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elementary statistics

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

The heights of the kindergarten children mentioned in Example 7.6 (p. 379) are approximately normally distributed with 39 and 2.a. If an individual kindergarten child is selected at random, what is the probability that he or she has a height between 38 and 40 inches?b. A classroom of 30 of
WageWeb (http://www.wageweb.com/health1.htm) is a service of HRPDI and provides compensation information on more than 170 benchmark positions in human resources. The October 2003 posting indicated that labor relation managers earn a mean annual salary of $86,700. Assume that annual salaries are
Based on 53 years of data compiled by the National Climatic Data Center (http://lwf.ncdc.noaa.gov/oa/climate/online/ccd/avgwind.html), the average speed of winds in Honolulu, Hawaii, equals 11.3 mph, as of June 2004. Assume that wind speeds are approximately normally distributed with a standard
TIMSS 2003 (Trends in International Mathematics and Science Study) focused on the mathematics and science achievement of eighth-graders throughout the world. A total of 45 countries (including the United States) participated in the study. The mean math exam score for U.S. students was 504 with a
According to the June 2004 Readers’ Digest article“Only in America,” the average amount that a 17-year-old spends on his or her high school prom is $638. Assume that the amounts spent are normally distributed with a standard deviation of$175.a. Find the probability that the mean cost to
WageWeb (http://www.wageweb.com/health1.htm) provides compensation information and services on more than 160 positions. As of October 1, 2003, the national average salary for a registered nurse (RN) was $47,858. Suppose the standard deviation is $7750.a. Find the probability that the mean of a
Referring to Example 7.6 (p. 379), what height would bound the lower 25% of all samples of size 25?
a. Find P(4 x 6) for a random sample of size 4 drawn from a normal population with 5 and 2.b. Use a computer to randomly generate 100 samples, each of size 4, from a normal probability distribution with 5 and 2. Calculate the mean, x, for each sample.c. How many of the sample
a. Find P(46 x 55) for a random sample size 16 drawn from a normal population with mean 50 and standard deviation 10.b. Use a computer to randomly generate 200 samples, each of size 16, from a normal probability distribution with mean 50 and standard deviation 10.Calculate the
Consider a normal population with 24.7 and 4.5.a. Calculate the z-score for an x of 21.5.b. Calculate the z-score for an x of 21.5 from a sample of size 25.c. Explain how 21.5 can have such different z-scores.
The Dean of Nursing tells students being recruited for the incoming class that 1 year after graduation, the university’s graduates can expect to be earning a mean weekly income of $675. Assume that the dean’s statement is true and that the weekly salaries 1 year after graduation are normally
The diameters of Red Delicious apples in a certain orchard are normally distributed with a mean of 2.63 inches and a standard deviation of 0.25 inch.a. What percentage of the apples in this orchard have diameters less than 2.25 inches?b. What percentage of the apples in this orchard are larger than
a. Find a value for e such that 95% of the apples in Exercise 7.50 are within e units of the mean, 2.63. That is, find e such that P(2.63 e x 2.63 e) 0.95.b. Find a value for E such that 95% of the samples of 100 apples taken from the orchard in Exercise 7.50 will have mean values within E
Americans spend billions of dollars on veterinary care each year, predicted to hit $31 billion this year. The health care services offered to animals rival those provided to humans, with the typical surgery costing from $1700 to $3000, or even more. In 2003, on average, dog owners spent $196 on
A study from the University of Michigan, as noted in Newsweek (March 25, 2002), stated that men average 16 hours of housework each week(up from an average of 12 hours in 1965). If we assume that the number of hours in which men engage in housework each week is normally distributed with a standard
An April 15, 2002, report in Time magazine stated that the average age for women to marry in the United States is now 25 years of age. If the standard deviation is assumed to be 3.2 years, find the probability that a random sample of 40 U.S.women would show a mean age at marriage of less than or
A tire manufacturer claims (based on years of experience with its tires) that the mean mileage is 35,000 miles and the standard deviation is 5000 miles. A consumer agency randomly selects 100 of these tires and finds a sample mean of 31,000.Should the consumer agency doubt the manufacturer’s
Let’s simulate the sampling distribution related to the disc jockey’s concern for “length of cut” in Exercise 7.62.a. Use a computer to randomly generate 50 samples, each of size 10, from a normal distribution with mean 135 and standard deviation 10.Find the “sample total” and the
a. Find the mean and standard deviation of x for a binomial probability distribution with n 16 and p 0.5.b. Use a computer to construct the probability distribution and histogram for the binomial probability experiment with n 16 and p 0.5.c. Use a computer to randomly generate 200 samples
a. Find the mean and standard deviation of x for a binomial probability distribution with n 200 and p 0.3.b. Use a computer to construct the probability distribution and histogram for the random variable x of the binomial probability experiment with n 200 and p 0.3.c. Use a computer to
A second sample of 100 ages as been collected from the U.S. 2000 census and is listed here.[EX07-67]14 6 59 64 39 12 8 34 27 4 16 18 17 33 56 60 65 73 53 43 26 42 60 87 58 42 82 21 35 64 58 53 36 66 63 66 39 62 58 49 31 27 39 35 12 28 28 20 3 54 41 41 63 39 37 23 79 43 28 17 12 45 52 10 11 32 32 23
Skillbuilder Applet Exercise simulates taking samples of size 50 from the population of American ages from the 2000 census, where 36.5 and 22.5 and the shape is skewed right.a. Click “1” for “# Samples.” Note the 50 data values and their mean. Change “slow” to “batch”and take at
The lengths of the lake trout in Conesus Lake are believed to have a normal distribution with a mean of 15.6 inches and a standard deviation of 3.8 inches.a. Kevin is going fishing at Conesus Lake tomorrow. If he catches one lake trout, what is the probability that it is less than 15.0 inches
Cigarette lighters manufactured by EasyVice Company are claimed to have a mean lifetime of 20 months with a standard deviation of 6 months. The money-back guarantee allows you to return the lighter if it does not last at least 12 months from the date of purchase.a. If the lifetimes of these
Aluminum rivets produced by Rivets Forever, Inc., are believed to have shearing strengths that are distributed about a mean of 13.75 with a standard deviation of 2.4. If this information is true and a sample of 64 such rivets is tested for shear strength, what is the probability that the mean
“Two heads are better than one.” If that’s true, then how good would several heads be? To find out, a statistics instructor drew a line across the chalkboard and asked her class to estimate its length to the nearest inch. She collected their estimates, which ranged from 33 to 61 inches, and
The sampling distribution of sample means is more than just a distribution of the mean values that occur from many repeated samples taken from the same population. Describe what other specific condition must be met in order to have a sampling distribution of sample means.
Student A states, “A sampling distribution of the standard deviations tells you how the standard deviation varies from sample to sample.” Student B argues, “A population distribution tells you that.” Who is right?Justify your answer.
Student A says it is the “size of each sample used” and Student B says it is the “number of samples used” that determines the spread of an empirical sampling distribution. Who is right? Justify your choice.
1.a. Construct the theoretical probability distribution for the drawing of a single number, with replacement, from this population.b. Draw a histogram of this probability distribution.c. Calculate the mean, , and the standard deviation, , for this population.
[EX08-001]a. What population was sampled to obtain the height data listed in Section 8.1?b. Describe the sample data using the mean and standard deviation, plus any other statistics that help describe the sample. Construct a histogram and comment on the shape of the distribution.
a. How is the distribution of the sample height data in Section 8.1 related to the distribution of the population and the sampling distribution of sample means?b. Using the techniques in Chapter 7, find the limits that would bound the middle 90% of the sampling distribution of sample means for
[EX08-005] A random sample of the amount paid (in dollars) for taxi fare from downtown to the airport was obtained:15 19 17 23 21 17 16 18 12 18 20 22 15 18 20 Use the data to find a point estimate for each of the following parameters.a. Meanb. Variancec. Standard deviation
[EX08-006] The number of engines owned per fire department was obtained from a random sample taken from the profiles of fire departments from across the United States (Firehouse/June 2003).29 8 7 33 21 26 6 11 4 54 7 4 Use the data to find a point estimate for each of the following parameters:a.
In each diagram at the bottom of the page, 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 and describe why it is your choice. . b. A A A
The use of a tremendously large sample does not solve the question of quality for an estimator.What problems do you anticipate with very large samples?
Explain why the standard error of sample means is 3 for the rivet example on page 399.
Find the level of confidence assigned to an interval estimate of the mean formed using the following intervals:a. x 1.28 x to x 1.28 xb. x 1.44 x to x 1.44 xc. x 1.96 x to x 1.96 xd. x 2.33 x to x 2.33 x
Find the level of confidence assigned to an interval estimate of the mean formed using the following intervals:a. x 1.15 x to x 1.15 xb. x 1.65 x to x 1.65 xc. x 2.17 x to x 2.17 xd. x 2.58 x to x 2.58 x
A stamp dealer wishes to purchase a stamp collection that is believed to contain approximately 7000 individual stamps and approximately 4000 first-day covers. Devise a plan that might be used to estimate the collection’s worth.
Using the Old Faithful eruption information in Applied Example 8.1 on page 400:a. What does “11:27 AM / 10 min.” mean? Explain.b. Did this eruption occur during the predicted time interval?c. What does “90% of the time” mean? Explain.
Discuss the conditions that must exist before we can estimate the population mean using the interval techniques of formula (8.1).
Determine the value of the confidence coefficient z(/2) for each situation described:a. 1 0.90b. 1 0.95
Determine the level of the confidence given the confidence coefficient z(/2) for each situation:a. z(/2) 1.645b. z(/2) 1.96c. z(/2) 2.575d. z(/2) 2.05
Given the information, the sampled population is normally distributed, n 16, x 28.7, and 6:a. Find the 0.95 confidence interval for .b. Are the assumptions satisfied? Explain.
Given the information, the sampled population is normally distributed, n 55, x 78.2, and 12:a. Find the 0.98 confidence interval for .b. Are the assumptions satisfied? Explain.
Given the information, n 86, x 128.5, and 16.4:a. Find the 0.90 confidence interval for .b. Are the assumptions satisfied? Explain.
Given the information, n 22, x 72.3, and 6.4:a. Find the 0.99 confidence interval for .b. Are the assumptions satisfied? Explain.
In your own words, describe the relationship between the following:a. Sample mean and point estimateb. Sample size, sample standard deviation, and standard errorc. Standard error and maximum error
In your own words, describe the relationship between the point estimate, the level of confidence, the maximum error, and the confidence interval.
Skillbuilder Applet Exercise demonstrates the effect that the level of confidence (1 )has on the width of a confidence interval. Consider sampling from a population where 300 and 80.a. Set the slider for level of confidence to 68%.Click “sample!” to construct one 68% confidence interval.
A machine produces parts with lengths that are normally distributed with 0.5. A sample of 10 parts has a mean length of 75.92.a. Find the point estimate for .b. Find the 98% confidence maximum error of estimate for .c. Find the 98% confidence interval for .
The Eurostar was Europe’s first international train, designed to take advantage of the Channel Tunnel that connects England with Continental Europe. It carries nearly 800 passengers and occasionally reaches a peak speed of more than 190 mph(http://www.o-keating.com/hsr/eurostar.htm). Assume the
In 2003, the Trends International Mathematics and Science Study (TIMSS) examined eighthgraders’proficiency in math and science. The mean mathematics scale score for the sample of eighthgrade students in the United States was 504, with a standard error of 8.4. Construct a 95% confidence interval
About 67% of married adults say they consult with their spouse before spending $352, the average of the amount that married adults say they consult with each other before spending.Source: Yankelovich Partner for Lutheran Brotherhooda. Based on the preceding information, what can you conclude about
[EX08-039] A certain adjustment to a machine will change the length of the parts it makes but will not affect the standard deviation. The length of the parts is normally distributed, and the standard deviation is 0.5 mm. After an adjustment is made, a random sample is taken to determine the mean
[EX08-040] The atomic weight of a reference sample of silver was measured at the National Institute of Standards and Technology (NIST) using two nearly identical mass spectrometers. This project was undertaken in conjunction with the redetermination of the Faraday constant. Following are 48
[EX08-041] The force required to extract a cork from a wine bottle is an important property of the cork. If the force is too little, the cork probably is not a good protector of the wine inside. If the force is too great, it will be difficult to remove. Neither is desirable. The no. 9 corks in
“College costs spike again” (October 19, 2005), an article that appeared on the CNN Money website, gave the latest figures from the College Board on annual tuition, fees, and room and board. The average total figure for private colleges is $27,516 and $11,354 for public colleges.Source:
“Rockies’ snow melt produces less water”(Applied Example 8.5) lists “14.36 inches” and“5.07 inches” as statistics and uses them as point estimates. Describe why these numbers are statistics and why they are also point estimates.
Using a computer or calculator, randomly select a sample of 40 single-digit numbers and find the 90% confidence interval for . Repeat several times, observing whether or not 4.5 is in the interval each time. Refer to Example 8.4, page 407. Describe your results.FYI Use commands for generating
The image of the public library is constantly changing, and their online services continue to grow. Usage of the library’s home page grew by 17% during the past 12 months. It has been estimated that the current average length of a visit to the library’s home page is approximately 20 minutes.The
You are testing a new detonating system for explosives and are concerned that the system is not reliable. State the null and alternative hypotheses.
Referring to Applied Example 8.11, state the instructor’s hypothesis, the alternative hypothesis.
Using the example of your friend’s party(pp. 417 and 422) with Ho: “Party will be a dud”versus Ha: “The party will be a great time,” describe the four possible decisions and the resulting actions as described in Example 8.12.
Using the information from Exercise 8.55, describe how the type II error in the party example represents a “lost opportunity.”
Describe the action that would result in a correct decision type A and a correct decision type B if each of the null hypotheses in Exercise 8.60 were tested.
The director of an advertising agency is concerned with the effectiveness of a television commercial.a. What null hypothesis is she testing if she commits a type I error when she erroneously says that the commercial is effective?b. What null hypothesis is she testing if she commits a type II error
The director of an advertising agency is concerned with the effectiveness of a television commercial.a. What null hypothesis is she testing if she makes a correct decision type A when she correctly says that the commercial is not effective?b. What null hypothesis is she testing if she makes a
A politician is concerned with winning an upcoming election.a. What null hypothesis is he testing if he commits a type I error when he erroneously says that he will win the election?b. What null hypothesis is he testing if he commits a type II error when he erroneously says that he will win the
a. If the null hypothesis is true, the probability of a decision error is identified by what name?b. If the null hypothesis is false, the probability of a decision error is identified by what name?
Suppose that a hypothesis test is to be carried out by using 0.05. What is the probability of committing a type I error?
Explain why is not always the probability of rejecting the null hypothesis.
Explain how assigning a small probability to an error controls the likelihood of its occurrence.
A normally distributed population is known to have a standard deviation of 5, but its mean is in question. It has been argued to be either 80 or 90, and the following hypothesis test has been devised to settle the argument. The null hypothesis, Ho: 80, will be tested using one randomly
Suppose the argument in Exercise 8.77 was to be settled using a sample of size 4; find and.
[EX08-079] 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
[EX08-080] As the quality-control inspector in Exercise 8.79 you are ready for the second phase of the inspection.Part 2 requires that the humidity percentage of 20 cork stoppers be determined while following the prescribed procedure.Specification Limits Nominal value: 6%Limits of specification:
In the example starting on page 427, the aircraft builder who is buying the rivets is concerned that the rivets might not meet the mean-strength spec. State the aircraft manufacturer’s null and alternative hypotheses.
Professor Hart does not believe a statement he heard: “The mean weight of college women is 54.4 kg.” State the null and alternative hypotheses he would use to challenge this statement.
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 football
Describe how the null hypothesis, as stated in Example 8.14 (p. 429), is a “starting point” for the decision to be made about the drying time for paint made with the new formula.
Assume that z is the test statistic and calculate the value of z for each of the following:a. Ho: 10, 3, n 40, x 10.6b. Ho: 120, 23, n 25, x 126.2c. Ho: 18.2, 3.7, n 140, x 18.93d. Ho: 81, 13.3, n 50, x 79.6
Assume that z is the test statistic and calculate the value of z for each of the following:a. Ho: 51, 4.5, n 40, x 49.6b. Ho: 20, 4.3, n 75, x 21.2c. Ho: 138.5, 3.7, n 14, x 142.93d. Ho: 815, 43.3, n 60, x 799.6
a. What decision is reached when the pvalue is greater than ?b. What decision is reached when is greater than the p-value?
For each of the following pairs of values, state the decision that will occur and why.a. p-value 0.014, 0.02b. p-value 0.118, 0.05c. p-value 0.048, 0.05d. p-value 0.064, 0.10
For each of the following pairs of values, state the decision that will occur and why.a. p-value 0.018, 0.01b. p-value 0.033, 0.05c. p-value 0.078, 0.05d. p-value 0.235, 0.10
The calculated p-value for a hypothesis test is 0.084. What decision about the null hypothesis would occur in the following:a. The hypothesis test is completed at the 0.05 level of significance.b. The hypothesis test is completed at the 0.10 level of significance.
a. A one-tailed hypothesis test is to be completed at the 0.05 level of significance.What calculated values of p will cause a rejection of Ho?b. A two-tailed hypothesis test is to be completed at the 0.02 level of significance.What calculated values of p will cause a“fail to reject Ho” decision?
Skillbuilder Applet Exercise estimates the pvalue for a one-tailed hypothesis test by simulating the taking of many samples.The given hypothesis test is for an Ho: 1500 versus Ha: 1500. Asample of 24 has been taken and the sample mean is 1451.a. Click “10” for “# of samples.” Note the
Skillbuilder Applet Exercise estimates the pvalue for a two-tailed hypothesis test by simulating the taking of many samples.The given hypothesis test is for Ho: 4 versus Ha: ≠ 4. A sample of 100 has been taken and the sample mean is 3.6.a. Click “10” for “# of samples.” Note the sample
Describe in your own words what the p-value measures.
a. Calculate the p-value, given Ha: 45 and z 2.3.b. Calculate the p-value, given Ha: 58 and z 1.8.
Calculate the p-value, given Ha: ≠ 245 and z 1.1.
Find the test statistic z and the p-value for each of the following situations.a. Ho: 22.5, Ha: 22.5; x 24.5, 6, n 36b. Ho: 200, Ha: 200; x 192.5, 40, n 50c. Ho: 12.4, Ha: ≠ 2.4; x 11.52, 2.2, n 16
Calculate the p-value for each of the following:a. Ho: 10, Ha: 10, z 1.48b. Ho: 105, Ha: 105, z 0.85c. Ho: 13.4, Ha: ≠ 13.4, z 1.17d. Ho: 8.56, Ha: 8.56, z 2.11e. Ho: 110, Ha: ≠ 110, z 0.93
Calculate the p-value for each of the following:a. Ho: 20, Ha: 20; x 17.8, 9, n 36b. Ho: 78.5, Ha: 78.5; x 79.8, 15, n 100c. Ho: 1.587, Ha: ≠ 1.587; x 1.602, 0.15, n 50
Find the value of z for each of the following:a. Ho: 35 versus Ha: 35 when p-value 0.0582b. Ho: 35 versus Ha: 35 when p-value 0.0166c. Ha: 35 versus Ha: ≠ 35 when p-value 0.0042
Using the MINITAB solution to the rivet example as shown on page 439, describe how MINITAB found each of the six numerical values it reported as results.
The following computer output was used to complete a hypothesis test.TEST OF MU 525.00 VS MU 525.00 THE ASSUMED SIGMA 60.0 N MEAN STDEV SE MEAN Z P VALUE 38 512.14 64.78 9.733 1.32 0.093a. State the null and alternative hypotheses.b. If the test is completed using 0.05, what decision and

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