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elementary statistics

Just The Essentials Of Elementary Statistics 10th Edition Robert Johnson, Patricia Kuby - Solutions

Descriptions of three nationwide poll results follow.Each of the polls is based on approximately 1020 randomly selected adults.a. Calculate the 95% confidence maximum error of estimate for the true binomial proportion based on binomial experiments with the same sample size and observed proportion
Adverse drug reactions to legally prescribed medicines are among the leading causes of drugrelated death in the United States. Suppose you investigate drug-related deaths in your city and find that 223 out of 250 incidences were caused by legally prescribed drugs and the rest were the result of
Karl Pearson once tossed a coin 24,000 times and recorded 12,012 heads.a. Calculate the point estimate for p P(head)based on Pearson’s results.b. Determine the standard error of proportion.c. Determine the 95% confidence interval estimate for p P(head).d. It must have taken Mr. Pearson many
When a single die is rolled, the probability of a “one” is 1/6, or 0.167. Let’s simulate 3000 rolls of a die. (Note: A Bernoulli experiment is like a “single”trial binomial experiment. That is, one roll of a die is one Bernoulli experiment with p 1/6;and 3000 rolls of a die either is a
The “rule of thumb,” stated on page 497, indicated that we would expect the sampling distribution of p to be approximately normal when“n 20 and both np and nq were greater than 5.”What happens when these guidelines are not followed?a. Use the following set of computer or calculator
Has the law requiring bike helmet use failed?Yankelovich Partners conducted a survey of bicycle riders in the United States. Only 60% of the nationally representative sample of 1020 bike riders reported owning a bike helmet.Source: http://www.cpsc.gov/library/helmet.htmla. Find the 95% confidence
Find the sample size n needed for a 95% interval estimate in Example 9.10.
According to a May 14, 2002, USA Snapshot, 81% of all drivers use their seat belts. You wish to conduct a survey in your city to determine what percent of the drivers use seat belts. Use the national figure of 81% for your initial estimate of p.a. Find the sample size if you want your estimate to
Lung cancer is the leading cause of cancer deaths in both women and men in the United States, Canada, and China. In several other countries, lung cancer is the number one cause of cancer deaths in men and the second or third cause among women. Only about 14% of all people who develop lung cancer
Find the value of P for each of the hypothesis tests in Exercise 9.93; state the decision using 0.05.
Determine the p-value for each of the following hypothesis-testing situations.a. Ho : p 0.5, Ha: p 0.5, z 1.48b. Ho : p 0.7, Ha: p 0.7, z2.26c. Ho : p 0.4, Ha: p 0.4, z 0.98d. Ho : p 0.2, Ha: p 0.2, z1.59
Find the critical region, critical values, for each of the hypothesis tests in Exercise 9.93; state the decision using 0.05.
Determine the test criteria that would be used to test the following hypotheses when z is used as the test statistic and the classical approach is used.a. Ho : p 0.5 and Ha: p 0.5, with 0.05b. Ho : p 0.5 and Ha: p 0.5, with 0.05c. Ho : p 0.4 and Ha: p 0.4, with 0.10d. Ho : p
The binomial random variable, x, may be used as the test statistic when testing hypotheses about the binomial parameter, p, when n is small(say, 15 or less). Use Table 2 in Appendix B and determine the p-value for each of the following situations.a. Ho: p 0.5, Ha: p 0.5, where n 15 and x
Use Table 2 in Appendix B and determine the critical region used in testing each of the following hypotheses. (Note: Since x is discrete, choose critical regions that do not exceed the value of given.)a. Ho : p 0.5 and Ha: p 0.5, where n 15 and 0.05b. Ho : p 0.5 and Ha: p 0.5, where
An insurance company states that 90% of its claims are settled within 30 days. A consumer group selected a random sample of 75 of the company’s claims to test this statement. If the consumer group found that 55 of the claims were settled within 30 days, do they have sufficient reason to support
A recent survey conducted by ZOOM and Applied Research & Consulting LLC reported that the events of September 11 have motivated kids to volunteer and that more than 80% volunteer. A disbeliever of this information took his own random sample of 500 kids in an attempt to show that the true percentage
In a poll conducted by the American Association of Retired Persons (AARP) of 1706 adults aged 45 and older, 72% agreed with the statement that “adults should be allowed to legally use marijuana for medical purposes if a physician recommends it.”Source: D&C, December 19, 2004, “Most older
The popularity of personal watercraft(PWCs, also known as jet skis) continues to increase, despite the apparent danger associated with their use. In fact, a sample of 54 reported watercraft accidents to the Game and Parks Commission in the state of Nebraska revealed that 85% of them involved PWCs,
The USA Snapshot “Facing a crowd isn’t easy” (May 30, 2002) reported that 35% of U.S.professional women fear public speaking. Suppose you conduct a survey of 1000 randomly chosen professional women to test Ho : p 0.35 versus Ha: p 0.35, where p represents the proportion who fear public
Refer to Applied Example 9.14.a. Find the probability that 139 or more heads result when a balanced coin is tossed fairly 250 times.b. Find the probability that 110 or fewer heads result when a balanced coin is tossed fairly 250 times.c. Find the probability that the results of fairly tossing a
The following computer output was used to complete a hypothesis test.Test for One Proportion Test of p 0.225 vs p 0.225 95% Lower Sample X N Sample p Bound Z-Value P-Value 1 61 200 0.305000 0.2514512.71 0.003a. State the null and alternative hypotheses.b. If the test is completed using
a. Calculate the standard deviation for each set.A: 5, 6, 7, 7, 8, 10 B: 5, 6, 7, 7, 8, 15b. What effect did the largest value changing from 10 to 15 have on the standard deviation?c. Why do you think 15 might be called an outlier?
The variance of shoe sizes for all manufacturers is 0.1024. What is the standard deviation?
Find:a. 2(10, 0.01)b. 2(12, 0.025)c. 2(10, 0.95)d. 2(22, 0.995)
Find these critical values by using Table 8 of Appendix B.a. 2(18, 0.01)b. 2(16, 0.025)c. 2(8, 0.10)d. 2(28, 0.01)e. 2(22, 0.95)f. 2(10, 0.975)g. 2(50, 0.90) h. 2(24, 0.99)
Using the notation of Exercise 9.118, name and find the critical values of 2. a. d. a = 0.05 n = 20 b. a=0.01 n=5 = 0.05 n=61 a=0.10 n=22 f. C. a=0.025 n = 18 = 0.05 n = 7
Using the notation of Exercise 9.118, name and find the critical values of 2. a. d. n = 14 a = 0.005 n = 16 a = 0.025 b. x n = 28 a = 0.25 n = 18 a = 0.02 C. f. x 2 n=8 a=0.01 n=15 a=0.10
For a chi-square distribution having 12 degrees of freedom, find the area under the curve for chi-square values ranging from 3.57 to 21.0.
For a chi-square distribution having 35 degrees of freedom, find the area under the curve between 2(35, 0.96) and 2(35, 0.15).
Find the test statistic for the hypothesis test:a. Ho : 2 532 vs. Ha: 2 532 using sample information n 18 and s2 785.b. Ho : 2 52 vs. Ha: 2 52 using sample information n 41 and s2 78.2.
Calculate the value for the test statistic, 2, for each of these situations:a. Ho : 2 20, n 15, s2 17.8b. Ho : 2 30, n 18, s 5.7c. Ho : 42, n 25, s 37.8d. Ho : 12, n 37, s2 163
Calculate the p-value for each of the following hypothesis tests.a. Ha: 2 20, n 15, 2 27.8b. Ha: 2 30, n 18, 2 33.4c. Ha: 2 42, df 25, 2 37.9d. Ha: 2 12, df 40, 2 26.3
Determine the critical region and critical value(s) that would be used to test the following using the classical approach:a. Ho : 0.5 and Ha: 0.5, with n 18 and 0.05b. Ho : 2 8.5 and Ha: 2 8.5, with n 15 and 0.01c. Ho : 20.3 and Ha: 20.3, with n 10 and 0.10d. Ho :
Complete the hypothesis test in Exercise 9.129a using the following:a. The p-value method and 0.01b. The classical method and 0.01
Complete the hypothesis test in Exercise 9.129b using the following:a. The p-value method and 0.05b. The classical method and 0.05
[EX09-137] Maybe even more important than how much they weigh, it is very important that the plates used in weightlifting be the same weight. When one of each weight is hanging on opposite ends of a bar, they need to balance. A random sample of twenty-four 25-lb weights used for weightlifting were
Farm real estate values in rural America fluctuate substantially from state to state and county to county, thus making it difficult for buyers purchasing land or landowners to know precisely what their property is actually worth. For example, the average value of ranch land in Missouri was $548 per
[EX09-140] A car manufacturer claims that the miles per gallon for a certain model has a mean equal to 40.5 miles with a standard deviation equal to 3.5 miles. Use the following data, obtained from a random sample of 15 such cars, to test the hypothesis that the standard deviation differs from 3.5.
[EX09-141] The dry weight of a cork is another quality that does not affect the ability of the cork to seal the bottle, but it is a variable that is monitored regularly. The weights of the no. 9 natural corks (24 mm in diameter by 45 mm in length) have a normal distribution. Ten randomly selected
Use a computer or calculator to find the p-value for the following hypothesis test: Ho: 2 7 vs. Ha: 2 7, if 2 6.87 for a sample of n 15.
Use a computer or calculator to find the p-value for the following hypothesis test:Ho : 12.4 vs. Ha: 12.4, if 2 36.59 for a sample of n 24.
The chi-square distribution was described on page 517 as a family of distributions. Let’s investigate these distributions and observe some of their properties.a. Use the MINITAB commands that follow and generate several large random samples of data from various chi-square distributions. Use df
You hurry to the local emergency department in hopes of immediate urgent care only to find yourself waiting for what seems like hours.The manager of a large emergency department believes that his new procedures have substantially reduced the wait time for the average urgent care patient. He
[EX09-150] Molds are used in the manufacture of contact lenses so that the lens material on proper preparation and curing will be consistent and meet designated dimensional criteria.Molds were fabricated and a critical dimension measured for 15 randomly selected molds. (Data have been doubly coded
A company claims that its battery lasts no less than 42.5 hours in continuous use in a specified toy. A simple random sample of batteries yields a sample mean life of 41.89 hours with a standard deviation of 4.75 hours. A computer calculates a test statistic of t1.09 and a p-value of 0.139. If
[EX09-152] Getting a college education today is almost as important as breathing and it’s expensive!It is not just the tuition, room, and board;textbooks are expensive too. It is very important for students, and their parents, to have an accurate estimate of total textbook costs. The total cost
[EX09-153] The total cost of required textbooks for nine freshman- or sophomore-level classes at 10 randomly selected New York private colleges was collected: 639.00 865.75 868.20 874.25 887.06 890.50 970.13 1013.22 1026.00 1048.96a. Construct a histogram and find the mean and standard deviation.b.
A manufacturer of television sets claims that the maintenance expenditures for its product will average no more than $50 during the first year following the expiration of the warranty. A consumer group has asked you to substantiate or discredit the claim. The results of a random sample of 50 owners
[EX09-155] In a large cherry orchard the average yield has been 4.35 tons per acre for the last several years. A new fertilizer was tested on 15 randomly selected 1-acre plots. The yields (in tons)from these plots follow: 3.56 5.00 4.88 4.93 3.92 4.25 5.12 5.13 4.79 4.45 5.35 4.81 3.48 4.45 4.72 At
[EX09-156] The water pollution readings at State Park Beach seem to be lower than that of the prior year. A sample of 12 readings (measured in coliform/100 mL) was randomly selected from the records of this year’s daily readings: 3.5 3.9 2.8 3.1 3.1 3.4 4.8 3.22.5 3.5 4.4 3.1 Does this sample
[EX09-157] It has been suggested that abnormal male children tend to occur more in children born to older-than-average parents. Case histories of 20 abnormal males were obtained, and the ages of the 20 mothers were as follows:31 21 29 28 34 45 21 41 27 31 43 21 39 38 32 28 37 28 16 39 The mean age
[EX09-158] Twenty-four oat-producing counties in the United States were randomly identified for the purpose of testing the claim, “the mean oat crop yield rate is less than 60 bushels peracre.” For each county identified, the yield rate, in bushels of oats per harvested acre, was obtained: 44.0
[EX09-159] Presented here are 100 measurements of the velocity of light in air (km/sec)recorded by Albert Michelson, an American physicist, from June 5 to July 2, 1879. The measurements have had 299,000 subtracted from them and then adjusted for corrections used by Michelson.In this form, the true
Even with a heightened awareness of beef quality, 82% of Americans indicated their recent burger-eating behavior has remained the same, according to a recent T.G.I. Friday’s restaurants random survey of 1027 Americans. In fact, half of Americans eat at least one beef burger each week.That’s a
A local auto dealership advertises that 90% of customers whose autos were serviced by their service department are pleased with the results. As a researcher, you take exception to this statement because you are aware that many people are reluctant to express dissatisfaction even if they are not
A Pew Internet & American Life Project study based on 1100 random telephone calls with children ages 12 to 17 and their parents was conducted from October 26 to November 28, 2004.The survey found that 13% of American teens do not use the Internet. The findings have a margin of sampling error of
The March 25, 2002, Newsweek article“Bringing Up Adultolescents” quoted an online survey by Monster-TRAK.com. The survey found that 60% of college students planned to live at home after graduation. How large of a sample size would you need to estimate the true proportion of students who plan on
The Kaiser Family Foundation conducted a national survey in 2003 of 17,685 seniors. The purpose of the survey was to capture detailed information about seniors’ prescription drug use, coverage, and experiences.Source: http://www.kff.org/medicare/med041905nr.cfma. If this were a random sample that
The owner of the Pizza Shack in Exercises 9.171 and 9.172 does not understand the use of the normal distribution and z in Exercise 9.172.Help the manager interpret the meaning of the results by redoing both hypothesis tests using x number of customers preferring the new crust as the test statistic
An instructor asks each of the 54 members of his class to write down “at random” one of the numbers 1, 2, 3, . . . , 13, 14, 15. Since the instructor believes that students like gambling, he considers that 7 and 11 are lucky numbers. He counts the number of students, x, who selected 7 or 11.
To test the hypothesis that the standard deviation on a standard test is 12, a sample of 40 randomly selected students was tested. The sample variance was found to be 155. Does this sample provide sufficient evidence to show that the standard deviation differs from 12 at the 0.05 level of
All tomatoes that a certain supermarket buys from growers must meet the store’s specifications of a mean diameter of 6.0 cm and a standard deviation of no more than 0.2 cm. The supermarket’s buyer visits a potential new supplier and selects a random sample of 36 tomatoes from the grower’s
The uniform length of nails is very important to a carpenter—the length of the nails being used are matched to the materials being fastened together, thereby making a small standard deviation an important property of the nails. A sample of 35 randomly selected 2-inch nails is taken from a large
[EX09-182] It is important that the force required to extract a cork from a wine bottle not have a large standard deviation. Years of production and testing indicate that the no. 9 corks in Applied Example 6.15(p. 330) have an extraction force that is normally distributed with a standard deviation
[EX09-183] A box of Corn Flakes that is labeled“NET WT. 14 OZ.” should have 14 oz or more of cereal inside. Twenty of these boxes were randomly selected and the weight of the contents(in ounces) determined. 14.52 14.47 14.80 14.60 14.45 14.25 14.15 14.12 14.36 14.39 14.50 14.29 14.28 14.60
[EX09-184] The foreman in Exercise 9.183 believes that the cereal-filling machine used for Corn Flakes needs to be replaced and that the new one he is considering will pay for the upgrade within a short time, mainly due to less variability in the fill amount. The new machine is started, and a test
The boxes of Corn Flakes in Exercises 9.183 and 9.184 that have more than 14.2 oz of cereal are being considered “too full.” Since the weights appear to be normally distributed for both fillingmachines, use the normal distribution and find the following information for the foreman.a. What
[EX09-186] Traffic gridlock is no small problem! In 2003, congestion-delayed travelers wasted 3.7 billion hours and 2.3 billion gallons of fuel for a total cost of more than $63 billion. It is estimated that half of all traffic delays are caused by car crashes. One variable often included in
a. What evidence do you have to show that the assumption of normality is reasonable?Explain.b. Estimate the mean amount of weekly exercise time for all cardiovascular technicians using a point estimate and a 95% confidence interval.c. The “Good News for Women” article in Section 9.1, “Get
a. Define the population whose amount of exercise time per week you would be interested in investigating.b. Collect the “times” from a sample of 40 members of your population.c. Find the mean and standard deviation for the amount of time exercised per week by the members of your sample.d.
Find each value:a. z(0.02)b. t(18, 0.95)c. 2(25, 0.95)
A random sample of 25 data values was selected from a normally distributed population for the purpose of estimating the population mean, . The sample statistics are n 25, x 28.6, and s 3.50.a. Find the point estimate for .b. Find the maximum error of estimate for the 0.95 confidence
Thousands of area elementary school students were recently given a nationwide standardized exam to test their composition skills. If 64 of a random sample of 100 students passed this exam, construct the 0.98 confidence interval estimate for the true proportion of all area students who passed the
State the null (Ho) and the alternative (Ha)hypotheses that would be used to test each of these claims:a. The mean weight of professional basketball players is no more than 225 lb.b. Approximately 40% of daytime students own their own car.c. The standard deviation for the monthly amounts of
Determine the level of significance, test statistic, critical region, and critical values(s)that would be used in completing each hypothesis test using the classical approach with 0.05.a. Ho : 43 vs. Ha: 43, 6b. Ho : 95 vs. Ha: 95, unknown, n 22c. Ho : p 0.80 vs. Ha: p
The automobile manufacturer of the Alero claims that the typical Alero will average 32 mpg of gasoline. An independent consumer group is somewhat skeptical of this claim and thinks the mean gas mileage is less than the 32 claimed. A sample of 24 randomly selected Aleros produced these sample
A coffee machine is supposed to dispense 6 fluid ounces of coffee into a paper cup. In reality, the amount dispensed varies from cup to cup. However, if the machine is operating properly, the standard deviation of the amounts dispensed should be 0.1 oz or less.A random sample of 15 cups produced a
An unhappy customer is frustrated with the waiting time at the post office when buying stamps. Upon registering his complaint, he was told, “You wait more than 1 minute for service no more than half of the time when you only buy stamps.” Not believing this to be the case, the customer collected
Student B says the range of a set of data may be used to obtain a crude estimate for the standard deviation of a population. Student A is not sure. How will student B correctly explain how and under what circumstances his statement is true?
Is it the null hypothesis or the alternative hypothesis that the researcher usually believes to be true? Explain.
When you reject a null hypothesis, student A says that you are expressing disbelief in the value of the parameter as claimed in the null hypothesis. Student B says that instead you are expressing the belief that the sample statistic came from a population other than the one related to the parameter
“Student’s t-distribution must be used when making inferences about the population mean, , when the population standard deviation,, is not known” is a true statement.Student A states that the z-score sometimes plays a role when the t-distribution is used.Explain the conditions that exist
Student A says that the percentage of the sample means that fall outside the critical values of the sampling distribution determined by a true null hypothesis is the pvalue for the test. Student B says that the percentage student A is describing is the level of significance. Who is correct? Explain.
Student A carries out a study in which she is willing to run a 1% risk of making a type I error. She rejects the null hypothesis and claims that her statistic is significant at the 99% level of confidence. Student B argues that student A’s claim is not properly worded. Who is correct? Explain.
Student A claims that when you employ a 95% confidence interval to determine an estimation, you do not know for sure whether or not your inference is correct (the parameter is contained within the interval). Student B claims that you do know; you have shown that the parameter cannot be less than
Student A says that the best way to improve a confidence interval estimate is to increase the level of confidence. Student B argues that using a high confidence level does not really improve the resulting interval estimate.Who is right? Explain.
Make up a set of three or more ordered pairs such that:a. r 0.0c. r1.0b. r1.0d. b1 0.0
The linear correlation coefficient, r, is a numerical value that ranges from 1.0 to 1.0.Write a sentence or two describing the meaning of r for each of these values:a. 0.93d. 0.08b. 0.89e. 2.3c. 0.03
Student A collected a set of bivariate data and calculated r, the linear correlation coefficient.Its value was 1.78. Student A proclaimed that there was no correlation between the two variables because the value of r was not between 1.0 and 1.0. Student B argued that 1.78 was impossible and
A test was administered to measure the mathematics ability of the people in a certain town. Some of the townspeople were surprised to find out that their test results and their shoe sizes correlated strongly. Explain why a strong positive correlation should not have been a surprise.
For the bivariate data, the extensions, and the totals shown on the table, find the following:a. SS(x)b. SS(y)c. SS(xy)d. The linear correlation coefficient, re. The slope, b1f. The y-intercept, b0 g. The equation of the line of best fit x y x 2 xy y 2 2 6 4 12 36 3 5 9 15 25 3 7 9 21 49 4 7 16 28
A research group reports a 2.3 correlation coefficient for two variables. What can you conclude from this information?
a. The situation described in Exercise 3.105 only occurred with the Minnesota Timberwolves during the 2003–2004 regular season. Use the Internet(search by the team name) to obtain the season team statistics for your favorite professional or intercollegiate basketball team, or see the coach of a
[EX03-001]Minnesota Timberwolves, 2003–2004 Regular Season Personal Fouls Points per Personal Fouls Points per Player per Game Game Player per Game Game Garnett 2.5 24.2 Madsen 2.4 3.6 Cassell 3 19.8 Martin 1.4 3.4 Sprewell 1.2 16.8 McLeod 1.2 2.7 Szczerbiak 1.5 10.2 Goldwire 1.0 2.6 Hudson 1.1
a. Verify, algebraically, that formula (3.2)for calculating r is equivalent to the definition formula (3.1).b. Verify, algebraically, that formula (3.6)is equivalent to formula (3.5).
[EX03-102] Yellowstone National Park’s Old Faithful has been a major tourist attraction for a long time. Understanding the duration of eruptions and the time between eruptions is necessary to predict the timing of the next eruption. The Old Faithful data set variables are as follows: date: an
[EX03-101] Cicadas are flying, plant-eating insects. One particular species, 13-year cicadas(Magicicada), spends five juvenile stages in underground burrows. During the 13 years underground, the cicadas grow from approximately the size of a small ant to nearly the size of an adult cicada.Every 13
[EX03-100] Relatively few business travelers use mass transit systems when visiting large cities. The payoff could be substantial—both in time and money—if they learned how to use the systems, as noted in the December 28, 2004, USA Today article “Mass transit could save business travelers big
[EX03-99] Sugar cane growers are interested in the relationship between the acres of crop harvested and the total sugar cane production(tons) of those acres. The data listed here are for the 2001 crop from 14 randomly selected sugar cane–producing counties in Louisiana.Acres Production Acres

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