Questions and Answers of Essentials Of Statistics

Two samples are selected from the same population.For each of the following, calculate how much difference is expected, on average, between the two sample means.a. One sample has n 5 4, the second
For each of the following, assume that the two samples are obtained from populations with the same mean, and calculate how much difference should be expected, on average, between the two sample
For each of the following, calculate the pooled variance and the estimated standard error for the sample mean differencea. The first sample has n 5 4 scores and a variance of s2 5 17, and the second
It appears that there is some truth to the old adage“That which doesn’t kill us makes us stronger.” Seery, Holman, and Silver (2010) found that individuals with some history of adversity report
In 1974, Loftus and Palmer conducted a classic study demonstrating how the language used to ask a question can influence eyewitness memory. In the study, college students watched a film of an
Explain how a z-score identies a precise location in a distribution for either a population or a sample of scores.
Using either the z-score denition or the z-score formula, transform X values into z-scores and transform z-scores into X values for both populations and samples.
Explain how z-scores establish a relationship among X, the mean, the standard deviation, and the value of z, and use that relationship to nd an unknown mean when given a z-score, a score, and the
Describe the effects of standardizing a distribution by transforming the entire set of scores into z-scores and explain the advantages of this transformation.
Use z-scores to transform any distribution into a standardized distribution with a predetermined mean and a predetermined standard deviation.
Explain how z-scores can help researchers use the data from a sample to draw inferences about populations.
What location in a distribution corresponds to z 5 22.00?a. Above the mean by 2 pointsb. Above the mean by a distance equal to 2 standard deviationsc. Below the mean by 2 pointsd. Below the mean by a
For a population with m 5 80 and s 5 12, what is the z-score corresponding to X 5 92?a. 10.50b. 11.00c. 11.20d. 112.00
For a sample with M 5 72 and s 5 4, what is the X value corresponding to z 5 22.00?a. X 5 70b. X 5 68c. X 5 64d. X 5 60
In a population with m 5 60, a score of X 5 58 corresponds to a z-score of z 5 20.50. What is the population standard deviation?a. 1b. 2c. 4d. Cannot be determined without additional information
In a sample with a standard deviation of s 5 8, a score of X 5 64 corresponds to z 5 20.50. What is the sample mean?a. M 5 56b. M 5 60c. M 5 68d. M 5 72
In a population of scores, X 5 45 corresponds to z 5 12.00 and X 5 30 corresponds to z 5 21.00. What is the population mean?a. 30b. 35c. 37.5d. 40
In a sample, X 5 70 corresponds to z 5 12.00 and X 5 65 corresponds to z 5 11.00. What are the sample mean and standard deviation?a. M 5 60 and s 5 5b. M 5 60 and s 5 10c. M 5 50 and s 5 10d. M 5 50
A population with m 5 80 and s 5 15 is transformed into z-scores. After the transformation, what is the mean for the population of z-scores?a. m 5 80b. m 5 1.00c. m 5 0d. Cannot be determined from
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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,
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
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

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