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elementary statistics
Just The Essentials Of Elementary Statistics 10th Edition Robert Johnson, Patricia Kuby - Solutions
Bad Question A survey includes this item: “Enter your height in inches.” It is expected that actual heights of respondents can be obtained and analyzed, but there are two different major problems with this item. Identify them.
Cigarette Nicotine Refer to Data Set 5 in Appendix B and consider the nicotine content of the 29 different cigarette brands. The average (mean) of those amounts is 0.94 mg. Is this result likely to be a good estimate of the average (mean) of all cigarettes smoked in the United States? Why or why
Merrill Lynch Client Survey The author received a survey from the investment firm of Merrill Lynch. It was designed to gauge his satisfaction as a client, and it had specific questions for rating the author’s personal Financial Consultant. The cover letter included this statement: “Your
Motorcycle Helmets The Hawaii State Senate held hearings when it was considering a law requiring that motorcyclists wear helmets. Some motorcyclists testified that they had been in crashes in which helmets would not have been helpful. Which important group was not able to testify? (See “A
Crime and Buses The Newport Chronicle claims that bus stops cause crime, because a study showed that crime rates are higher in cities with bus stops than in rural areas that have no bus stops. What is wrong with that claim?
Telephone Surveys The Hartford Insurance Company has hired you to poll a sample of adults about their car purchases. What is wrong with using people with telephone numbers listed in directories as the population from which the sample is drawn?
“900” Numbers In an ABC Nightline poll, 186,000 viewers each paid 50 cents to call a “900” telephone number with their opinion about keeping the United Nations in the United States. The results showed that 67% of those who called were in favor of moving the United Nations out of the United
Mail Survey When author Shere Hite wrote Woman and Love: A Cultural Revolution in Progress, she based conclusions on 4500 replies that she received after mailing 100,000 questionnaires to various women’s groups. Are her conclusions likely to be valid in the sense that they can be applied to the
Census Data After the last national Census was conducted, the Poughkeepsie Journal ran this front-page headline: “281,421,906 in America.” What is wrong with this headline?
Chocolate Health Food The New York Times published an article that included these statements: “At long last, chocolate moves toward its rightful place in the food pyramid, somewhere in the high-tone neighborhood of red wine, fruits and vegetables, and green tea. Several studies, reported in the
a. How would you graphically describe the 100 “ages” in the preceding random sample taken from the 2000 census distribution?Construct the graph.b. Using the graph that you constructed in parta, describe the shape of the distribution of sample data.c. How well did the sample describe the
a. How would you numerically describe the 100 “ages” in the preceding random sample taken from the 2000 census distribution?Calculate the statistics.b. How well do the statistics calculated in part a compare with the parameters from the 2000 census? Be specific.c. If another sample was
Manufacturers use random samples to test whether or not their product is meeting specifications.These samples could be people, manufactured parts, or even samples during the manufacturing of potato chips.a. Do you think that all random samples taken from the same population will lead to the same
Refer to Table 7.1 in Example 7.1(p. 363) and explain why the samples are equally likely; that is, why P(0) 0.04, and why P(2) 0.12.
Consider the set of even single-digit integers{0, 2, 4, 6, 8}.a. Make a list of all the possible samples of size 3 that can be drawn from this set of integers.(Sample with replacement; that is, the first number is drawn, observed, and then replaced[returned to the sample set] before the next
Using the telephone numbers listed in your local directory as your population, randomly obtain 20 samples of size 3. From each telephone number identified as a source, take the fourth, fifth, and sixth digits. (For example, for 245-8269, you would take the 8, the 2, and the 6 as your sample of size
Using a set of five dice, roll the dice and determine the mean number of dots showing on the five dice. Repeat the experiment until you have 25 sample means.a. Draw a dotplot showing the distribution of the 25 sample means. (See Example 7.2, p. 364.)b. Describe the distribution of x’s in part
Considering the population of five equally likely integers in Example 7.2:a. Verify and for the population in Example 7.2.b. Table 7.3 lists 30 x values. Construct a grouped frequency distribution to verify the frequency distribution shown in Figure 7.4.c. Find the mean and standard deviation
a. Using a computer or a random-numbers table, simulate the drawing of 100 samples, each of size 5, from the uniform probability distribution of single-digit integers, 0 to 9.b. Find the mean for each sample.c. Construct a histogram of the sample means.(Use integer values as class midpoints.)d.
a. Use a computer to draw 200 random samples, each of size 10, from the normal probability distribution with mean 100 and standard deviation 20.b. Find the mean for each sample.c. Construct a frequency histogram of the 200 sample means.d. Describe the sampling distribution shown in the histogram in
Skillbuilder Applet Exercise simulates taking samples of size 4 from an approximately normal population, where 65.15 and 2.754.a. Click “1” for “# Samples.” Note the four data values and their mean. Change “slow” to“batch” and take at least 1000 samples using the “500” for
Skillbuilder Applet Exercise simulates sampling from a skewed population, where 6.029 and 10.79.a. Change the “# Observations per sample”to “4.” Using batch and 500, take 1000 samples of size 4.b. Compare the mean and standard deviation for the sample means with and . Compare the
An April 2004 article on HearTheIssues.com stated that Americans have an average of 2.24 televisions per household (source: Nielsen Media Research).If the standard deviation for the number of televisions in a U.S. household is 1.2 and a random sample of 80 American households is selected, the mean
An April 2004 article on HearTheIssues.com stated that Americans watch an average of 4.0 hours of television per person per day (source:Nielsen Media Research). If the standard deviation for the number of hours of television watched per day is 2.1 and a random sample of 250 Americans is selected,
According to The World Factbook, 2004, the total fertility rate (estimated mean number of children born per woman) for Madagascar is 5.7. Suppose that the standard deviation of the total fertility rate is 2.6. The mean number of children for a sample of 200 randomly selected women is one value of
The USDA Economics and Statistics System at Cornell University maintains a Poultry Yearbook in which they list monthly, quarterly, and annual facts about the poultry industry. The 2004 yearbook lists the annual consumption of turkey meat as 17.71 pounds per person. Suppose the standard deviation
a. Use a computer to randomly select 100 samples of size 6 from a normal population with mean 20 and standard deviation 4.5.b. Find mean x for each of the 100 samples.c. Using the 100 sample means, construct a histogram, find mean x, and find the standard deviation sx.d. Compare the
a. Use a computer to randomly select 200 samples of size 24 from a normal population with mean 20 and standard deviation 4.5.b. Find mean x for each of the 200 samples.c. Using the 200 sample means, construct a histogram, find mean x , and find the standard deviation sx.d. Compare the
Consider a normal population with 43 and 5.2. Calculate the z-score for an x of 46.5 from a sample of size 16.
Consider a population with 43 and 5.2.a. Calculate the z-score for an x of 46.5 from a sample of size 35.b. Could this z-score be used in calculating probabilities using Table 3 in Appendix B? Why or why not?
In Example 7.5, explain how 0.4772 was obtained and what it is.
The local bakery bakes more than a thousand 1-pound loaves of bread daily, and the weights of these loaves varies. The mean weight is 1 lb. and 1 oz., or 482 grams. Assume the standard deviation of the weights is 18 grams and a sample of 40 loaves is to be randomly selected.a. This sample of 40 has
Consider the approximately normal population of heights of male college students with mean 69 inches and standard deviation 4 inches. A random sample of 16 heights is obtained.a. Describe the distribution of x, height of male college students.b. Find the proportion of male college students
The amount of fill (weight of contents) put into a glass jar of spaghetti sauce is normally distributed with mean 850 grams and standard deviation 8 grams.a. Describe the distribution of x, the amount of fill per jar.b. Find the probability that one jar selected at random contains between
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 2.63e) 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
A sampling distribution is a distribution listing all the sample statistics that describe a particular sample. True/False
The histograms of all sampling distributions are symmetrical. True/False
The mean of the sampling distribution of x’s is equal to the mean of the sample. True/False
The standard error of the mean is the standard deviation of the population from which the samples have been taken. True/False
The standard error of the mean increases as the sample size increases. True/False
The shape of the distribution of sample means is always that of a normal distribution. True/False
A probability distribution of a sample statistic is a distribution of all the values of that statistic that were obtained from all possible samples. True/False
The sampling distribution of sample means provides us with a description of the three characteristics of a sampling distribution of sample medians. True/False
A frequency sample is obtained in such a way that all possible samples of a given size have an equal chance of being selected. True/False
We do not need to take repeated samples in order to use the concept of the sampling distribution. True/False
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.
a. Explain why the IQ score is a continuous variable.b. What are the mean and the standard deviation for the distribution of IQ scores? SAT scores? Standard scores?c. Express, algebraically or as an equation, the relationship between standard scores and IQ scores and between standard scores and SAT
Percentage, proportion, or probability—in your own words, using between 25 and 50 words for each, describe the following:a. How percentage is different than the other twob. How proportion is different than the other twoc. How probability is different than the other twod. How all three are
Find the area under the standard normal curve between z 0 and z 1.37.
Find the area under the normal curve that lies between the following pairs of z-values.a. z 0 to z 1.30b. z 0 to z 1.28c. z 0 to z 3.20d. z 0 to z1.98
Find the probability that a data value picked at random from a normal population will have a standard score (z) that lies between the following pairs of z-values.a. z 0 to z 2.10b. z 0 to z 2.57c. z 0 to z1.20d. z 0 to z1.57
Find the area under the standard normal curve to the right of z 2.03, P(z 2.03).
Find the area under the standard normal curve to the left of z 1.73, P(z 1.73).
Find the area under the standard normal curve between 1.39 and the mean, P(1.39 z 0.00).
Find the area under the standard normal curve to the left of z1.53, P(z1.53).
Find the area under the standard normal curve between z1.83 and z 1.23, P (1.83 z 1.23).
Find the area under the standard normal curve between z2.46 and z 1.46, P (2.46 z 1.46).
Find the probability that a data value picked at random from a normally distributed population will have a standard score (z) that corresponds to the following:a. Between 0 and 0.84b. To the right of 0.84c. To the left of 0.84d. Between 0.84 and 0.84
Find the following areas under the normal curve.a. To the right of z 0.00b. To the right of z 1.05c. To the right of z2.3d. To the left of z 1.60e. To the left of z1.60 6.18 Find the probability that a data value picked at random from a normally distributed population will have a standard
Find the following:a. P(2.05 z 0.00)b. P (1.83 z 2.07)c. P(z1.52)d. P(z0.43)6.21 Find the following:a. P(0.00 z 0.74)b. P(1.17 z 1.94)c. P(z 1.25)d. P(z 1.75)
Find the following:a. P(3.05 z 0.00)b. P (2.43 z 1.37)c. P(z2.17)d. P(z 2.43)
Find the area under the standard normal curve between z 0.75 and z 2.25, P(0.75 z 2.25).
Find the area under the standard normal curve between z2.75 and z1.28, P (2.75 z1.28).
Find the area under the normal curve that lies between the following pairs of z-values:a. z1.20 to z 1.22b. z1.75 to z 1.54c. z1.30 to z 2.58d. z3.5 to z 0.35
Find the probability that a data value picked at random from a normally distributed population will have a standard score (z) that lies between the following pairs of z-values:a. z2.75 to z 1.38b. z 0.67 to z 2.95c. z2.95 to z1.18
Find the z-score for the standard normal distribution shown on each of the following diagrams. a. 0.3729 b. 0.1808 . d. 0.3051 e. 0 z 0.4590 f. z 0 z 0 0.4515 0.4870
Find the standard score (z) shown on each of the following diagrams. a. 0 Z 0.05 b. 0 0.025 C. 0 Z 0.01
Find the standard score (z) shown on each of the following diagrams. a. 0.7673 0 Z b. Z 0 0.7190 3 C. 0.1515, Z
Find a value of z such that 40% of the distribution lies between it and the mean. (There are two possible answers.)
Find the standard z-score that corresponds to the following:a. Eighty percent of the distribution is below (to the left of) this value.b. The area to the right of this value is 0.15.
Find the two z-scores that bound the middle 50% of a normal distribution.
Find the two standard scores (z) that correspond to the following:a. The middle 90% of a normal distribution is bounded by them.b. The middle 98% of a normal distribution is bounded by them.
a. Find the z-score for the 80th percentile of the standard normal distribution.b. Find the z-scores that bound the middle 75% of the standard normal distribution.
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