happen?
0.73
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
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
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: 60% of all Wing Foot stores show a profit the first year; 73% 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(B|A), if P(A) = 0.60 and P(B|not A) = 0.34.
0.80
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
Find the area under the standard normal curve over the interval specified below. To the left of z = 2
0.977
Let z be a random variable with a standard normal distribution. Find the indicated probability below. P(z ≥ -2.1)
0.982
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
Find the area under the standard normal curve over the interval specified below. To the right of z = -3
0.999
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
A coin is to be tossed 1000 times. What is the probability that the 785th toss is heads?
1/2
x
101 0 125 0 137 0 121 0 0 0
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 25 2 6 19 27 36 29 41 18 10 8 21 32 28 30 17 20 34 14 36 Find the interquartile range.
15.5
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%
Assume that the following data represent baseball batting averages for a random sample of National League players near the end of the baseball season. Multiply each data value by 1000 to "clear" the decimals. 0.193 0.258 0.154 0.293 0.159 0.297 0.261 0.251 0.182 0.125 0.106 0.260 0.306 0.306 0.279 0.289 0.319 0.253 0.215 0.251 0.247 0.260 0.265 0.183 0.113 0.201
193 258 154 293 159 297 261 251 182 125 106 260 306 306 279 289 319 253 215 251 247 260 265 183 113 201
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 = 4.3 and standard deviation σ = 0.2 Convert the following x interval from a laboratory test to a z interval. 4.7 > x
2 > z
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.) 252314315284255245292335244342
20
Suppose that x has a distribution with μ = 20 and σ = 3. If a random sample is taken of size n = 43, find ux
20.00
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 5.75 6.00 6.50 7.25 y 12 31 41 52 56 Find b for the equation of the least-squares line y=a + bx.
20.195
fraction
284/955
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: 59 52 67 86 72 66 97 88 85 91 91 92 69 68 87 86 73 61 70 75 72 73 85 84 90 57 77 76 84 93 58 47 Make a stem-and-leaf display for these data.
4 7 = 47 years 4 7 5 2 7 8 9 6 1 6 7 8 9 7 0 2 2 3 3 5 6 7 8 4 4 5 5 6 6 7 8 9 0 1 1 2 3 7
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
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%
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 (with hat over it)
57.60
xCompute 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
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 7.00 7.25 8.00 y 54 50 83 77 81 find x (with hat over it)
6.80
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. x: 22 17 13 33 26
6.97
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
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%
In your biology class, your final grade is based on several things: a lab score, score on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 25% of your total grade, each major test is worth 22.5%, and the final exam is worth 30%. Compute the weighted average for the following scores: 92 on the lab, 83 on the first major test, 95 on the second major test, and 82 on the final exam. Round your answer to the nearest hundredth.
87.65
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 parameter?
A numerical descriptive measure of a population
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
uppose that the mean time for a certain car to go from 0 to 60 miles per hour was 6.8 seconds. Suppose that you want to set up a statistical test to challenge the claim of 6.8 seconds. What would you use for the null hypothesis?
H0 : μ = 6.8 seconds
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
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. Upper Canyon: Number of injuries per Landing Point BetweenNorth Canyon and Phantom Ranch 3 4 2 2 4 5 9 12 4 2 4 Lower Canyon: Number of injuries per Landing Point BetweenBright Angel and Lava Falls 11 2 2 0 9 10 3 14 4 0 2 13 32 The mean, median, and mode for Upper Canyon are 4.636, 4.0, and 4, respectively. The mean, median, and mode for Lower Canyon are 5.357, 3.0, and 2, respectively.Compare the mean, median, and mode found in Upper Canyon and Lower Canyon, respectively.
Lower Canyon mean is greater than Upper Canyon, Lower Canyon median is smaller than Upper Canyon, and Lower Canyon mode is smaller than Upper Canyon.
smallest range of premiums
Pennsylvania has the smallest range of premiums. 0 0
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
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.q
Simple random sample
Can a low barometer reading be used to predict maximum wind speed of an approaching tropical cyclone? Let x be the lowest pressure (in millibars) as a cyclone approaches, and let y be the maximum wind speed (in miles per hour) of the cyclone. Suppose a random sample of cyclones gave the following information. x 1014 935 980 955 995 y 50 80 60 135 84 Given that the value of r is -0.556, should y increase as x increases, does the value of r imply that y should tend to increase, decrease, or remain the same? Explain.
Since r is negative, as x increases, y decreases.
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.
Suppose twenty-two communities have an average of = 123.6 reported cases of larceny per year. Assume that σ is known to be 36.8 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 lengths of the confidence intervals. As the confidence levels increase, do the confidence intervals increase in length?
The 90% confidence level has a confidence interval length of 25.8; the 95% confidence level has a confidence interval length of 30.8; and the 98% confidence level has a confidence interval length of 36.6. As the confidence level increases, the confidence interval lengths increases.`
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.
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.
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.
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.
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. 261 271 236 244 279 296 284 299 288 288 247 256 338360 341 333 261 266 287 296 313 311 307 307 279 283 277 283 385 275 279 281 288 289 297 331 281 278 276 328 261 328 298 303 304 305 315 313 283 284 261 267 271 281 297 280 311 0 0 0
approximately mound-shaped symmetric
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
Suppose an airline found that about 5% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose that the airline overbooks this flight by selling 247 ticket reservations for an airplane with only 243 seats. Let n = 247 represent the number of ticket reservations. Let r represent the number of people with reservations who show up for the flight. Which expression represents the probability that a seat will be available for everyone who shows up holding a reservation: Expression I :P(r ≥ 247) Expression II :P(r ≥ 243) Expression III :P(r ≤ 247) Expression IV :P(r ≤ 243) Expression V :P(r = 243)
expression IV
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
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
75% chebysv interval
for x-values: -31.86 to 53.26 and for y-values: -17.06 to 34.46
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:1303922322425 -13 -13 -22 y:7 -4 2716231816 -4 -5 -7 The sample means for x and y are 10.70 and 8.70, respectively. Compute a 75% Chebyshev interval around the mean for x-values and also for y-values. Round your answers to the nearest hundredth.
for x-values: -31.86 to 53.26 and for y-values: -17.06 to 34.46
coefficient of variation 2
for x-values: -33.36 to 55.76 and for y-values: -19.50 to 36.90
At a certain excavation site, archaeological studies have used the method of tree-ring dating in an effort to determine when people lived in there. Wood from several excavations gave a mean of (year) 619 with a standard deviation of 42 years. The distribution of dates was more or less mound-shaped and symmetrical about the mean. Use the empirical rule to estimate a range of years centered about the mean in which about 99.7% of the data (tree-ring dates) will be found.
from 493 to 745
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
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
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 TRUE OR FALSE: The distribution is approximately mound shaped.
true
Suppose a certain species of fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean μ = 20.5 kilograms and standard deviation σ = 3.7 kilograms. Let x be the weight of a fawn in kilograms. Convert the following z interval to a x interval. 1.2 < z
x > 24.94
Suppose a certain species of fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean μ = 30 kilograms and standard deviation σ = 4 kilograms. Let x be the weight of a fawn in kilograms. Convert the following x interval to a z interval. Round to the nearest hundredth. x < 44.0
z < 3.50
