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business statistics in practice

The Practice Of Statistics 5th Edition Daren S. Starnes, Josh Tabor - Solutions

Construction zones Every road has one at some point—construction zones that have much lower speed limits. To see if drivers obey these lower speed limits, a police officer uses a radar gun to measure the speed (in miles per hours, or mph) of a random sample of 10 drivers in a 25 mph construction
Heat through the glass How well materials conduct heat matters when designing houses, for example.Conductivity is measured in terms of watts of heat power transmitted per square meter of surface per degree Celsius of temperature difference on the two sides of the material. In these units, glass has
Healthy bones The recommended daily allowance(RDA) of calcium for women between the ages of 18 and 24 years is 1200 milligrams (mg). Researchers who were involved in a large-scale study of women’s bone health suspected that their participants had significantly lower calcium intakes than the RDA.
Taking stock An investor with a stock portfolio worth several hundred thousand dollars sued his broker due to the low returns he got from the portfolio at a time when the stock market did well overall. The investor’s lawyer wants to compare the broker’s performance against the market as a
Pressing pills A drug manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each batch of tablets produced is measured to control the compression process. The target value for the hardness is m = 11.5.
Filling cola bottles Bottles of a popular cola are supposed to contain 300 milliliters (ml) of cola.There is some variation from bottle to bottle because the filling machinery is not perfectly precise.An inspector measures the contents of six randomly selected bottles from a single day’s
Pressing pills Refer to Exercise 77. Construct and interpret a 95% confidence interval for the population mean m. What additional information does the confidence interval provide?
Filling cola bottles Refer to Exercise 78. Construct and interpret a 95% confidence interval for the population mean m. What additional information does the confidence interval provide?
Fast connection? How long does it take for a chunk of information to travel from one server to another and back on the Internet? According to the site internettrafficreport.com, a typical response time is 200 milliseconds (about one-fifth of a second).Researchers collected data on response times of
Water! A blogger claims that U.S. adults drink an average of five 8-ounce glasses of water per day.Skeptical researchers ask a random sample of 24 U.S. adults about their daily water intake. A graph of the data shows a roughly symmetric shape with no outliers. The figure below displays Minitab
Tests and CIs The P-value for a two-sided test of the null hypothesis H0 : m = 10 is 0.06.(a) Does the 95% confidence interval for m include 10?Why or why not?(b) Does the 90% confidence interval for m include 10?Why or why not?84. Tests and CIs The P-value for a two-sided test of the null
Right versus left The design of controls and instruments affects how easily people can use them. A student project investigated this effect by asking 25 right-handed students to turn a knob (with their right hands) that moved an indicator. There were two identical instruments, one with a right-hand
Floral scents and learning We hear that listening to Mozart improves students’ performance on tests.Maybe pleasant odors have a similar effect. To test this idea, 21 subjects worked two different but roughly equivalent paper-and-pencil mazes while wearing a mask. The mask was either unscented or
Growing tomatoes Researchers suspect that Variety A tomato plants have a higher average yield than Variety B tomato plants. To find out, researchers randomly select 10 Variety A and 10 Variety B tomato plants.Then the researchers divide in half each of 10 small plots of land in different locations.
Music and memory Does listening to music while studying hinder students’ learning? Two AP® Statistics students designed an experiment to find out.They selected a random sample of 30 students from their medium-sized high school to participate. Each subject was given 10 minutes to memorize two
The power of tomatoes Refer to Exercise 87.Explain two ways that the researchers could have increased the power of the test to detect m = 0.5.
Music and memory Refer to Exercise 88. Which of the following changes would give the test a higher power to detect m = −1: using a = 0.01 or a = 0.10? Explain.
Significance and sample size A study with 5000 subjects reported a result that was statistically significant at the 5% level. Explain why this result might not be particularly large or important.
Sampling shoppers A marketing consultant observes 50 consecutive shoppers at a supermarket, recording how much each shopper spends in the store. Explain why it would not be wise to use these data to carry out a significance test about the mean amount spent by all shoppers at this supermarket.
Do you have ESP? A researcher looking for evidence of extrasensory perception (ESP) tests 500 subjects.Four of these subjects do significantly better (P < 0.01)than random guessing.(a) Is it proper to conclude that these four people have ESP? Explain your answer.(b) What should the researcher now
Ages of presidents Joe is writing a report on the backgrounds of American presidents. He looks up the ages of all the presidents when they entered office. Because Joe took a statistics course, he uses these numbers to perform a significance test about the mean age of all U.S. presidents. Explain
The reason we use t procedures instead of z procedures when carrying out a test about a population mean is that(a) z requires that the sample size be large.(b) z requires that you know the population standard deviation s.(c) z requires that the data come from a random sample or randomized
You are testing H0 : m = 10 against Ha : m < 10 based on an SRS of 20 observations from a Normal population.The t statistic is t = −2.25. The P-value(a) falls between 0.01 and 0.02.(b) falls between 0.02 and 0.04.(c) falls between 0.04 and 0.05.(d) falls between 0.05 and 0.25.(e) is greater than
You are testing H0 : m = 10 against Ha : m ≠ 10 based on an SRS of 15 observations from a Normal population.What values of the t statistic are statistically significant at the a = 0.005 level?(a) t > 3.326 (d) t < −3.326 or t > 3.326(b) t > 3.286 (e) t < −3.286 or t > 3.286(c) t > 2.977
After checking that conditions are met, you perform a significance test of H0 : m = 1 versus Ha : m ≠ 1. You obtain a P-value of 0.022. Which of the following must be true?(a) A 95% confidence interval for m will include the value 1.(b) A 95% confidence interval for m will include the value 0.(c)
Does Friday the 13th have an effect on people’s behavior? Researchers collected data on the number of shoppers at a sample of 45 nearby grocery stores on Friday the 6th and Friday the 13th in the same month. The dotplot and computer output below summarize the data on the difference in the number
The most important condition for sound conclusions from statistical inference is that(a) the data come from a well-designed random sample or randomized experiment.(b) the population distribution be exactly Normal.(c) the data contain no outliers.(d) the sample size be no more than 10% of the
Vigorous exercise helps people live several years longer (on average). Whether mild activities like slow walking extend life is not clear. Suppose that the added life expectancy from regular slow walking is just 2 months. A statistical test is more likely to find a significant increase in mean life
A researcher plans to conduct a significance test at the a = 0.01 significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a Type II error for the particular alternative value of
Is your food safe? (8.1) “Do you feel confident or not confident that the food available at most grocery stores is safe to eat?” When a Gallup Poll asked this question, 87% of the sample said they were confident.26 Gallup announced the poll’s margin of error for 95% confidence as ±3
Spinning for apples (6.3 or 7.3) In the “Ask Marilyn”column of Parade magazine, a reader posed this question: “Say that a slot machine has five wheels, and each wheel has five symbols: an apple, a grape, a peach, a pear, and a plum. I pull the lever five times. What are the chances that
Stating hypotheses State the appropriate null and alternative hypotheses in each of the following settings.Be sure to define the parameter.(a) The average height of 18-year-old American women is 64.2 inches. You wonder whether the mean height of this year’s female graduates from a large local
Fonts and reading ease Does the use of fancy type fonts slow down the reading of text on a computer screen? Adults can read four paragraphs of text in the common Times New Roman font in an average time of 22 seconds. Researchers asked a random sample of 24 adults to read this text in the ornate
Strong chairs? A company that manufactures classroom chairs for high school students claims that the mean breaking strength of the chairs that they make is 300 pounds. One of the chairs collapsed beneath a 220-pound student last week. You wonder whether the manufacturer is exaggerating the breaking
Flu vaccine A drug company has developed a new vaccine for preventing the flu. The company claims that fewer than 5% of adults who use its vaccine will get the flu. To test the claim, researchers give the vaccine to a random sample of 1000 adults. Of these, 43 get the flu.(a) Do these data provide
Roulette An American roulette wheel has 18 red slots among its 38 slots. To test if a particular roulette wheel is fair, you spin the wheel 50 times and the ball lands in a red slot 31 times. The resulting P-value is 0.0384.(a) Interpret the P-value in context.(b) Are the results statistically
Radon detectors Radon is a colorless, odorless gas that is naturally released by rocks and soils and may concentrate in tightly closed houses. Because radon is slightly radioactive, there is some concern that it may be a health hazard. Radon detectors are sold to homeowners worried about this risk,
Better barley Does drying barley seeds in a kiln increase the yield of barley? A famous experiment by William S. Gosset (who discovered the t distributions)investigated this question. Eleven pairs of adjacent plots were marked out in a large field. For each pair, regular barley seeds were planted
An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are(a) H0 : p^ = 0.5; Ha : p^ > 0.5(b)
You are thinking of conducting a one-sample t test about a population mean m using a 0.05 significance level. Which of the following statements is correct?(a) You should not carry out the test if the sample does not have a Normal distribution.(b) You can safely carry out the test if there are no
To determine the reliability of experts who interpret lie detector tests in criminal investigations, a random sample of 280 such cases was studied. The results were Suspect’s True Status Examiner’s Decision Innocent Guilty“Innocent” 131 15“Guilty” 9 125 If the hypotheses are H0: suspect
A significance test allows you to reject a null hypothesis H0 in favor of an alternative Ha at the 5% significance level. What can you say about significance at the 1% level?(a) H0 can be rejected at the 1% significance level.(b) There is insufficient evidence to reject H0 at the 1%significance
A random sample of 100 likely voters in a small city produced 59 voters in favor of Candidate A. The observed value of the test statistic for testing the null hypothesis H0 : p = 0.5 versus the alternative hypothesis Ha : p > 0.5 is(a) z =0.59 − 0.5Å0.59(0.41)100(d) z =0.5 −
A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are
A 95% confidence interval for a population mean m is calculated to be (1.7, 3.5). Assume that the conditions for performing inference are met. What conclusion can we draw for a test of H0 : m = 2 versus Ha : m ≠ 2 at the a = 0.05 level based on the confidence interval?(a) None. We cannot carry
In a test of H0 : p = 0.4 against Ha : p ≠ 0.4, a random sample of size 100 yields a test statistic of z = 1.28.The P-value of the test is approximately equal to(a) 0.90. (c) 0.05. (e) 0.10.(b) 0.40. (d) 0.20.
An SRS of 100 postal employees found that the average time these employees had worked at the postal service was 7 years with standard deviation 2 years. Do these data provide convincing evidence that the mean time of employment m for the population of postal employees has changed from the value of
Are TV commercials louder than their surrounding programs? To find out, researchers collected data on 50 randomly selected commercials in a given week. With the television’s volume at a fixed setting, they measured the maximum loudness of each commercial and the maximum loudness in the first 30
A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay $100 for the upgrade.For the upgrade to be profitable, the company needs to sell it to more than 20% of their customers.You contact a random sample of 60 customers and find that
“I can’t get through my day without coffee” is a common statement from many students. Assumed benefits include keeping students awake during lectures and making them more alert for exams and tests. Students in a statistics class designed an experiment to measure memory retention with and
A government report says that the average amount of money spent per U.S. household per week on food is about $158. A random sample of 50 households in a small city is selected, and their weekly spending on food is recorded. The sample data have a mean of $165 and a standard deviation of$20. Is
Find and interpret the percentile of an individual value within a distribution of data.
Estimate percentiles and individual values using a cumulative relative frequency graph.
Find and interpret the standardized score (z-score) of an individual value within a distribution of data.
Describe the effect of adding, subtracting, multiplying by, or dividing by a constant on the shape, center, and spread of a distribution of data.
Shoes How many pairs of shoes do students have?Do girls have more shoes than boys? Here are data from a random sample of 20 female and 20 male students at a large high school:Female: 50 26 26 31 57 19 24 22 23 38 13 50 13 34 23 30 49 13 15 51 Male: 14 7 6 5 12 38 8 7 10 10 10 11 4 5 22 7 5 10 35
Old folks Here is a stemplot of the percents of residents aged 65 and older in the 50 states:7 0 8 8 9 8 10 019 11 16777 12 01122456778999 13 0001223344455689 14 023568 15 24 16 9 Key: 15|2 means 15.2% of this state’s residents are 65 or older(a) Find and interpret the percentile for Colorado,
Math test Josh just got the results of the statewide Algebra 2 test: his score is at the 60th percentile.When Josh gets home, he tells his parents that he got 60 percent of the questions correct on the state test.Explain what’s wrong with Josh’s interpretation.
Blood pressure Larry came home very excited after a visit to his doctor. He announced proudly to his wife,“My doctor says my blood pressure is at the 90th percentile among men like me. That means I’m better off than about 90% of similar men.” How should his wife, who is a statistician,
Growth charts We used an online growth chart to find percentiles for the height and weight of a 16-yearold girl who is 66 inches tall and weighs 118 pounds.According to the chart, this girl is at the 48th percentile for weight and the 78th percentile for height.Explain what these values mean in
Run fast Peter is a star runner on the track team. In the league championship meet, Peter records a time that would fall at the 80th percentile of all his race times that season. But his performance places him at the 50th percentile in the league championship meet.Explain how this is possible.
Text me The percentile plot below shows the distribution of text messages sent and received in a two-day period by a random sample of 16 females from a large high school.(a) Describe the student represented by the highlighted point.(b) Use the graph to estimate the median number of texts. Explain
Foreign-born residents The following percentile plot shows the distribution of the percent of foreign-born residents in the 50 states.(a) The highlighted point is for Maryland. Describe what the graph tells you about this state.(b) Use the graph to estimate the 30th percentile of the distribution.
Shopping spree The figure below is a cumulative relative frequency graph of the amount spent by 50 consecutive grocery shoppers at a store.(a) Estimate the interquartile range of this distribution.Show your method.(b) What is the percentile for the shopper who spent $19.50?(c) Draw the histogram
Light it up! The graph below is a cumulative relative frequency graph showing the lifetimes(in hours) of 200 lamps.4(a) Estimate the 60th percentile of this distribution.Show your method.(b) What is the percentile for a lamp that lasted 900 hours?(c) Draw a histogram that corresponds to this graph.
SAT versus ACT Eleanor scores 680 on the SAT Mathematics test. The distribution of SAT scores is symmetric and single-peaked, with mean 500 and standard deviation 100. Gerald takes the American College Testing (ACT) Mathematics test and scores 27. ACT scores also follow a symmetric, single-peaked
Comparing batting averages Three landmarks of baseball achievement are Ty Cobb’s batting average of 0.420 in 1911, Ted Williams’s 0.406 in 1941, and George Brett’s 0.390 in 1980. These batting averages cannot be compared directly because the distribution of major league batting averages has
Measuring bone density Individuals with low bone density have a high risk of broken bones (fractures).Physicians who are concerned about low bone density(osteoporosis) in patients can refer them for specialized testing. Currently, the most common method for testing bone density is dual-energy X-ray
Comparing bone density Refer to the previous exercise.One of Judy’s friends, Mary, has the bone density in her hip measured using DEXA. Mary is 35 years old. Her bone density is also reported as 948 g/cm2, but her standardized score is z = 0.50. The mean bone density in the hip for the reference
Baseball salaries Brad Lidge played a crucial role as the Phillies’ “closer,” pitching the end of many games throughout the season. Lidge’s salary for the 2008 season was $6,350,000.(a) Find the percentile corresponding to Lidge’s salary.Explain what this value means.(b) Find the z-score
Baseball salaries Did Ryan Madson, who was paid$1,400,000, have a high salary or a low salary compared with the rest of the team? Justify your answer by calculating and interpreting Madson’s percentile and z-score.Refer to the dotplot and summary statistics of salaries for players on the World
The scores on Ms. Martin’s statistics quiz had a mean of 12 and a standard deviation of 3. Ms. Martin wants to transform the scores to have a mean of 75 and a standard deviation of 12. What transformations should she apply to each test score? Explain.
Mr. Olsen uses an unusual grading system in his class. After each test, he transforms the scores to have a mean of 0 and a standard deviation of 1. Mr. Olsen then assigns a grade to each student based on the transformed score. On his most recent test, the class’s scores had a mean of 68 and a
Tall or short? Mr. Walker measures the heights (in inches) of the students in one of his classes. He uses a computer to calculate the following numerical summaries:Mean Std. dev. Min Q1 Med Q3 Max 69.188 3.20 61.5 67.75 69.5 71 74.5 Next, Mr. Walker has his entire class stand on their chairs, which
Teacher raises A school system employs teachers at salaries between $28,000 and $60,000. The teachers’union and the school board are negotiating the form of next year’s increase in the salary schedule.(a) If every teacher is given a flat $1000 raise, what will this do to the mean salary? To the
Tall or short? Refer to Exercise 19. Mr. Walker converts his students’ original heights from inches to feet.(a) Find the mean and median of the students’ heights in feet. Show your work.(b) Find the standard deviation and IQR of the students’heights in feet. Show your work.
Teacher raises Refer to Exercise 20. If each teacher receives a 5% raise instead of a flat $1000 raise, the amount of the raise will vary from $1400 to $3000, depending on the present salary.(a) What will this do to the mean salary? To the median salary? Explain your answers.(b) Will a 5% raise
Cool pool? Coach Ferguson uses a thermometer to measure the temperature (in degrees Celsius) at 20 different locations in the school swimming pool.An analysis of the data yields a mean of 25°C and a standard deviation of 2°C. Find the mean and standard deviation of the temperature readings in
Measure up Clarence measures the diameter of each tennis ball in a bag with a standard ruler. Unfortunately, he uses the ruler incorrectly so that each of his measurements is 0.2 inches too large. Clarence’s data had a mean of 3.2 inches and a standard deviation of 0.1 inches. Find the mean and
Jorge’s score on Exam 1 in his statistics class was at the 64th percentile of the scores for all students. His score falls(a) between the minimum and the first quartile.(b) between the first quartile and the median.(c) between the median and the third quartile.(d) between the third quartile and
When Sam goes to a restaurant, he always tips the server $2 plus 10% of the cost of the meal. If Sam’s distribution of meal costs has a mean of $9 and a standard deviation of $3, what are the mean and standard deviation of the distribution of his tips?(a) $2.90, $0.30(b) $2.90, $2.30(c) $9.00,
Scores on the ACT college entrance exam follow a bell-shaped distribution with mean 18 and standard deviation 6. Wayne’s standardized score on the ACT was −0.5. What was Wayne’s actual ACT score?(a) 5.5 (b) 12 (c) 15 (d) 17.5 (e) 21
George has an average bowling score of 180 and bowls in a league where the average for all bowlers is 150 and the standard deviation is 20. Bill has an average bowling score of 190 and bowls in a league where the average is 160 and the standard deviation is 15. Who ranks higher in his own league,
What is the interquartile range (IQR) for the distribution of absences?(a) 1 (c) 3 (e) 14(b) 2 (d) 5 The number of absences during the fall semester was recorded for each student in a large elementary school. The distribution of absences is displayed in the following cumulative relative frequency
If the distribution of absences was displayed in a histogram, what would be the best description of the histogram’s shape?(a) Symmetric(b) Uniform(c) Skewed left(d) Skewed right(e) Cannot be determined The number of absences during the fall semester was recorded for each student in a large
Travel time (1.2) The dotplot below displays data on students’ responses to the question “How long does it usually take you to travel to school?” Describe the shape, center, and spread of the distribution. Are there any outliers? www** 60 Travel time (minutes) 0 20 40 80 100
Lefties (1.1) Students were asked, “Are you righthanded, left-handed, or ambidextrous?” The responses are shown below (R = right-handed;L = left-handed; A = ambidextrous).R R R R R R R R R R R L R R R R R R R R R R R R R R R A R R R R A R R L R R R R L A R R R R R R R R(a) Make an appropriate
Estimate the relative locations of the median and mean on a density curve.
Use the 68–95–99.7 rule to estimate areas (proportions of values) in a Normal distribution.
Use Table A or technology to find (i) the proportion of z-values in a specified interval, or (ii) a z-score from a percentile in the standard Normal distribution.
Use Table A or technology to find (i) the proportion of values in a specified interval, or (ii) the value that corresponds to a given percentile in any Normal distribution.
Determine whether a distribution of data is approximately Normal from graphical and numerical evidence.
Density curves Sketch a density curve that might describe a distribution that is symmetric but has two peaks.
Density curves Sketch a density curve that might describe a distribution that has a single peak and is skewed to the left.
Biking accidents Accidents on a level, 3-mile bike path occur uniformly along the length of the path.The figure below displays the density curve that describes the uniform distribution of accidents.(a) Explain why this curve satisfies the two requirements for a density curve.(b) The proportion of
Where’s the bus? Sally takes the same bus to work every morning. The amount of time (in minutes) that she has to wait for the bus to arrive is described by the uniform distribution below.(a) Explain why this curve satisfies the two requirements for a density curve.(b) On what percent of days does
Biking accidents What is the mean m of the density curve pictured in Exercise 35? (That is, where would the curve balance?) What is the median? (That is, where is the point with area 0.5 on either side?)
Where’s the bus? What is the mean m of the density curve pictured in Exercise 36? What is the median?
Mean and median The figure below displays two density curves, each with three points marked. At which of these points on each curve do the mean and the median fall? (a) ABC (b) A B C
Mean and median The figure below displays two density curves, each with three points marked. At which of these points on each curve do the mean and the median fall? (a) ABC (b) AB C

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