PSY STATS Quizzes 5-8
For a population with µ = 40 and σ = 8, what is the z-score corresponding to X = 46? +0.50 +0.75 +1.00 +1.50
+0.75
For a population with µ = 80 and σ = 10, what is the z-score corresponding to X = 95? +0.25 +0.50 +0.75 +1.50
+1.50
For a population with µ = 80 and σ = 6, what is the z-score corresponding to X = 68? -0.50 -2.00 +2.00 -12.00
-2.00
For any distribution, what is the z-score corresponding to the mean? 0 1 N Z
0
If an entire population with μ = 60 and s = 8 is transformed into z-scores, then the distribution of z-scores will have a mean of ____ and a standard deviation of ____. 0 and 1 60 and 1 0 and 8 60 and 8 (unchanged)
0 and 1
A normal distribution has a mean of µ = 40 with σ = 10. What proportion of the scores in this distribution are greater than X = 55? 0.3085 0.6915 0.0668 0.9332
0.0668
A random sample of n = 9 scores is obtained from a normal population with µ = 40 and σ = 6. What is the probability that the sample mean will be greater than M = 43? 0.3085 0.6915 0.9332 0.0668
0.0668
A normal distribution has a mean of µ = 70 with σ = 12. If one score is randomly selected from this distribution, what is the probability that the score will be less than X = 55? 0.3944 0.1056 0.8944 0.7888
0.1056
A random sample of n = 4 scores is obtained from a normal population with µ = 20 and σ = 4. What is the probability that the sample mean will be greater than M = 22? 0.50 1.00 0.1587 0.3085
0.1587
A normal distribution has a mean of µ = 70 with σ = 12. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 79? 0.7734 0.2266 0.2734 0.3085
0.2266
What is the probability of randomly selecting a z-score greater than z = 0.75 from a normal distribution? 0.7734 0.2266 0.2734 0.4532
0.2266
John drives to work each morning and the trip takes an average of µ = 38 minutes. The distribution of driving times is approximately normal with a standard deviation of σ = 5 minutes. For a randomly selected morning, what is the probability that John's drive to work will take between 36 and 40 minutes? 0.0793 0.1526 0.1554 0.3108
0.3108
A normal distribution has a mean of µ = 100 with σ = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 80 and X = 100? 0.8413 0.1587 0.3413 0.6826
0.3413
A normal distribution has a mean of µ = 100 with σ = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 90 and X = 110? 0.6915 0.3085 0.1915 0.3830
0.3830
What proportion of a normal distribution is located between the mean and z = 1.40? 0.9192 0.0808 0.4192 0.8384
0.4192
A sample of n = 16 individuals is selected from a population with μ = 60 and σ = 6 and a treatment is administered to the sample. After treatment, the sample mean is M = 63. What is the value of Cohen's d for this sample? 0.33 0.50 2.00 3.00
0.50
A sample of n = 16 scores is selected from a population with μ = 100 and σ = 32. If the sample mean is M = 104, what is the z-score for this sample mean? 2.00 1.00 0.50 0.25
0.50
A random sample of n = 16 scores is obtained from a normal population with µ = 40 and σ = 8. What is the probability that the sample mean will be within 2 points of the population mean? 0.3830 0.6826 0.8664 0.9544
0.6826
A normal distribution has a mean of µ = 70 with σ = 12. If one score is randomly selected from this distribution, what is the probability that the score will be less than X = 76? 0.1915 0.3085 0.6915 0.3830
0.6915
A vertical line is drawn through a normal distribution at z = 0.50, and separates the distribution into two sections. What proportion of the distribution is in the larger section? 0.6915 0.3085 0.1915 0.3830
0.6915
A normal distribution has a mean of µ = 70 with σ = 12. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 58? 0.8413 0.1577 0.3413 0.6826
0.8413
A vertical line is drawn through a normal distribution at z = 1.20. What proportion of the distribution is on the left-hand side of the line? 0.8849 0.1151 0.3849 0.7698
0.8849
What is the probability of randomly selecting a z-score less than z = 1.25 from a normal distribution. 0.8944 0.1056 0.3944 0.2112
0.8944
For a particular population a sample of n = 4 scores has an expected mean value of 10. For the same population, a sample of n = 25 scores would have an expected mean value of ____. 4 8 10 20
10
A sample of n = 100 scores is selected from a population with μ = 80 with σ = 20. On average, how much error is expected between the sample mean and the population mean? 0.2 points 0.8 points 2 points 4 points
2 points
For a sample with M = 50 and s = 12, what is the X value corresponding to z = -0.25? 47 53 46 54
47
For a population with µ = 40 and σ = 8, what is the X value corresponding to z = 1.50? 44 50 52 58
52
For a population with µ = 80 and σ = 10, what is the X value corresponding to z = -0.50? -5 85 75 79.5
75
If all the possible random samples with n = 36 scores are selected from a normal population with µ = 80 and σ = 18, and the mean is calculated for each sample, then what is the average of all the sample means? 2 6 80 It cannot be determined without additional information.
80
Last week Sarah had exams in Math, Spanish and English. On the Math exam, the mean was µ = 40 with σ = 5 and Sarah had a score of X = 45. On the Spanish exam, the mean was µ = 60 with s = 8 and Sarah had a score of X = 68. On the English exam, the mean was µ = 70 with s = 8 and Sarah had a score of X = 78. For which class should Sara expect the better grade? Math Spanish English Grades are the same.
Grades are the same.
Under what circumstances can a very small treatment effect still be significant? If the sample size (n) is very large If the sample standard deviation (σ) is very large If the standard error of M (σ M) is very large All of the other three factors will result in a significant treatment effect.
If the sample size (n) is very large
Last week, Sarah had exams in Math, Spanish, and English. On the Math exam, the mean was µ = 30 with s = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was µ = 60 with s = 8 and Sarah had a score of X = 68. On the English exam, the mean was µ = 70 with s = 8 and Sarah had a score of X = 70. For which class should Sara expect the better grade? Math Spanish English Grades are the same.
Math
Which of the following z-score values represents the location closest to the mean? z = +0.50 z = +1.00 z = -1.00 z = -2.00
z = +0.50
For a population with a standard deviation of σ = 6, what is the z-score corresponding to a score that is 12 points above the mean? z = 1 z = 2 z = 6 z = 12
z = 2
Which of the following represents the probability of a Type II error? µ σ β α
β
On an exam with μ = 52, you have a score of X = 44. Which of the following values for the standard deviation would give you the highest position in the class distribution? σ = 2 σ = 4 σ = 8 σ = 10
σ = 10
On an exam with μ = 52, you have a score of X = 56. Which of the following values for the standard deviation would give you the highest position in the class distribution? σ = 2 σ = 4 σ = 8 σ = 10
σ = 2
What symbol is used to identify the standard error of M? σM µ σ MM
σM
What proportion of a normal distribution is located between the mean and z = -0.40? 0.6554 0.3446 0.1554 0.3108
0.1554
A vertical line is drawn through a normal distribution at z = 0.80. What proportion of the distribution is on the right-hand side of the line? 0.7881 0.2119 0.2881 0.5762
0.2119
John drives to work each morning and the trip takes an average of µ = 38 minutes. The distribution of driving times is approximately normal with a standard deviation of σ = 5 minutes. For a randomly selected morning, what is the probability that John's drive to work will take less than 35 minutes? 0.6554 0.3446 0.7257 0.2743
0.2743
A normal distribution has a mean of µ = 100 with σ = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 90 and X = 120? 0.1498 0.4672 0.5328 0.2996
0.5328
What proportion of a normal distribution is located between z = -1.50 and z = +1.50? 0.9332 0.0668 0.4332 0.8664
0.8664
A sample of n = 4 scores is selected from a population with μ = 50 and σ = 12. If the sample mean is M = 56, what is the z-score for this sample mean? 0.50 1.00 2.00 4.00
1.00
A jar contains 10 red marbles and 30 blue marbles. What is the probability of randomly selecting a red marble from the jar? 10/30 10/40 1/10 1/40
10/40
If random samples, each with n = 36 scores, are selected from a normal population with µ = 80 and σ = 18, how much difference, on average, should there be between a sample mean and the population mean? 2 points 3 points 6 points 18 points
3 points
A sample of n = 16 scores is selected from a population with μ = 80 with σ = 20. On average, how much error would be expected between the sample mean and the population mean? 20 points 5 points 4 points 1.25 points
5 points
Samples of size n = 9 are selected from a population with μ = 80 with σ = 18. What is the standard error for the distribution of sample means? 80 18 6 2
6
For a population with µ = 80 and σ = 20, the distribution of sample means based on n = 16 will have an expected value of ____ and a standard error of ____. 5; 80 80; 5 20; 20 80; 1.25
80; 5
Which combination of factors will produce the smallest value for the standard error? A large sample and a large standard deviation A small sample and a large standard deviation A large sample and a small standard deviation A small sample and a small standard deviation
A large sample and a small standard deviation
A researcher administers a treatment to a sample of participants selected from a population with µ = 80. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis? A sample mean near 80 for a small sample A sample mean near 80 for a large sample A sample mean much different than 80 for a small sample A sample mean much different than 80 for a large sample
A sample mean much different than 80 for a large sample
A researcher administers a treatment to a sample of participants selected from a population with µ = 80. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis? A sample mean near 80 with α = .05 A sample mean near 80 with α = .01 A sample mean much different than 80 with α = .05 A sample mean much different than 80 with α = .01
A sample mean much different than 80 with α = .05
Which combination of factors will increase the chances of rejecting the null hypothesis? A large standard error and a large alpha level A large standard error and a small alpha level A small standard error and a large alpha level A small standard error and a small alpha level
A small standard error and a large alpha level
Which of the following accurately describes a hypothesis test? A descriptive technique that allows researchers to describe a sample A descriptive technique that allows researchers to describe a population An inferential technique that uses the data from a sample to draw inferences about a population An inferential technique that uses information about a population to make predictions about a sample
An inferential technique that uses the data from a sample to draw inferences about a population
What is the relationship between the alpha level, the size of the critical region, and the risk of a Type I error? As the alpha level increases, the size of the critical region increases and the risk of a Type I error increases. As the alpha level increases, the size of the critical region increases and the risk of a Type I error decreases. As the alpha level increases, the size of the critical region decreases and the risk of a Type I error increases. As the alpha level increases, the size of the critical region decreases and the risk of a Type I error decreases.
As the alpha level increases, the size of the critical region increases and the risk of a Type I error increases.
What is the consequence of a Type I error? Concluding that a treatment has an effect when it really does Concluding that a treatment has no effect when it really has no effect Concluding that a treatment has no effect when it really does Concluding that a treatment has an effect when it really has no effect
Concluding that a treatment has an effect when it really has no effect
What is the consequence of a Type II error? Concluding that a treatment has an effect when it really does Concluding that a treatment has no effect when it really has no effect Concluding that a treatment has no effect when it really does Concluding that a treatment has an effect when it really has no effect
Concluding that a treatment has no effect when it really does
Which of the following are requirements of a random sample? Every individual has an equal chance of being selected. The probabilities cannot change during a series of selections. There must be sampling with replacement. There must be at least 100 observations.
Every individual has an equal chance of being selected.
The critical boundaries for a hypothesis test are z = +1.96 and 1.96. If the z-score for the sample data is z = 1.90, then what is the correct statistical decision? Fail to reject H1 Fail to reject H0 Reject H1 Reject H0
Fail to reject H0
Even if a treatment has an effect, it is still possible to obtain a sample mean that is very similar to the original population mean. What outcome is likely if this happens? Reject H0 and make a Type I error. Correctly reject H0. Fail to reject H0 and make a Type II error. Correctly fail to reject H0.
Fail to reject H0 and make a Type II error.
Which of the following is an accurate definition of a Type II error? Rejecting a false null hypothesis Rejecting a true null hypothesis Failing to reject a false null hypothesis Failing to reject a true null hypothesis
Failing to reject a false null hypothesis
Under what circumstances is distribution of sample means normal? It is always normal Only if the population distribution is normal If the sample size is greater than 30 If the population is normal or if the sample size is greater than 30
If the population is normal or if the sample size is greater than 30
Which of the following correctly describes the effect of increasing the alpha level (for example, from .01 to .05)? Increase the likelihood of rejecting H0 and increase the risk of a Type I error. Decrease the likelihood of rejecting H0 and increase the risk of a Type I error. Increase the likelihood of rejecting H0 and decrease the risk of a Type I error. Decrease the likelihood of rejecting H0 and decrease the risk of a Type I error.
Increase the likelihood of rejecting H0 and increase the risk of a Type I error.
What happens to the standard error of M as sample size increases? It also increases. It decreases. It stays constant. The standard error does not change in a predictable manner when sample size increases.
It decreases.
What happens to the expected value of M as sample size increases? It also increases. It decreases. It stays constant. The expected value does not change in a predictable manner when sample size increases.
It stays constant.
A sample with M = 85 and s = 12 is transformed into z-scores. After the transformation, what are the values for the mean and standard deviation for the sample of z-scores? M = 85 and s = 12 M = 0 and s = 12 M = 85 and s = 1 M = 0 and s = 1
M = 0 and s = 1
A treatment is administered to a sample of n = 9 individuals selected from a population with a mean of µ = 80 and a standard deviation of σ = 12. After treatment, the effect size is measured by computing Cohen's d, and a value of d = 0.50 is obtained. Based on this information, what is the mean for the treated sample? M = 6 M = 82 M = 86 This cannot be answered without knowing the sample size
M = 86
For an exam with a mean of M = 74 and a standard deviation of s = 8, Mary has a score of X = 80, Bob's score corresponds to z = +1.50, and Sue's score is located above the mean by 10 points. If the students are placed in order from smallest score to largest score, what is the correct order? Bob, Mary, Sue Sue, Bob, Mary Mary, Bob, Sue Mary, Sue, Bob
Mary, Sue, Bob
A random sample of n = 4 scores is selected from a population. Which of the following distributions will definitively be normal? The scores in the sample will form a normal distribution. The scores in the population will form a normal distribution. The distribution of sample means will form a normal distribution. None of the distributions - the sample, the population, the distribution of sample means -will definitely be normal.
None of the distributions - the sample, the population, the distribution of sample means -will definitely be normal.
Which of the following accurately describes the critical region? Outcomes with a very low probability if the null hypothesis is true Outcomes with a high probability if the null hypothesis is true Outcomes with a very low probability whether or not the null hypothesis is true Outcomes with a high probability whether or not the null hypothesis is true
Outcomes with a very low probability if the null hypothesis is true
Even if a treatment has no effect, it is still possible to obtain an extreme sample mean that is very different from the population mean. What outcome is likely if this happens? Reject H0 and make a Type I error. Correctly reject H0. Fail to reject H0 and make a Type II error. Correctly fail to reject H0.
Reject H0 and make a Type I error.
A two-tailed hypothesis test is being used to evaluate a treatment effect with α = .05. If the sample data produce a z-score of z = 2.24, then what is the correct decision? Reject the null hypothesis and conclude that the treatment has no effect. Reject the null hypothesis and conclude that the treatment has an effect. Fail to reject the null hypothesis and conclude that the treatment has no effect. Fail to reject the null hypothesis and conclude that the treatment has an effect.
Reject the null hypothesis and conclude that the treatment has an effect.
What is measured by the numerator of the z-score test statistic? The average distance between M and µ that would be expected if H0 was true The actual distance between M and µ The position of the sample mean relative to the critical region Whether or not there is a significant difference between M and µ
The actual distance between M and µ
What is measured by the denominator of the z-score test statistic? The average distance between M and µ that would be expected if H0 was true The actual distance between M and µ The position of the sample mean relative to the critical region Whether or not there is a significant difference between M and µ
The average distance between M and µ that would be expected if H0 was true
A random sample of n = 36 scores is selected from a population. Which of the following distributions will definitively be normal? The scores in the sample will form a normal distribution. The scores in the population will form a normal distribution. The distribution of sample means will form a normal distribution. None of the distributions - the sample, the population, the distribution of sample means - will definitely be normal.
The distribution of sample means will form a normal distribution.
A researcher conducts a hypothesis test to evaluate the effect of a treatment. The hypothesis test produces a z-score of z = 2.37. Assuming that the researcher is using a two-tailed test, what decision should be made? The researcher should reject the null hypothesis with α = .05 but not with α = .01. The researcher should reject the null hypothesis with either α = .05 or α = .01. The researcher should fail to reject H0 with either α = .05 or α = .01. The researcher should ignore the results.
The researcher should reject the null hypothesis with α = .05 but not with α = .01.
A sample of n = 25 individuals is selected from a population with µ = 80 and a treatment is administered to the sample. What is expected if the treatment has no effect? The sample mean should be very different from 80 and should lead you to reject the null hypothesis. The sample mean should be very different from 80 and should lead you to fail to reject the null hypothesis. The sample mean should be close to 80 and should lead you to reject the null hypothesis. The sample mean should be close 80 and should lead you to fail to reject the null hypothesis.
The sample mean should be close 80 and should lead you to fail to reject the null hypothesis.
When is there a risk of a Type I error? Whenever H0 is rejected Whenever H1 is rejected Whenever the decision is "fail to reject H0" The risk of a Type I error is independent of the decision from a hypothesis test.
Whenever H0 is rejected
A normal distribution has a mean of µ = 80 with σ = 20. What score separates the highest 15% of the distribution from the rest of the scores? X = 59.2 X = 100.8 X = 95 X = 65
X = 100.8
A normal distribution has a mean of µ = 24 with σ = 3. What is the minimum score needed to be in the top 14% of the distribution? X = 20.76 X = 27.24 X = 25.08 X = 24.42
X = 27.24
A distribution with µ = 35 and s = 8 is being standardized so that the new mean and standard deviation will be µ = 50 and s = 10. In the new, standardized distribution your score is X = 45. What was your score in the original distribution? X = 30 X = 31 X = 39 X = 45
X = 31
A distribution with µ = 55 and s = 6 is being standardized so that the new mean and standard deviation will be µ = 50 and s = 10. When the distribution is standardized, what value will be obtained for a score of X = 58 from the original distribution? X = 53 X = 55 X = 58 X = 61
X = 55
A sample has M = 72 and s = 4. In this sample, what is the X value corresponding to z = -2.00? X = 70 X = 68 X = 64 X = 60
X = 64
A normal distribution has a mean of µ = 80 with σ = 20. What score separates the lowest 30% of the distribution from the rest of the scores? X = 90.4 X = 69.6 X = 110 X = 50
X = 69.6
By selecting a larger alpha level, a researcher is ____. attempting to make it more difficult to reject H0 less able to detect a treatment effect increasing the risk of a Type I error decreasing the risk of a Type I error
increasing the risk of a Type I error
A normal distribution has µ = 80 and σ = 10. What is the probability of randomly selecting a score greater than 90 from this distribution? p = 0.8413 p = 0.1587 p = 0.3085 p = 0.6915
p = 0.1587
A population with µ = 85 and s = 12 is transformed into z-scores. After the transformation, what is the standard deviation for the population of z-scores? s = 12 s = 1.00 s = 0 s = 4.
s = 1.00
What term is used to identify the mean of the distribution of sample means? the expected value of M the standard error of M the sample mean the central limit mean
the expected value of M
What term is used to identify the standard deviation of the distribution of sample means? the expected value of M the standard error of M the sample mean the central limit mean
the standard error of M
The distribution of sample means ____. is always a normal distribution will be normal only if the population distribution is normal will be normal only if the sample size is at least n = 30 will be normal if either the population is normal or the sample size is n > 30
will be normal if either the population is normal or the sample size is n > 30
Which of the following represents the deviation score? x- µ Z s (x- µ)/s
x- µ
What z-score values form the boundaries for the middle 60% of a normal distribution? z = +0.25 and z = -0.25 z = +0.39 and z = -0.39 z = +0.52 and z = -0.52 z = +0.84 and z = -0.84
z = +0.84 and z = -0.84
In a sample with M = 40 and s = 8, what is the z-score corresponding to X = 38? z = -0.25 z = -0.50 z = 0.25 z = 0.50
z = -0.25
What z-score value separates the top 70% of a normal distribution from the bottom 30%? z = 0.52 z = 0.84 z = -0.52 z = -0.84
z = -0.52
A sample of n = 16 scores is obtained from a population with μ = 50 and σ = 16. If the sample mean is M = 54, then what is the z-score for the sample mean? z = 0.25 z = 0.50 z = 1.00 z = 4.00
z = 1.00
If a sample of n = 4 scores is obtained from a population with μ = 70 and σ = 12, then what is the z-score corresponding to a sample mean of M = 76? z = 0.25 z = 0.50 z = 1.00 z = 2.00
z = 1.00
What z-score value separates the top 10% of a normal distribution from the bottom 90%? z = 1.28 z = 0.25 z = -1.28 z = -0.25
z = 1.28
A sample of n = 20 scores has a mean of M = 45 and a standard deviation of s = 8. In this sample, what is the z-score corresponding to X = 57? z = 12/20 = 0.60 z = 1.00 z = 1.50 z = 2.00
z = 1.50
A random sample of n = 4 scores is obtained from a population with a mean of µ = 80 and a standard deviation of σ = 10. If the sample mean is M = 90, what is the z-score for the sample mean? z = 20.00 z = 5.00 z = 2.00 z = 1.00
z = 2.00
You have a score of X = 65 on an exam. Which set of parameters would give you the best grade on the exam? μ = 60 and σ = 10 μ = 60 and σ = 5 μ = 70 and σ = 10 μ = 70 and σ = 5
μ = 60 and σ = 5