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essentials of statistics

Essentials Of Statistics For The Behavioral Sciences 9th Edition Frederick J Gravetter, Larry B. Wallnau, Lori Ann B. Forzano - Solutions

A sample with a mean of M 5 50 and a standard deviation of s 5 12 is being transformed into z-scores. After the transformation, what is the standard deviation for the sample of z-scores?a. 0b. 1c. n 2 1d. n
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.
Last week Sarah had exams in math and in Spanish. On the math exam, the mean was m 5 30 with s 5 5, and Sarah had a score of X 5 45.On the Spanish exam, the mean was m 5 60 with s 5 6 and Sarah had a score of X 565.For which class should Sara expect the better grade?a. Mathb. Spanishc. The grades
A set of scores has a mean of m 5 63 and a standard deviation of s 58.If these scores are standardized so that the new distribution has m 5 50 and s 5 10, what new value would be obtained for a score of X 5 59 from the original distribution?a. The score would still be X 5 59.b. 45c. 46d. 55
A distribution with m 5 35 and s 5 8 is being standardized so that the new mean and standard deviation will be m 5 50 and s 510.When the distribution is standardized, what value will be obtained for a score of X 5 39 from the original distribution?a. X 5 54b. X 5 55c. X 5 1.10d. Impossible to
Using z-scores, a sample with M 5 37 and s 5 6 is standardized so that the new mean is M 5 50 and s 510.How does an individual’s z-score in the new distribution compare with his/her z-score in the original sample?a. New z 5 old z 1 13b. New z 5 (10/6)(old z)c. New z 5 old zd. Cannot be determined
For the past 20 years, the high temperature on April 15th has averaged m 5 62 degrees with a standard deviation of s 54.Last year, the high temperature was 72 degrees. Based on this information, last year’s temperature on April 15th was .a. A little above averageb. Far above averagec. Above
A score of X 5 73 is obtained from a population. Which set of population parameters would make X 5 73 and extreme, unrepresentative score?a. m 5 65 and s 5 8b. m 5 65 and s 5 3c. m 5 70 and s 5 8d. m 5 70 and s 5 3
Under what circumstances would a score that is 15 points above the mean be considered an extreme score?a. When the mean is much larger than 15b. When the standard deviation is much larger than 15c. When the mean is much smaller than 15d. When the standard deviation is much smaller than 15
For a population with a standard deviation of s 5 20, find the z-score for each of the following locations in the distribution.a. Above the mean by 5 pointsb. Above the mean by 2 pointsc. Below the mean by 10 pointsd. Below the mean by 30 points
For a sample with a standard deviation of s 5 12, describe the location of each of the following z-scores in terms of its position relative to the mean. For example, z 5 11.00 is a location that is 12 points above the mean.a. z 5 22.00b. z 5 10.75c. z 5 11.00d. z 5 21.50.
For a population with m 5 40 and s 5 8: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 5 44 X 5 48 X 5 56 X 5 38 X 5 34 X 5 32b. Find the
For a population with m 5 80 and s 5 9, 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 5 83 X 5 75 X 5 91 X 5 67 X 5 85 X 5 68
A sample has a mean of M 5 90 and a standard deviation of s 5 20.a. Find the z-score for each of the following X values.X 5 95 X 5 98 X 5 105 X 5 80 X 5 88 X 5 76b. Find the X value for each of the following z-scores.z 5 21.00 z 5 0.50 z 5 21.50 z 5 0.75 z 5 21.25 z 5 2.60
A sample has a mean of M 5 60 and a standard deviation of s 57.For this sample, find the z-score for each of the following X values.X 5 69 X 5 72 X 5 63 X 5 54 X 5 49 X 5 52
Find the z-score corresponding to a score of X 5 30 for each of the following distributions.a. m 5 50 and s 5 20b. m 5 50 and s 5 10c. m 5 20 and s 5 5d. m 5 20 and s 5 2
Find the X value corresponding to z 5 0.75 for each of the following distributions.a. m 5 90 and s 5 4b. m 5 90 and s 5 8c. m 5 90 and s 5 12d. m 5 90 and s 5 20
Find the z-score corresponding to X 5 40 and the X value corresponding to z 5 0.25 for each of the following populations.a. m 5 50 and s 5 20b. m 5 50 and s 5 4c. m 5 30 and s 5 8d. m 5 30 and s 5 4
Find the z-score corresponding to X 5 24 and the X value corresponding to z 5 1.50 for each of the following samples.a. M 5 20 and s 5 12b. M 5 20 and s 5 4c. M 5 30 and s 5 8d. M 5 30 and s 5 10
A score that is 12 points below the mean corresponds to a z-score of z 5 21.50. What is the standard deviation?
A score that is 20 points above the mean corresponds to a z-score of z 5 1.25. What is the standard deviation?
For a population with a standard deviation of s 5 14, a score of X 5 24 corresponds to z 5 20.50. What is the population mean?
For a population with a mean of m 5 45, a score of X 5 54 corresponds to z 5 1.50. What is the population standard deviation?
For a sample with a standard deviation of s 5 6, a score of X 5 30 corresponds to z 5 21.50. What is the sample mean?
For a sample with a mean of M 5 63, a score of X 5 54 corresponds to z 5 20.75. What is the sample standard deviation?
In a population distribution, a score of X 5 57 corresponds to z 5 20.25 and a score of X 5 87 corresponds to z 5 1.25. Find the mean and standard deviation for the population. (Hint: Sketch the distribution and locate the two scores on your sketch.)
In a sample distribution, a score of X 5 21 corresponds to z 5 21.00 and a score of X 5 12 corresponds to z 5 22.50. Find the mean and standard deviation for the sample.
A distribution of exam scores has a mean of m 5 42.a. If your score is X 5 46, which standard deviation would give you a better grade: s 5 5 or s 5 10?b. If your score is X 5 38, which standard deviation would give you a better grade: s 5 5 or s 5 10?
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 5 70, on an exam with M 5 82 and s 5 8; or a score of X 5 60 on an exam with m 5 72 and s 5 12.b. A score of X 5 58, on an exam with m 5 49 and s 5 6; or a
A population with a mean of m 5 41 and a standard deviation of s 5 4 is transformed into a standardized distribution with m 5 100 and s 520.Find the new, standardized score for each of the following values from the original population.a. X 5 39b. X 5 36c. X 5 45d. X 5 50
A sample with a mean of M 5 62 and a standard deviation of s 5 5 is transformed into a standardized distribution with m 5 50 and s 510.Find the new, standardized score for each of the following values from the original population.a. X 5 61b. X 5 55c. X 5 65d. X 5 74
A population consists of the following N 5 6 scores:2, 4, 1, 2, 7, 2.a. Compute m and s for the population.b. Find the z-score for each score in the populationc. Transform the original population into a new population of N 5 5 scores with a mean of m 5 50 and a standard deviation of s 5 10.
A sample consists of the following n 5 5 scores: 8, 4, 10, 0, 3.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 5 100 and s 5 20.
For each of the following populations, would a score of X 5 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. m 5 75 and s 5 15b. m 5 80 and s 5 2c. m 5 90 and s 5 20d. m 5 93 and s 5 3
Dene probability and calculate (from information provided or from frequency distribution graph) the probability of a specic outcome as a proportion, decimal, and percentage.
Use the unit normal table to nd the following: (1) proportions/probabilities for specic z-score values, and (2) z-score locations that correspond to specic proportions.
Calculate the probability for a specic X value.
Calculate the score (X value) corresponding to a specic proportion in a distribution.
Explain how probability can be used to evaluate a treatment effect by identifying likely and very unlikely outcomes.
An introductory psychology class with n 5 44 students has 9 freshman males, 15 freshman females, 8 sophomore males, and 12 sophomore females. If one student is randomly selected from this class, what is the probability of getting a sophomore?a. 8 24b. 20 24c. 20 44d. 14 44
A jar contains 10 red marbles and 20 blue marbles. If one marble is selected from this jar, what is the probability that the marble will be red?a. 1 30b. 1 20c. 10 30d. 10 20
Random sampling requires sampling with replacement. What is the goal of sampling with replacement?a. It ensures that every individual has an equal chance of selection.b. It ensures that the probabilities stay constant from one selection to the next.c. It ensures that the same individual is not
What is the probability of randomly selecting a z-score less than z = 0.25 from a normal distribution?a. 0.5987b. 0.4013c. 20.5987d. 20.4013
In a normal distribution, what z-score value separates the highest 90% of the scores from the rest of the distribution?a. z 5 1.28b. z 5 21.28c. z 5 0.13d. z 5 20.13
In a normal distribution, what z-score value separates the lowest 20% of the distribution from the highest 80%?a. z 5 0.20b. z 5 0.80c. z 5 0.84d. z 5 20.84
The population of SAT scores forms a normal distribution with a mean of m 5 500 and s 5100.What proportion of the population consists of individuals with SAT scores lower than 400?a. 0.1587b. 0.8413c. 0.34.13d. 20.15.87
A normal distribution has m 5 100 and s 520.What is the probability of randomly selecting a score of less than 130 from this distribution?a. p 5 0.9032b. p 5 0.9332c. p 5 0.0968d. p 5 0.0668
For a normal distribution with m 5 70 and s 5 10, what is the minimum score necessary to be in the top 60% of the distribution?a. 67.5b. 62.5c. 65.2d. 68.4
Which of the following accurately describes a score of X 5 52 or larger in a normal distribution with m 5 40 and s 5 5?a. It is an extreme, very unlikely score.b. It is higher than average but not extreme or unlikely.c. It is a little above average.d. It is an average, representative score.
For a normal distribution with m 5 60 and s 5 10, what X values form the boundaries between the middle 95% of the distribution and the extreme 5% in the tails?a. 51.6 and 68.4b. 47.2 and 72.8c. 43.5 and 65.5d. 40.4 and 79.6
An individual is selected from a normal population with a mean of m 5 80 with s 5 20, and a treatment is administered to the individual. After treatment, the individual’s score is found to be X 5105.How likely is it that a score this large (or larger) would be obtained if the treatment has no
What are the two requirements for a random sample?
Define sampling with replacement and explain why is it used.
Around Halloween each year the grocery store sells three-pound bags of candy containing a mixture of three different mini-bars: Snickers, Milky Way, and Twix. If the bag has an equal number of each of the three bars, then what are the probabilities for each of the following?a. Randomly selecting a
A psychology class consists of 28 males and 52 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. and if a random sample of n 5 3 students is selected and the first two are both females,
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 5 2.00b. z 5 0.75c. z 5 21.40d. z 5 20.67
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 5 1.00b. z 5 0.50c. z 5 21.25d. z 5 20.40
Draw a vertical line through a normal distribution for each of the following z-score locations. Find the proportion of the distribution located between the mean and the z-score.a. z 5 1.80b. z 5 0.55c. z 5 21.10d. z 5 20.85
Find each of the following probabilities for a normal distribution.a. p(z . 2.25)b. p(z . 21.20)c. p(z , 0.40)d. p(z , 21.75)
What proportion of a normal distribution is located between each of the following z-score boundaries?a. z 5 20.50 and z 5 10.50b. z 5 20.85 and z 5 10.85c. z 5 21.60 and z 5 11.60
Find each of the following probabilities for a normal distribution.a. p(21.80 , z , 0.20)b. p(20.40 , z , 1.40)c. p(0.25 , z , 1.25)d. p(20.90 , z , 20.60)
Find the z-score location of a vertical line that separates a normal distribution as described in each of the following.a. 15% in the tail on the rightb. 40% in the tail on the leftc. 75% in the body on the rightd. 60% in the body on the left
Find the z-score boundaries that separate a normal distribution as described in each of the following.a. The middle 20% from the 80% in the tailsb. The middle 25% from the 75% in the tailsc. The middle 70% from the 30% in the tailsd. The middle 90% from the 10% in the tails
A normal distribution has a mean of m 5 90 and a standard deviation of s 515.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 5 93b. X 5 110c. X 5 85d. X 5 70
A normal distribution has a mean of m 5 60 and a standard deviation of s 516.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 5 64b. X 5 80c. X 5 52d. X 5 28
For a normal distribution with a mean of m 5 85 and a standard deviation of s 5 20, find the proportion of the population corresponding to each of the following.a. Scores greater than 89b. Scores less than 72c. Scores between 70 and 100
In 2014, the New York Yankees had a team batting average of m 5 245 (actually 0.245 but we will avoid the decimals). Of course, the batting average varies from game to game, but assuming that the distribution of batting averages for 162 games is normal with a standard deviation of s 5 40 points,
IQ test scores are standardized to produce a normal distribution with a mean of m 5 100 and a standard deviation of s515.Find the proportion of the population in each of the following IQ categories.a. Genius or near genius: IQ over 140b. Very superior intelligence: IQ from 120 to 140c. Average or
The distribution of scores on the SAT is approximately normal with a mean of m 5 500 and a standard deviation of s 5100.For the population of students who have taken the SAT:a. What proportion have SAT scores less than 400?b. What proportion have SAT scores greater than 650?c. What is the minimum
According to a recent report, the average American consumes 22.7 teaspoons of sugar each day (National Geographic Magazine, August 2013). Assuming that the distribution is approximately normal with a standard deviation of s 5 4.5, find each of the following values.a. What proportion of people
A recent report indicates that 2-year-old children from well-educated suburban families watched an average of m 5 60 minutes of television each day. Assuming that the distribution of television-watching times is normal with a standard deviation of s 5 25 minutes, find each of the following
A report in 2010 indicates that Americans between the ages of 8 and 18 spend an average of m 5 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 s 5 2.5 hours and find the
Seattle, Washington, averages m 5 34 inches of annual precipitation. Assuming that the distribution of precipitation amounts is approximately normal with a standard deviation of s 5 6.5 inches, determine whether each of the following represents a fairly typical year, an extremely wet year, or an
Define the mean, and calculate both the population mean and the sample mean.
Explain the alternative definitions of the mean as the amount each individual receives when the total is divided equally and as a balancing point.
Calculate a weighted mean.
Find n, SX, and M using scores in a frequency distribution table.
Describe the effect on the mean and calculate the outcome for each of the following: changing a score, adding or removing a score, adding or subtracting a constant from each score, and multiplying or dividing each score by a constant.
Define and calculate the median, and nd the precise median for a continuous variable.
Dene and determine the mode(s) for a distribution, including the major and minor modes for a bimodal distribution.
Explain how the three measures of central tendency—mean, median, and mode—are related to each other for symmetrical and skewed distributions and predict their relative values based on the shape of the distribution.
Explain when each of the three measures of central tendency—mean, median, and mode—should be used, and identify the advantages and disadvantages of each.
A sample of n 5 5 scores has a mean of M 5 12.What is SX for this sample?a. 12 5 5 2.40b. 5 12 5 0.417c. 5(12) 5 60d. Cannot be determined from the information given 2.A sample has a mean of M 5?
If one person with a score of X 5 58 is removed from the sample, what effect will it have on the sample mean?a. The sample mean will increase.b. The sample mean will decrease.c. The sample mean will remain the same.d. Cannot be determined from the information given.
One sample of n 5 4 scores has a mean of M 5 10, and a second sample of n 5 4 scores has a mean of M 5 20.If the two samples are combined, then what value will be obtained for the mean of the combined sample?a. Equal to 15b. Greater than 15 but less than 20c. Less than 15 but more than 10d. None of
What is the mean for the sample presented in the following frequency distribution table?a. 2.0b. 2.5c. 3.0d. 3.5
A population of N 5 10 scores has a mean of 30.If every score in the distribution is multiplied by 3, then what is the value of the new mean?a. Still 30b. 33c. 60d. 90
What is the median for the following set of scores?Scores: 1, 5, 7, 19a. 5b. 5.5c. 6d. 6.5
What is the median for the sample presented in the following frequency distribution table?a. 1.5b. 2.0c. 2.5d. 3.0
Find the precise median for the following scores measuring a continuous variable.Scores: 1, 4, 5, 5, 5, 6, 7, 8a. 5b. 5.17c. 5.67d. 6
For the sample shown in the frequency distribution table, what is the mode?a. 4b. 3c. 2.5d. 2
If the mean, median, and mode are all computed for a distribution of scores, which of the following statements cannot be true?a. No one had a score equal to the mean.b. No one had a score equal to the median.c. No one had a score equal to the mode.d. All of the other three statements cannot be true.
What is the mode for the following set of n 5 7 scores? Scores: 2, 4, 4, 5, 7, 8, 10a. 4b. 5c. 5.5d. 6
For a distribution of scores, the mean is equal to the median. What is the most likely shape of this distribution?a. Symmetricalb. Positively skewedc. Negatively skewedd. Impossible to determine the shape
For a positively skewed distribution with a mode of X 5 20 and a median of X 5 25, what is the most likely value for the mean?a. Greater than 25b. Less than 20c. Between 20 and 25d. Cannot be determined from the information given
For a negatively skewed distribution, what is the most probable order for the three measures of central tendency from smallest to largest?a. Mean, median, modeb. Mean, mode, medianc. Mode, mean, mediand. Mode, median, mean
A researcher is measuring problem-solving times for a sample of n 5 20 laboratory rats. However, one of the rats fails to solve the problem so the researcher has an undetermined score. What is the best measure of central tendency for these data?a. The meanb. The medianc. The moded. Central tendency
What is the best measure of central tendency for an extremely skewed distribution of scores?a. The meanb. The medianc. The moded. Central tendency cannot be determined for a skewed distribution.
One item on a questionnaire asks students to identify their preferred costume for the school mascot from three different choices. What is the best measure of central tendency for the data from this question?a. The meanb. The medianc. The moded. Central tendency cannot be determined for these data.
Although the three measures of central tendency appear to be very simple to calculate, there is always a chance for errors. The most common sources of error are listed next.a. Many students find it very difficult to compute the mean for data presented in a frequency distribution table. They tend to

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