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statistics for experimentert
Statistics For The Behavioral Sciences 10th Edition Frederick J Gravetter, Larry B. Wallnau - Solutions
SAT scores for a normal distribution with mean of μ = 500 with σ = 100.What SAT score separates the top 10% of the distribution from the rest?a. 128b. 628c. 501.28d. 372
For a normal distribution with a mean of μ = 40 and σ = 4, what is the probability of selecting an individual with a score greater than 46?a. 0.0668b. 0.4452c. 0.9332d. 0.0548
For a normal distribution with a mean of μ = 500 and σ = 100, what is the probability of selecting an individual with a score less than 400?a. 0.1587b. 0.8413c. 0.34.13d. –0.15.87
Calculate the score (X-value) corresponding to a specific proportion in a distribution.
Calculate the probability for a specific X-value.
What z-score separates the lowest 10% of the distribution from the rest?a. z = 0.90b. z = –0.90c. z = 1.28d. z = –1.28
A vertical line is drawn through a normal distribution at z = –1.00. How much of the distribution is located between the line and the mean?a. 15.87%b. 34.13%c. 84.13%d. –15.87%
What proportion of a normal distribution is located in the tail beyond a z-score of z = –1.50?a. –0.0668b. –0.9332c. 0.0668d. 0.9332
Use the unit normal table to find the following: (1) proportions/probabilities for specific z-score values and (2) z-score locations that correspond to specific proportions.
A jar contains 20 red marbles and 10 blue marbles. If you take a random sample of n = 3 marbles from this jar, and the first two marbles are both red, what is the probability that the third marble also will be red?a. 20 30b. 18 28c. 1 30d. 1 28
A colony of laboratory rats contains 18 white rats and 7 spotted rats. What is the probability of randomly selecting a white rat from this colony?a. 1 18b. 1 25c. 17 25d. 18 25
A survey of the students in a psychology class revealed that there were 19 females and 8 males. Of the 19 females, only 4 had no brothers or sisters, and 3 of the males were also the only child in the household. If a student is randomly selected from this class, then what is the probability of
Define probability and calculate (from information provided or from frequency distribution graph) the probability of a specific outcome as a proportion, decimal, and percentage.
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 s = 10.
In a sample distribution, X = 56 corresponds to z = 1.00, and X = 47 corresponds to z = −0.50.Find the mean and standard deviation for the sample.
For a sample with a mean of M = 51, a score of X = 59 corresponds to z = 2.00. What is the sample standard deviation?
For a sample with a standard deviation of s = 8, a score of X = 65 corresponds to z = 1.50. What is the sample mean?
A sample has a mean of M = 25 and a standard deviation of s = 5.For this sample, find the X value corresponding to each of the following z-scores.z = 0.40 z = 1.20 z = 2.00 z = −0.80 z = −0.60 z = −1.40
A sample has a mean of M = 30 and a standard deviation of s = 8.Find the z-score for each of the following X values from this sample.X = 32 X = 34 X = 36 X = 28 X = 20 X = 18
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 of μ = 100 and a standard deviation of σ = 20.
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 = 61b. X = 70c. X = 85d. X = 94
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 values from the original population.a. X = 39b. X = 43c. X = 35d. X = 28
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 = 70, on an exam with M = 82 andσ = 8; or a score of X = 60 on an exam withμ = 72 and σ = 12.b. A score of X = 58, on an exam with μ = 49 andσ = 6; or a
For each of the following populations, would a score of X = 85 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 = 75 and σ = 15b. μ = 80 and σ = 2c. μ = 90 and σ = 20d. μ = 93 and σ = 3
In a population distribution, a score of X = 28 corresponds to z = −1.00 and a score of X = 34 corresponds to z = −0.50. Find the mean and standard deviation for the population. (Hint: Sketch the distribution and locate the two scores on your sketch.)
For a population with a mean of μ = 70, a score of X = 64 corresponds to z = −1.50. What is the population standard deviation?
For a population with a standard deviation of σ = 12, a score of X = 44 corresponds to z = −0.50. What is the population mean?
A score that is 9 points above the mean corresponds to a z-score of z = 1.50. What is the population standard deviation?
A score that is 6 points below the mean corresponds to a z-score of z = −2.00. What is the population standard deviation?
Find the z-score corresponding to a score of X = 45 for each of the following distributions.a. μ = 40 and σ = 20b. μ = 40 and σ = 10c. μ = 40 and σ = 5d. μ = 40 and σ = 2
A population has a mean of μ = 60 and a standard deviation of σ = 12.a. For this population, find the z-score for each of the following X values.X = 69 X = 84 X = 63 X = 54 X = 48 X = 45b. For the same population, find the score (X value)that corresponds to each of the following z-scores.z = 0.50
For a population with a mean of μ = 100 and a standard deviation of σ = 20,a. Find the z-score for each of the following X values.X = 108 X = 115 X = 130 X = 90 X = 88 X = 95b. Find the score (X value) that corresponds to each of the following z-scores.z = −0.40 z = −0.50 z = 1.80 z = 0.75 z
For a population with μ = 40 and σ = 11, find the z-score for each of the following X values. (Note: You probably will need to use a formula and a calculator to find these values.)X = 45 X = 52 X = 41 X = 30 X = 25 X = 38
For a population with μ = 60 and σ = 12,a. Find the z-score for each of the following X values. (Note: You should be able to find these values using the definition of a z-score.You should not need to use a formula or do any serious calculations.)X = 75 X = 48 X = 84 X = 54 X = 78 X = 51b. Find
For a distribution with a standard deviation ofσ = 20, describe the location of each of the following z-scores in terms of its position relative to the mean.For example, z = +1.00 is a location that is 20 points above the mean.a. z = +2.00b. z = +0.50c. z = −1.00d. z = −0.25
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 5 points.b. Above the mean by 2 points.c. Below the mean by 20 points.d. Below the mean by 15 points.
Under what circumstances would a score that is 20 points above the mean be considered to be an extreme, unrepresentative value?a. when the population mean is much larger than 20b. when the population standard deviation is much larger than 20c. when the population mean is much smaller than 20d. when
Under what circumstances would a score that is 15 points above the mean be considered to be near the center of the distribution?a. when the population mean is much larger than 15b. when the population standard deviation is much larger than 15c. when the population mean is much smaller than 15d.
In N = 25 games last season, the college basketball team averaged μ = 74 points with a standard deviation of σ = 6.In their final game of the season, the team scored 90 points. Based on this information, the number of points scored in the final game was _____.a. a little above averageb. far above
If a sample with M = 60 and s = 8 is transformed into z-scores, then the resulting distribution of z-scores will have a mean of ______ and a standard deviation of _____.a. 0 and 1b. 60 and 1c. 0 and 8d. 60 and 8 (unchanged)
For a sample with a standard deviation of s = 5, what is the z-score corresponding to a score that is located 10 points below the mean?a. −10b. +2c. −2d. cannot answer without knowing the mean
For a sample with M = 60 and s = 8, what is the z-score corresponding to X = 62?a. 2b. 4c. 0.25d. 0.50
Describe the effects of transforming an entire sample into z-scores and explain the advantages of this transformation.
Transform X values into z-scores and transform z-scores into X values for a sample.
Using z-scores, a population with μ = 37 and σ = 6 is standardized so that the new mean is μ = 50 and σ = 10.How does an individual’s z-score in the new distribution compare with his/her z-score in the original population?a. new z = old z + 13b. new z = (10/6)(old z)c. new z = old zd. cannot
A distribution with μ = 35 and σ = 8 is being standardized so that the new mean and standard deviation will be μ = 50 and σ = 10.In the new, standardized distribution your score is X = 60.What was your score in the original distribution?a. X = 45b. X = 43c. X = 1.00d. impossible to determine
A distribution with μ = 47 and σ = 6 is being standardized so that the new mean and standard deviation will be μ = 100 and σ = 20.What is the standardized score for a person with X = 56 in the original distribution?a. 110b. 115c. 120d. 130
Which of the following is an advantage of transforming X values into z-scores?a. All negative numbers are eliminated.b. The distribution is transformed to a normal shape.c. All scores are moved closer to the mean.d. None of the other options is an advantage.
A population has μ = 50 and σ = 10.If these scores are transformed into z-scores, the population of z-scores will have a mean of ____ and a standard deviation of ____.a. 50 and 10b. 50 and 1c. 0 and 10d. 0 and 1
A population with μ = 85 and σ = 12 is transformed into z-scores. After the transformation, the population of z-scores will have a standard deviation of _____a. σ = 12b. σ = 1.00c. σ = 0d. cannot be determined from the information given
A population of scores has σ = 10.In this population, a score of X = 60 corresponds to z = −1.50. What is the population mean?a. −30b. 45c. 75d. 90
A population of scores has σ = 4.In this population, an X value of 58 corresponds to z = 2.00. What is the population mean?a. 54b. 50c. 62d. 66
A population of scores has μ = 44.In this population, an X value of 40 corresponds to z = −0.50. What is the population standard deviation?a. 2b. 4c. 6d. 8
Explain how z-scores establish a relationship among X, μ, σ, and the value of z, and use that relationship to find an unknown mean when given a z-score, a score, and the standard deviation, or find an unknown standard deviation when given a z-score, a score, and the mean.
For a population with μ = 100 and σ = 20, what is the z-score corresponding to X = 105?a. +0.25b. +0.50c. +4.00d. +5.00
Of the following z-score values, which one represents the location closest to the mean?a. z = +0.50b. z = +1.00c. z = −1.00d. z = −2.00
Of the following z-score values, which one represents the most extreme location on the left-hand side of the distribution?a. z = +1.00b. z = +2.00c. z = −1.00d. z = −2.00
Using either the z-score definition or the z-score formula, transform X values into z-scores and transform z-scores into X values.
Explain how a z-score identifies a precise location in a distribution.
Last week Sarah had a score of X = 43 on a Spanish exam and a score of X = 75 on an English exam. For which exam should Sarah expect the better grade?a. Spanishb. Englishc. The two grades should be identical.d. Impossible to determine without more information
For a distribution of exam scores with μ = 70, which value for the standard deviation would give the highest grade to a score of X = 75?a. σ = 1b. σ = 2c. σ = 5d. σ = 10
If your exam score is X = 60, which set of parameters would give you the best grade?a. μ = 65 and σ = 5b. μ = 65 and σ = 2c. μ = 70 and σ = 5d. μ = 70 and σ = 2
Describe the two general purposes for transforming X values into z-scores.
On an exam with a mean of M 5 78, you obtain a score of X 5 84.a. Would you prefer a standard deviation of s 5 2 or s 5 10? (Hint: Sketch each distribution and find the location of your score.)b. If your score were X 5 72, would you prefer s 5 2 or s 5 10? Explain your answer.
A population has a mean of m 5 50 and a standard deviation of s 5 20.a. Would a score of X 5 70 be considered an extreme value (out in the tail) in this sample?b. If the standard deviation were s 5 5, would a score of X 5 70 be considered an extreme value?
Wegesin and Stern (2004) found greater consistency(less variability) in the memory performance scores for younger women than for older women. The following data represent memory scores obtained for two women, one older and one younger, over a series of memory trials.a. Calculate the variance of the
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
For the data in the following sample:10, 6, 8, 6, 5a. Find the mean and the standard deviation.b. Now change the score of X 5 10 to X 5 0, and find the new mean and standard deviation.c. Describe how one extreme score influences the mean and standard deviation.
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 5 scores. Note that there are three scores clustered
For the following population of N 5 6 scores:2, 9, 6, 8, 9, 8a. 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
For the following sample of n 5 8 scores: 0, 1, 1 2, 0, 3, 1 2, 0, and 1: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 parta,
Compute the mean and standard deviation for the following sample of n 5 4 scores: 82, 88, 82, and 86.Hint: To simplify the arithmetic, you can subtracted 80 points from each score to obtain a new sample consisting of 2, 8, 2, and 6.Then, compute the mean and standard deviation for the new sample.
a. After 6 points have been added to every score in a sample, the mean is found to be M 5 70 and the standard deviation is s 513.What were the values for the mean and standard deviation for the original sample?b. After every score in a sample is multiplied by 3, the mean is found to be M 5 48 and
A population has a mean of m 5 50 and a standard deviation of s 5 10.a. If 3 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 2, then what would be the new values for the mean
Calculate SS, variance, and standard deviation for the following sample of n 5 5 scores: 2, 9, 5, 5, 9.
For the following sample of n 5 6 scores: 0, 11, 5, 10, 5, 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 standard deviation (as done in Example 4.6).c. Compute SS, variance, and standard deviation for the
Why is the formula for sample variance different from the formula for population variance?
For the following set of scores: 1, 4, 3, 5, 7a. If the scores are a population, what are the variance and standard deviation?b. If the scores are a sample, what are the variance and standard deviation?
For the following population of N 5 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
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, 3, 4, 0 Sample B: 2, 5, 0, 3
In words, explain what is measured by SS, variance, and standard deviation.
For which of the following pairs of distributions would the mean difference be easiest to see?a. M 5 45 with s 5 5 compared to M 5 50 with s 5 5.b. M 5 45 with s 5 5 compared to M 5 55 with s 5 5.c. M 5 45 with s 5 10 compared to M 5 50 with s 5 10.d. M 5 45 with s 5 10 compared to M 5 55 with s 5
Under what circumstances would a score that is above the mean by 5 points appear to be very close to the mean?a. When the mean is much greater than 5b. When the mean is much less than 5c. When the standard deviation is much greater than 5d. When the standard deviation is much less than 5
What symbols are used for the mean and standard deviation for a sample in a research report?a. The mean is identified by the letter M and the standard deviation is represented by a lowercase s.b. The mean is identified by the letter M and the standard deviation is represented by SD.c. The mean is
A population has a mean of m 5 35 and a standard deviation of s 55.After 3 points are added to every score in the population, what are the new values for the mean and standard deviation?a. m 5 35 and s 5 5b. m 5 35 and s 5 8c. m 5 38 and s 5 5d. m 5 38 and s 5 8
How is the standard deviation represented in a frequency distribution graph?a. By a vertical line located at a distance of one standard deviation above the mean.b. By two vertical lines located one standard deviation above the mean and one standard deviation below the mean.c. By a horizontal line
Describe the appearance of a distribution based on the values for the mean and standard deviation.
Explain how the mean and standard deviation are affected when a constant is added to every score or when every score is multiplied by a constant.
Which of the following is an example of an unbiased statistic.a. the sample meanb. the sample variance (dividing by n 2 1)c. both the sample mean and the sample variance (dividing by n 2 1)d. neither the sample mean nor the sample variance (dividing by n 2 1)
A researcher selects all the possible samples with n 5 3 scores from a population and computes the sample variance, dividing by n – 1, for each sample. If the population variance is s2 5 6, then what is the average value for all of the sample variances?a. 6b. greater than 6c. less than 6d.
What is meant by a biased statistic.a. The average value for the statistic overestimates the corresponding population parameter.b. The average value for the statistic underestimates the corresponding population parameter.c. The average value for the statistic either overestimates or underestimates
Define biased and unbiased statistics.
What is the variance for the following sample of n 5 4 scores? Scores; 2, 5, 1, 2a. 34/3 5 11.33b. 9/4 5 2.25c. 9/3 5 3d. Ï3 5 173
What is the value of SS, the sum of the squared deviations, for the following sample? Scores: 1, 4, 0, 1a. 36b. 18c. 9d. 3
If sample variance is computed by dividing by n, instead of n 2 1, how will the obtained values be related to the corresponding population variance.a. They will consistently underestimate the population variance.b. They will consistently overestimate the population variance.c. The average value
Calculate SS, the sum of the squared deviations, for a sample using either the definitional or the computational formula and describe the circumstances in which each formula is appropriate.
What is the standard deviation for the following population of scores?Scores: 1, 3, 7, 4, 5a. 20b. 5c. 4d. 2
Each of the following is the sum of the scores for a population of N 5 4 scores. For which population would the definitional formula be a better choice than the computational formula for calculating SS.a. SX 5 9b. SX 5 12c. SX 5 15d. SX 5 19
What is the value of SS, the sum of the squared deviations, for the following population of N 5 4 scores? Scores: 1, 4, 6, 1a. 0b. 18c. 54d. 122 5 144
Calculate SS, the sum of the squared deviations, for a population using either the definitional or the computational formula and describe the circumstances in which each formula is appropriate.
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