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Essentials Of Statistics For The Behavioral Sciences 8th Edition Frederick J Gravetter, Larry B. Wallnau - Solutions

A population of N = 15 scores has a mean of m = 8. One score in the population is changed from X = 20 to X = 5. What is the value for the new population mean?
A sample of n = 7 scores has a mean of M = 16. One score in the sample is changed from X = 6 to X = 20. What is the value for the new sample mean?
A sample of n = 7 scores has a mean of M = 5. After one new score is added to the sample, the new mean is found to be M = 6. What is the value of the new score? (Hint: Compare the values for ∑X before and after the score was added.)
A population of N = 8 scores has a mean of m = 16. After one score is removed from the population, the new mean is found to be m = 15. What is the value of the score that was removed?
A sample of n = 9 scores has a mean of M = 13. After one score is added to the sample, the mean is found to be M = 12. What is the value of the score that was added?
A sample of n = 9 scores has a mean of M = 20. One of the scores is changed and the new mean is found to be M = 22. If the changed score was originally X = 7, what is its new value?
One sample of n = 12 scores has a mean of M = 7 and a second sample of n = 8 scores has a mean of M = 12. If the two samples are combined, what is the mean for the combined sample?
One sample has a mean of M = 8 and a second sample has a mean of M = 16. The two samples are combined into a single set of scores. a. What is the mean for the combined set if both of the original samples have n = 4 scores? b. What is the mean for the combined set if the first sample has n = 3 and
One sample has a mean of M = 5 and a second sample has a mean of M = 10. The two samples are combined into a single set of scores.a. What is the mean for the combined set if both of the original samples have n = 5 scores?b. What is the mean for the combined set if the first sample
A researcher conducts a study comparing two different treatments with a sample of n = 16 participants in each treatment. The study produced thefollowing data:a. Calculate the mean for each treatment. Based on the two means, which treatment produces the higher scores? b. Calculate the median for
Schmidt (1994) conducted a series of experiments examining the effects of humor on memory. In one study, participants were shown a list of sentences, of which half were humorous and half were nonhumorous. A humorous example is, €œIf at first youdon€™t succeed, you are probably
Stephens, Atkins, and Kingston (2009) conducted a research study demonstrating that swearing can help reduce pain. In the study, each participant was asked to plunge a hand into icy water and keep it there as long as the pain would allow. In one condition, the participants repeatedly yelled their
Earlier in this chapter (p. 67), we mentioned a research study demonstrating that alcohol consumption increases attractiveness ratings for members of the opposite sex (Jones, Jones, Thomas, & Piper, 2003). In the actual study, college-age participants were recruited from bars and restaurants near
In words, explain what is measured by each of the following: a. SS b. Variance c. Standard deviation
For the following sample of n = 7 scores:8 6 = 2 6 3 5a. Sketch a histogram showing the sample distribution.b. Locate the value of the sample mean in your sketch, and make an estimate of the standarddeviation (as done in Example 4.5).c. Compute SS, variance, and standard deviation for the sample.
For the following population of N = 6 scores: 11 0 2 9 9 5 a. Calculate the range and the standard deviation. (Use either definition for the range.) b. Add 2 points to each score and compute the range and standard deviation again. Describe how adding a constant to each score influences measures of
The range is completely determined by the two extreme scores in a distribution. The standard deviation, on the other hand, uses every score.a. Compute the range (choose either definition) and the standard deviation for the following sample of n = 5 scores. Note that there are three scores clustered
A population has a mean of m = 30 and a standard deviation of s = 5.a. If = points were added to every score in the population, what would be the new values for the mean and standard deviation?b. If every score in the population were multiplied by 3, what would be the new values for the mean and
a. After 3 points have been added to every score in a sample, the mean is found to be M = 83 and the standard deviation is s = 8. What were the values for the mean and standard deviation for the original sample?b. After every score in a sample has been multiplied by 4, the mean is found to be M =
For the following sample of n = 4 scores: 82, 88, 82, and 86:a. Simplify the arithmetic by first subtracting 80 points from each score to obtain a new sample of 2, 8, 2, and 6. Then, compute the mean and standard deviation for the new sample.b. Using the values you obtained in part a, what are the
For the following sample of n = 8 scores:a. Simplify the arithmetic by first multiplying each score by 2 to obtain a new sample of 0, 2, 1, 0, 6, 1, 0, and 2. Then, compute the mean and standard deviation for the new sample.b. Using the values you obtained in part a, what are the values for the
For the data in the following sample:a. Find the mean and the standard deviation.b. Now change the score of X = 8 to X = 18, and find the new mean and standard deviation.c. Describe how one extreme score influences the mean and standard deviation.
Calculate SS, variance, and standard deviation for the following sample of n = 4 scores: 7, 4, 2, 1.
Calculate SS, variance, and standard deviation for the following population of N = 8 scores: 0, 0, 5, 0, 3, 0, 0, 4.
Calculate SS, variance, and standard deviation for the following population of N = 6 scores: 1, 6, 10, 9, 4, 6.
Calculate SS, variance, and standard deviation for the following sample of n = 5 scores: 10, 4, 8, 5, 8. (Note: The definitional formula for SS works well with these scores.) Calculate SS, variance, and standard deviation for the following sample of n = 5 scores: 10, 4, 8, 5, 8.
In an extensive study involving thousands of British children, Arden and Plomin (2006) found significantly higher variance in the intelligence scores for males than for females. Following are hypothetical data, similar to the results obtained in the study. Note that the scores are not regular IQ
Within a population, the differences that exist from one person to another are often called diversity. Researchers comparing cognitive skills for younger adults and older adults, typically find greater differences (greater diversity) in the older population(Morse, 1993). Following are typical data
In the previous problem we noted that the differences in cognitive skills tend to be bigger among older people than among younger people. These differences are often called diversity. Similarly, the differences in performance from trial to trial for the same person are often called consistency.
Explain why the formulas for sample variance and population variance are different.
A population has a mean of m = 80 and a standard deviation of s = 20.a. Would a score of X = 70 be considered an extreme value (out in the tail) in this sample?b. If the standard deviation were s = 5, would a score of X = 70 be considered an extreme value?
On an exam with a mean of M = 78, you obtain a score of X = 84.a. Would you prefer a standard deviation of s = 2 or s = 10? b. If your score were X = 72, would you prefer s = 2 or s = 10? Explain your answer.
Calculate the mean and SS (sum of squared deviations) for each of the following samples. Based on the value for the mean, you should be able to decide which SS formula is better to use. Sample A: 1 4 8 5 Sample B: 3 0 9 4
For the following population of N = 6 scores: 3 1 4 3 3 4a. Sketch a histogram showing the population distribution.b. Locate the value of the population mean in your sketch, and make an estimate of the standard deviation (as done in Example 4.2).c. Compute SS, variance, and standard deviation for
Find the z-score corresponding to a score of X = 45 for each of the following distributions. a. μ = 40 and σ = 20 b. μ = 40 and σ = 10 c. μ = 40 and σ = 5 d. μ = 40 and σ = 2
Find the X value corresponding to z = 0.25 for each of the following distributions. a. μ = 40 and σ = 4 b. μ = 40 and σ = 8 c. μ = 40 and σ = 16 d. μ = 40 and σ = 32
In a population distribution, a score of X = 28 corresponds to z = 21.00 and a score of X = 34 corresponds to z = 20.50. Find the mean and standard deviation for the population.
In a sample distribution, X = 56 corresponds to z = 1.00, and X = 47 corresponds to z = 20.50. Find the mean and standard deviation for the sample.
A distribution has a standard deviation of σ = 10. Find the z-score for each of the following locations in the distribution. a. Above the mean by = points. b. Above the mean by 2 points. c. Below the mean by 20 points. d. Below the mean by 15 points.
For each of the following populations, would a score of X = 50 be considered a central score (near the middle of the distribution) or an extreme score (far out in the tail of the distribution)? a. μ = 45 and σ = 10 b. μ = 45 and σ = 2 c. μ = 90 and σ = 20 d. μ = 60 and σ = 20
A distribution of exam scores has a mean of μ = 78. a. If your score is X = 70, which standard deviation would give you a better grade: σ = 4 or σ = 8? b. If your score is X = 80, which standard deviation would give you a better grade: σ = 4 or σ = 8?
For each of the following, identify the exam score that should lead to the better grade. In each case, explain your answer. a. A score of X = 74 on an exam with M = 82 and σ = 8; or a score of X = 40 on an exam with μ = 50 and σ = 20. b. A score of X = 51 on an exam with μ = 45 and σ = 2; or
A distribution with a mean of μ = 38 and a standard deviation of σ = 5 is transformed into a standardized distribution with μ = 50 and σ = 10. Find the new, standardized score for each of the following valuesfrom the original population. a. X = 39 b. X = 43 c. X = 35 d. X = 28
A distribution with a mean of μ = 76 and a standard deviation of σ = 12 is transformed into a standardized distribution with μ = 100 and σ = 20. Find the new, standardized score for each of the following values from the original population. a. X = 61 b. X = 70 c. X = 85 d. X = 94
A population consists of the following N = 5 scores: 0, 6, 4, 3, and 12.a. Compute μ and σ for the population.b. Find the z-score for each score in the population.c. Transform the original population into a new population of N = 5 scores with a mean ofμ = 100 and a standard deviation of σ = 20.
A sample consists of the following n = 7 scores: 5, 0, 4, 5, 1, 2, and 4.a. Compute the mean and standard deviation for the sample.b. Find the z-score for each score in the sample.c. Transform the original sample into a new sample with a mean of M = 50 and σ = 10.
For a distribution with a standard deviation of Ïƒ = 20, describe the location of each of the following z-scores in terms of its position relative to the mean. For example, z = 11.00 is a location that is 20 points above the mean.
For a population with μ = 80 and σ = 10,a. Find the z-score for each of the following X values.b. Find the score (X value) that corresponds to each of the following z-scores. (Again, you should not need a formula or any serious calculations.)
For a population with Î¼ = 40 and Ïƒ = 11, find the z-score for each of the following X values.
For a population with a mean of Î¼ = 100 and a standard deviation of Ïƒ = 20,a. Find the z-score for each of the following X values.b. Find the score (X value) that corresponds to each of the following z-scores.
A population has a mean of Î¼ = 60 and a standard deviation of Ïƒ = 12.a. For this population, find the z-score for each of the following X values.b. For the same population, find the score (X value) that corresponds to each of the following z-scores.
A sample has a mean of M = 30 and a standard deviation of Ïƒ = 8. Find the z-score for each of the following X values from this sample.
A sample has a mean of M = 25 and a standard deviation of Ïƒ = 5. For this sample, find the X value corresponding to each of the following z-scores.
A local hardware store has a “Savings Wheel” at the checkout. Customers get to spin the wheel and, when the wheel stops, a pointer indicates how much they will save. The wheel can stop in any one of 50 sections. Of the sections, 10 produce 0% off, 20 sections are for 10% off, 10 sections for
Find the z-score boundaries that separate a normal distribution as described in each of the following. a. The middle 30% from the 70% in the tails. b. The middle 40% from the 60% in the tails. c. The middle 50% from the 50% in the tails. d. The middle 60% from the 40% in the tails.
A normal distribution has a mean of μ = 70 and a standard deviation of σ = 8. For each of the following scores, indicate whether the tail is to the right or left of the score and find the proportion of the distribution located in the tail. a. X = 72 b. X = 76 c. X = 66 d. X = 60
A normal distribution has a mean of μ = 30 and a standard deviation of σ = 12. For each of the following scores, indicate whether the body is to the right or left of the score and find the proportion of the distribution located in the body.a. X = 33b. X = 18c. X = 24d. X = 39
For a normal distribution with a mean of μ = 60 and a standard deviation of σ = 10, find the proportion of the population corresponding to each of the following. a. Scores greater than 65. b. Scores less than 68. c. Scores between 50 and 70.
IQ test scores are standardized to produce a normal distribution with a mean of μ = 100 and a standard deviation of σ 515. Find the proportion of the population in each of the following IQ categories. a. Genius or near genius: IQ greater than 140 b. Very superior intelligence: IQ between 120 and
The distribution of SAT scores is normal with μ = 500 and σ = 100. a. What SAT score, X value, separates the top 15% of the distribution from the rest? b. What SAT score, X value, separates the top 10% of the distribution from the rest? c. What SAT score, X value, separates the top 2% of the
According to a recent report, people smile an average of μ = 62 time per day. Assuming that the distribution of smiles is approximately normal with a standard deviation of σ = 18, find each of the following values. a. What proportion of people smile more than 80 times a day? b. What proportion of
A recent newspaper article reported the results of a survey of well-educated suburban parents. The responses to one question indicated that by age 2, children were watching an average of μ = 60 minutes of television each day. Assuming that the distribution of television-watching times is normal
Information from the Department of Motor Vehicles indicates that the average age of licensed drivers is μ = 45.7 years with a standard deviation of σ = 12.5 years. Assuming that the distribution of drivers’ ages is approximately normal, a. What proportion of licensed drivers are older than 50
A consumer survey indicates that the average household spends μ = $185 on groceries each week. The distribution of spending amounts is approximately normal with a standard deviation of σ = $25. Based on this distribution, a. What proportion of the population spends more than $200 per week on
A psychology class consists of 14 males and 36 females. If the professor selects names from the class list using random sampling,a. What is the probability that the first student selected will be a female?b. If a random sample of n = 3 students is selected and the first two are both females,
A report in 2010 indicates that Americans between the ages of 8 and 18 spend an average of μ = 7.5 hours per day using some sort of electronic device such as smart phones, computers, or tablets. Assume that the distribution of times is normal with a standard deviation of σ = 2.5 hours and find
Rochester, New York, averages μ = 21.9 inches of snow for the month of December. The distribution of snowfall amounts is approximately normal with a standard deviation of σ = 6.5 inches. This year, a local jewelry store is advertising a refund of 50% off of all purchases made in December, if
What are the two requirements that must be satisfied for a random sample?
Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the tail is on the right or left side of the line and find the proportion in the tail. a. z = 1.00 b. z = 0.50 c. z = - 1.25 d. z = - 0.40
Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the body is on the right or left side of the line and find the proportion in the body. a. z = 2.50 b. z = 0.80 c. z = -0.50 d. z =- 0.77
Find each of the following probabilities for a normal distribution.
What proportion of a normal distribution is located between each of the following z-score boundaries? a. z = -0.25 and z = +0.25 b. z = -0.67 and z = +0.67 c. z = -1.20 and z = +1.20
Find each of the following probabilities for a normal distribution.
Find the z-score location of a vertical line that separates a normal distribution as described in each of the following. a. 5% in the tail on the left b. 30% in the tail on the right c. 65% in the body on the left d. 80% in the body on the right
Describe the distribution of sample means (shape, expected value, and standard error) for samples of n = 100 selected from a population with a mean of µ = 40 and a standard deviation of σ = 10.
A sample of n = 4 scores has a mean of µ = 75. Find the z-score for this sample: a. If it was obtained from a population with µ = 80 and σ = 10. b. If it was obtained from a population with µ = 80 and σ = 20. c. If it was obtained from a population with µ = 80 and σ = 40.
A normal distribution has a mean of µ = 60 and a standard deviation of σ = 18. For each of the following samples, compute the z-score for the sample mean and determine whether the sample mean is a typical, representative value or an extreme value for a sample of this size. a. µ = 67 for n = 4
A random sample is obtained from a normal population with a mean of µ = 95 and a standard deviation of σ = 40. The sample mean is µ = 86. a. Is this a representative sample mean or an extreme value for a sample of n = 16 scores? b. Is this a representative sample mean or an extreme value for a
The population of IQ scores forms a normal distribution with a mean of µ = 100 and a standard deviation of σ = 15. What is the probability of obtaining a sample mean greater than µ = 97, a. for a random sample of n = 9 people? b. for a random sample of n = 25 people?
The scores on a standardized mathematics test for 8th-grade children in New York State form a normal distribution with a mean of µ = 70 and a standard deviation of σ = 10. a. What proportion of the students in the state have scores less than X = 75? b. If samples of n = 4 are selected from the
A normal distribution has a mean of µ = 54 and a standard deviation of σ = 6. a. What is the probability of randomly selecting a score less than X = 51? b. What is the probability of selecting a sample of n = 4 scores with a mean less than µ = 51? c. What is the probability of selecting a sample
A population of scores forms a normal distribution with a mean of µ = 80 and a standard deviation of σ = 10. a. What proportion of the scores have values between 75 and 85? b. For samples of n = 4, what proportion of the samples will have means between 75 and 85? c. For samples of n = 16, what
For random samples of size n = 25 selected from a normal distribution with a mean of µ = 50 and a standard deviation of σ = 20, find each of the following: a. The range of sample means that defines the middle 95% of the distribution of sample means. b. The range of sample means that defines the
The distribution ages for students at the state college is positively skewed with a mean of µ = 21.5 and a standard deviation of σ = 3. a. What is the probability of selecting a random sample of n = 4 students with an average age greater than 23? (Careful: This is a trick question.) b. What is
At the end of the spring semester, the Dean of Students sent a survey to the entire freshman class. One question asked the students how much weight they had gained or lost since the beginning of the school year. The average was a gain of µ = 9 pounds with a standard deviation of σ = 6. The
A sample is selected from a population with a mean of µ = 40 and a standard deviation of σ = 8. a. If the sample has n = 4 scores, what is the expected value of µ and the standard error of M? b. If the sample has n = 16 scores, what is the expected value of µ and the standard error of M?
Jumbo shrimp are those that require 10 to 15 shrimp to make a pound. Suppose that the number of jumbo shrimp in a 1-pound bag averages µ = 12.5 with a standard deviation of σ = 1, and forms a normal distribution. What is the probability of randomly picking a sample of n = 25 1-pound bags that
The average age for licensed drivers in the county is µ = 40.3 years with a standard deviation of σ = 13.2 years. a. A researcher obtained a random sample of n = 16 parking tickets and computed an average age of M = 38.9 years for the drivers. Compute the z-score for the sample mean and find the
Callahan (2009) conducted a study to evaluate the effectiveness of physical exercise programs for individuals with chronic arthritis. Participants with doctor-diagnosed arthritis either received a Tai Chi course immediately or were placed in a control group to begin the course 8 weeks later. At the
Xu and Garcia (2008) conducted a research study demonstrating that 8-month-old infants appear to recognize which samples are likely to be obtained from a population and which are not. In the study, the infants watched as a sample of n = 5 ping-pong balls was selected from a large box. In one
A population has a standard deviation of σ = 24.a. On average, how much difference should exist between the population mean and the sample mean forn = 4 scores randomly selected from the population?b. On average, how much difference should exist for a sample of n = 9 scores?c. On average, how much
For a population with a mean of µ = 70 and a standard deviation of σ = 20, how much error, on average, would you expect between the sample mean (M) and the population mean for each of the following sample sizes?a. n = 4 scoresb. n = 16 scoresc. n = 25 scores
For a population with a standard deviation of σ = 20, how large a sample is necessary to have a standard error that is: a. less than or equal to = points? b. less than or equal to 2 points? c. less than or equal to 1 point?
For a population with σ = 12, how large a sample is necessary to have a standard error that is: a. less than 4 points? b. less than 3 points? c. less than 2 point?
For a sample of n = 25 scores, what is the value of the population standard deviation (s) necessary to produce each of the following a standard error values? a. σM = 10 points? b. σM = 5 points? c. σM = 2 points?
For a population with a mean of µ = 80 and a standard deviation of σ = 12, find the z-score corresponding to each of the following samples. a. µ = 83 for a sample of n = 4 scores b. µ = 83 for a sample of n = 16 scores c. µ = 83 for a sample of n = 36 scores
The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following: a. An increase in the difference between the sample mean and the original population mean. b.
In a study examining the effect of alcohol on reaction time, Liguori and Robinson (2001) found that even moderate alcohol consumption significantly slowed response time to an emergency situation in a driving simulation. In a similar study, researchers measured reaction time 30 minutes after
The researchers cited in the previous problem (Liguori & Robinson, 2001) also examined the effect of caffeine on response time in the driving simulator. In a similar study, researchers measured reaction time 30 minutes after participants consumed one 6-ounce cup of coffee. Using the same driving
There is some evidence indicating that people with visible tattoos are viewed more negatively than people without visible tattoos (Resenhoeft, Villa, & Wiseman, 2008). In a similar study, a researcher first obtained overall ratings of attractiveness for a woman with no tattoos shown in a color

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