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Elementary Statistics 11th Edition Robert R. Johnson, Patricia J. Kuby - Solutions
Consider the null hypothesis in Applied Example 8.11, “Ho: Teaching techniques have no significant effect on students’ exam scores.” Describe the actions that would result in a correct decision type A and correct decision type B if Ho were tested.
a. If the null hypothesis is true, what decision error could be made? b. If the null hypothesis is false, what decision error could be made? c. If the decision “reject Ho” is made, what decision error could have been made? d. If the decision “fail to reject Ho” is made, what decision
In each diagram below, I and II represent sampling distributions of two statistics that might be used to estimate a parameter. In each case, identify the statistic that you think would be the better estimator, or neither, and describe why it is your choice.
a. If a is assigned the value 0.001, what are we saying about the type I error? b. If a is assigned the value 0.05, what are we saying about the type I error? c. If a is assigned the value 0.10, what are we saying about the type I error?
a. If b is assigned the value 0.001, what are we saying about the type II error? b. If b is assigned the value 0.05, what are we saying about the type II error? c. If b is assigned the value 0.10, what are we saying about the type II error?
The conclusion is the part of the hypothesis test that communicates the findings of the test to the reader. As such, it needs special attention so that the reader receives an accurate picture of the findings. a. Carefully describe the “attitude” of the statistician and the statement of the
Suppose that there are two statistics that will serve as an estimator for the same parameter. One of them is biased, and the other is unbiased. a. Everything else being equal, explain why you usually would prefer an unbiased estimator to a biased estimator. b. If a statistic is unbiased, does
Find the power of a test when the probability of the type II error is: a. 0.01 b. 0.05 c. 0.10
a. Find a, the probability of the type I error.b. Find b, the probability of the type II error.
Suppose the argument in Exercise 8.81 was to be settled using a sample of size 4; find a and b.
You are a quality-control inspector and are in a position to make the decision as to whether a large shipment of cork stoppers for use in bottling still (versus bubbly) wine passes inspection. Once you inspect the mandatory number in the approved manner, you will make a decision to accept or reject
As the quality-control inspector in Exercise 8.83, you are ready for the second phase of the inspection. Listed are three different samples, each taken from different lots. Review the sample results and answer these questions for each sample separately.a. Construct a dotplot of the data. b.
State the null and alternative hypotheses used to test each of the following claims. a. The mean reaction time is greater than 1.25 seconds. b. The mean score on that qualifying exam is less than 335. c. The mean selling price of homes in the area is not $230,000. d. The mean weight of college
State the null hypothesis Ho and the alternative hypothesis Ha that would be used for a hypothesis test related to each of the following statements: a. The mean age of the students enrolled in evening classes at a certain college is greater than 26 years. b. The mean weight of packages shipped on
Identify the four possible outcomes and describe the situation involved with each with regard to the aircraft manufacturer’s testing and buying of rivets. Which is the more serious error: the type I or type II error? Explain.
A manufacturer wishes to test the hypothesis that “by changing the formula of its toothpaste, it will give its users improved protection.”The null hypothesis represents the idea that “the change will not improve the protection,” and the alternative hypothesis is “the change will improve
Suppose we want to test the hypothesis that the mean hourly charge for automobile repairs is at least $60 per hour at the repair shops in a nearby city. Explain the conditions that would exist if we make an error in decision by committing a type I error. What about a type II error?
Assume that z is the test statistic and calculate the value of z_ for each of the following:
Assume that z is the test statistic and calculate the value of z_ for each of the following:c. Ho: m = 138.5, s = 3.7, n = 14, x = 142.93 d. Ho: m = 815, s = 43.3, n = 60, x = 799.6
There are only two possible decisions that can result from a hypothesis test. a. State the two possible decisions. b. Describe the conditions that will lead to each of the two decisions identified in part a.
For each of the following pairs of values, state the decision that will occur and why. a. p-value = 0.014, a = 0.02 b. p-value = 0.118, a = 0.05 c. p-value = 0.048, a = 0.05 d. p-value = 0.064, a = 0.10
For each of the following pairs of values, state the decision that will occur and why. a. p-value = 0.018, a = 0.01 b. p-value = 0.033, a = 0.05 c. p-value = 0.078, a = 0.05 d. p-value = 0.235, a = 0.10
A random sample of 81 female American college students were each issued a stopwatch and asked to time themselves as they prepared to attend class on the following Thursday morning. The instructions were to start the watch as soon as their feet touched the floor as they got up and to turn it off as
Using the notation of Exercise 9.8, name and find the following critical values of t:
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.
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), Table 2 in Appendix B provides the probabilities for each value of x separately, thereby making it unnecessary to estimate probabilities of
Use Table 2 in Appendix B to determine the critical region used in testing each of the following hypotheses. a. Ho: p = 0.5 and Ha: p > 0.5 where n = 15 and a = 0.05 b. Ho: p = 0.5 and Ha: p ≠ 0.3 where n = 14 and a = 0.05 c. Ho: p = 0.4 and Ha: p < 0.4, where n = 10 and a = 0.05 d. Ho: p =
You are testing the hypothesis and have decided to reject this hypothesis if after 15 trials you observe 14 or more successes. a. If the null hypothesis is true and you observe 13 successes, which of the following will you do? (1) Correctly fail to reject Ho. (2) Correctly reject Ho. (3) Commit a
You are testing the null hypothesis p = 0.4 and will reject this hypothesis if z_ is less than _2.05. a. If the null hypothesis is true and you observe z equal to - 2.12 which of the following will you do? (1) Correctly fail to reject Ho. (2) Correctly reject Ho. (3) Commit a type I error. (4)
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, does it have sufficient reason to support
The full-time student body of a college is composed of 50% males and 50% females. Does a random sample of students (30 male, 20 female) from an introductory chemistry course show sufficient evidence to reject the hypothesis that the proportion of male and of female students who take this course is
A politician claims that she will receive 60% of the vote in an upcoming election. The results of a properly designed random sample of 100 voters showed that 50 of those sampled will vote for her. Is it likely that her assertion is correct at the 0.05 level of significance? a. Solve using the
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 watercraft accidents reported to the Game and Parks Commission in the state of Nebraska revealed that 85% of them involved PWCs
An April 21, 2009, USA Today article titled “On road, it’s do as I say, not as I do” reported that 58% of U.S. adults speed up to beat a yellow light. Suppose you conduct a survey in your hometown of 150 randomly selected adults and find that 71 out of the 150 admit to speeding up to beat a
Find the values of t that bound the middle 0.95 of the distribution for df = 12.
A recent survey conducted by Lieberman Research Worldwide and Charles Schwab reported that the “High Cost of Living” was the top concern that most surprised young adults as they began life on their own. Twenty-six percent reported “High Cost of Living” as their top concern. A disbeliever of
September is Library Card Sign-up Month. According to a nationwide Harris Poll during August 2008, 68% of American adults own a library card. Suppose you conduct a survey of 1000 randomly chosen adults in order to test Ho: p = 0.68 versus Ha: p < 0.68 where p represents the proportion of adults
Show that the hypothesis test completed as Example 9.13 was unnecessary because the confidence interval had already been completed in Example 9.8.
The following computer output was used to complete a hypothesis test. a. State the null and alternative hypotheses. b. If the test is completed using a = 0.05 what decision and conclusion are reached? c. Verify the “Sample p.”
Using the computer output and information in Exercise 9.113, determine the value of the following: a. Hypothesized value of population proportion b. Sample proportion c. Test statistic
Reliable Equipment has developed a machine, The Flipper, that will flip a coin with predictable results. They claim that a coin flipped by The Flipper will land heads up at least 88% of the time. What conclusion would result in a hypothesis test, using a = 0.05 when 200 coins are flipped and the
Refer to Applied Example 9.14. a. State the Polish statisticians’ hypothesis. b. Is their hypothesis the null or alternative hypothesis? Explain. c. State the null hypothesis. State the alternative hypothesis. d. Explain the meaning of, “6.2 percent on either side of 50 percent.” e. What
a. Calculate the standard deviation for each set.b. 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?
Find: a. x2(10, 0.01) b. x2(12, 0.025) c. x2(10, 0.95) d. x2(22, 0.995)
Find the values of t that bound the middle 0.80 of the distribution for df = 26
Find these critical values by using Table 8 of Appendix B. a. x2(18, 0.01) b. x2(16, 0.025) c. x2(8, 0.10) d. x2(28, 0.01) e. x2(22, 0.95) f. x2(10, 0.975) g. x2(50, 0.90) h. x2(24, 0.99)
Using the notation of Exercise 9.120, name and find the critical values of x2.
Using the notation of Exercise9.120, name and find the critical values of x2.
a. What value of chi-square for 5 degrees of freedom subdivides the area under the distribution curve such that 5% is to the right and 95% is to the left? b. What is the value of the 95th percentile for the chi-square distribution with 5 degrees of freedom? c. What is the value of the 90th
a. The central 90% of the chi-square distribution with 11 degrees of freedom lies between what values? b. The central 95% of the chi-square distribution with 11 degrees of freedom lies between what values? c. The central 99% of the chi-square distribution with 11 degrees of freedom lies between
Use a computer or calculator to find the area (a) to the left, and (b) to the right of x2 = 20.2 with df = 15
Use a computer or calculator to find the area (a) to the left, and (b) to the right of x2 = 14.7 with df = 24
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test these claims: a. The standard deviation has increased from its previous value of 24. b. The standard deviation is no larger than 0.5 oz. c. The standard deviation is not equal to 10. d. The variance is
a. Find the first percentile of Student’s t-distribution with 24 degrees of freedom. b. Find the 95th percentile of Student’s t-distribution with 24 degrees of freedom. c. Find the first quartile of Student’s t-distribution with 24 degrees of freedom.
State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test these claims: a. The variance has decreased from 34.5. b. The standard deviation of shoe size is more than 0.32. c. The standard deviation is at least 5.5. d. The variance is at most 35. e. The
Find the test statistic for the hypothesis test: a. Ho: s2 = 532 versus Ha: σ 2 > 532 using sample information n = 18 and s2 = 785 b. Ho: s2 = 52 versus. Ha: σ 2 ≠ 52 using sample information n = 41 and s2 = 78.2
Calculate the value for the test statistic, x2_, for each of these situations:
Calculate the p-value for each of the following hypothesis tests.
Determine the critical region and critical value(s) that would be used to test the following using the classical approach:
Complete the hypothesis test in Exercise 9.131a using the following: a. The p-value method and a = 0.01 b. The classical method and a = 0.01
Complete the hypothesis test in Exercise 9.131b using the following: a. The p-value method and a = 0.05 b. The classical method and a = 0.05
In the past the standard deviation of weights of certain 32.0-oz packages filled by a machine was 0.25 oz. A random sample of 20 packages showed a standard deviation of 0.35 oz. Is the apparent increase in variability significant at the 0.10 level of significance? Assume package weight is normally
Variation in the life of a battery is expected, but too much variation would be of concern to the consumer, who would never know if the purchased battery might have a very short life. A random sample of 30 AA batteries of a particular brand produced a standard deviation of 350 hours. If a standard
A random sample of 51 observations was selected from a normally distributed population. The sample mean was x = 98.2 and the sample variance was s2 = 37.5 Does this sample show sufficient reason to conclude that the population standard deviation is not equal to 8 at the 0.05 level of significance?
Find the percent of the Student’s t-distribution that lies between the following values: a. df = 12 and t ranges from - 1.36 to 2.68 b. df = 15 and t ranges from - 1.75 to 2.95
A commercial farmer harvests his entire field of a vegetable crop at one time. Therefore, he would like to plant a variety of green beans that mature all at one time (small standard deviation between maturity times of individual plants). A seed company has developed a new hybrid strain of green
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 the property is actually worth. For example, the average value of ranchland in Missouri was $548 per
Using the computer output in Exercise 9.141, determine the values of the following terms: a. Hypothesized value of population standard deviation b. Sample standard deviation c. Degrees of freedom—how were they calculated? d. Relationship between sample variance and standard deviation e. Test
Maybe even more important than how much they weigh is 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 randomly selected and their
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. Use a =
Refer to Applied Example 9.20, “Ceramic Floor Tile,” on page 461. First you need to complete a preliminary investigation of the 26 randomly selected surface heights: a. Present and describe the sample of surface heights using a histogram, the mean, and the standard deviation. b. Check the
Refer to Applied Example 9.20, “Ceramic Floor Tile,” and Exercise 9.145 to continue the investigation of the floor tile manufacturing process. a. What are the assumptions for a chi-square test of standard deviation? Do any of the answers in Exercise 9.145 help resolve the assumption
The dry weight of a cork is another quality that does not affect the ability of the cork to seal a 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 corks were
Use a computer or calculator to find the p-value for the following hypothesis test: Ho: s2 = 7 versus Ha: s2 = 7 if x2 = 6.87 for a sample of n = 15
Use a computer or calculator to find the p-value for the following hypothesis test: Ho: s = 12.4 versus Ha: s_12.4, if x2 = 36.59 for a sample of n = 24.
The chi-square distribution was described on page 454 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
How important is the assumption "the sampled population is normally distributed" for the use of the chi-square distributions? Use a computer and the two sets of MINITAB commands that can be found in the Student Solutions Manual to simulate drawing 200 samples of size 10 from each of two different
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 the large emergency department believes that his new procedures have substantially reduced the wait time for the average urgent care patient. He
A natural gas utility is considering a contract for purchasing tires for its fleet of service trucks. The decision will be based on expected mileage. For a sample of 100 tires tested, the mean mileage was 36,000 and the standard deviation was 2000 miles. Estimate the mean mileage that the utility
One of the objectives of a large medical study was to estimate the mean physician fee for cataract removal. For 25 randomly selected cases, the mean fee was found to be $3550 with a standard deviation of $275. Set a 99% confidence interval on m, the mean fee for all physicians. Assume fees are
Oranges are selected at random from a large shipment that just arrived. The sample is taken to estimate the size (circumference, in inches) of the oranges. The sample data are summarized as follows: n = 100 ∑x = 878.2, and ∑(x - x)2 = 49.91 a. Determine the sample mean and standard deviation.
Molds are used in the manufacture of contact lenses so that the lens material for 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 to ensure
Getting a college education today is almost as important as breathing and its 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 of
The total cost of required textbooks for nine freshman- or sophomore-level classes at 10 randomly selected New York private colleges was collected:a. Construct a histogram and find the mean and standard deviation. b. Demonstrate how this set of data satisfies the assumptions for inference. c.
A manufacturer of television sets claims that the maintenance expenditures for its product will average no more than $110 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
What would be a good state for you to live in if you like extreme temperatures? If you like a moderate climate? Explain why your preferred area has the weather patterns it has.
The water pollution readings at State Park Beach seem to be lower than those of the prior year. A sample of 12 readings (measured in coliform/100 mL) was randomly selected from the records of this years daily readings:Does this sample provide sufficient evidence to conclude that the
It has been suggested that abnormal male children tend to be born to older-than-average parents. Case histories of 20 abnormal males were obtained, and the ages of the 20 mothers were as follows:The mean age at which mothers in the general population give birth is 28.0 years. a. Calculate the
Twenty-four oat-producing counties were randomly identified from across Minnesota for the purpose of testing the claim The mean oat crop yield rate is greater than 60 bushels per acre. For each county identified, the yield rate, in bushels of oats per harvested acre, was
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 were 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
The marketing research department of an instant coffee company conducted a survey of married men to determine the proportion of married men who prefer their brand. Of the 100 men in the random sample, 20 prefer the company’s brand. Use a 95% confidence interval to estimate the proportion of all
A company is drafting an advertising campaign that will involve endorsements by noted athletes. For the campaign to succeed, the endorser must be both highly respected and easily recognized. A random sample of 100 prospective customers is shown photos of various athletes. If the customer recognizes
A local auto dealership advertises that 90% of customers whose autos were serviced by the 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. A research experiment was
Use a computer or calculator to find the area to the left of t = - 2.12 with df = 18 Draw a sketch showing the question with the answer.
According to a nationwide study by the U.S. Department of Education that was mentioned in “Beating bullies without a fight,” an article in the September 22 2009, Democrat and Chronicle, 79% of children between the ages of 12 and 18 were bullied at least once in the past six months. You wish to
The May 30, 2008, online article “Live with Your Parents After Graduation?” quoted a 2007 survey conducted by Monster-TRAK.com. The survey found that 48% 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
The chief executive officer (CEO) of a small business wishes to hire your consulting firm to conduct a simple random sample of its customers. She wants to determine the proportion of her customers who consider her company the primary source of their products. She requests the margin of error in the
In obtaining the sample size to estimate a proportion, the formula n = [z(a/2)]2 pq/E2 is used. If a reasonable estimate of p is not available, it is suggested that p = 0.5 be used because this will give the maximum value for n. Calculate the value of pq = p(1 = p) for p = 0.1, 0.2, 0.3,. , 0.8,
A machine is considered to be operating in an acceptable manner if it produces 0.5% or fewer defective parts. It is not performing in an acceptable manner if more than 0.5% of its production is defective. The hypothesis Ho: p = 0.005 is tested against the hypothesis Ha: p > 0.005 by taking a random
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