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essentials of statistics

Questions and Answers of Essentials Of Statistics

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
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
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
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
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
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
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,
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
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
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
A sample of n 5 9 scores has SX 5 108.What is the sample mean?
A population of N 57 scores has a mean of m 5 13.What is the value of SX for this population?
One sample of n 5 10 scores has a mean of 8 and a second sample of n 5 5 scores has a mean of 2.If the two samples are combined, what is the mean for the combined sample?
One sample has a mean of M 5 6 and a second sample has a mean of M 5 12.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
A sample with a mean of M 5 8 has SX 5 56.How many scores are in the sample?
Find the mean for the scores in the following frequency distribution table:X f 6 1 5 4 4 2 3 2 2 1
In a sample of n 5 6 scores, five of the scores are each above the mean by one point. Where is the sixth score located relative to the mean?
A population has a mean of m 5 40.a. If 5 points are added to each score, what is the value for the new mean?b. If each score is multiplied by 3, what is the value for the new mean?
Solve the following problems.a. After 8 points are added to each score in a sample, the mean is found to be M 5 40.What was the value for the original mean?b. After every score in a sample is
A sample of n 5 8 scores has a mean of M 5
If one score is changed from X 5 20 to X 5 4, what is the value of the new sample mean?
A sample of n 5 5 scores has a mean of M 5 12.If one new score with a value of X 5 18 is added to the sample, then what is the mean for the new sample?
A population of N 5 10 scores has a mean of m 5 12.If one score with a value of X 5 21 is removed from the population, then what is the value of the new population mean?
A sample of n 5 6 scores has a mean of M 514.After one new score is added, the new sample has a mean of M 5 12.What is the value of the score that was added?

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