Psych Stats Exam 2 Part 2
effect size
a measurement of the absolute magnitude of the power of a treatment
significant or statistically significant
a result that is very unlikely to occur when the null hypothesis is true
a hypothesis test
a statistical method that uses sample data to evaluate an educated guess about a population
directional hypothesis test or one-tailed test
a statistical method wherein an education guess is made about the direction of the effect
A researcher expects a treatment to produce an increase in the population mean. Assuming a normal distribution, what is the critical z score for a one tailed test with α = .01? a. +2.33 b. +1.65 c. ±2.58 d. ±2.33
a. +2.33
A random sample of n = 4 scores is selected from a normally distributed population with µ = 80 and s = 10. What is the probability that the sample mean will be greater than 90? a. 0.0228 b. 0.9778 c. 0.3085 d. 0.1587
a. 0.0228
In the same way that it is possible to compute a z-score for an X value, it also is possible to compute a z-score for a sample mean. If a sample of n = 25 scores is selected from a normal population, what is the probability that the sample mean will have a z-score greater than z = 1.00? a. 0.1587 b. 0.0228 c. 0. 3085 d. 0.0668
a. 0.1587
If random samples, each with n = 4 scores are selected from a population with µ = 80 and σ = 10, then how much distance is expected on average between the sample means and the population mean? a. 10/√4 = 5 points b. 4(10) = 40 points c. 10 points d. 10/4 = 2.5 points
a. 10/√4 = 5 points
How is the power of a hypothesis test related to sample size and the alpha level? a. A larger sample and a larger alpha level will both increase power. b. A larger sample will decrease power but a larger alpha will increase power. c. A larger sample and a larger alpha level will both decrease power. d. A larger sample will increase power but a larger alpha will decrease power.
a. A larger sample and a larger alpha level will both increase power.
A sample is selected from a population with μ = 80 and σ = 10, and a treatment is administered to the sample. If other factors are held constant, then what is the effect of increasing the standard deviation to σ = 15? a. It decreases the size of the z-score (closer to 0) and decreases the likelihood of rejecting the null hypothesis. b. It increases the size of the z-score (farther from 0) and decreases the likelihood of rejecting the null hypothesis. c. It decreases the size of the z-score (closer to 0) and increases the likelihood of rejecting the null hypothesis. d. It increases size of the z-score (farther from 0) and increases the likelihood of rejecting the null hypothesis.
a. It decreases the size of the z-score (closer to 0) and decreases the likelihood of rejecting the null hypothesis.
A sample is selected from a population with μ = 40 and σ = 8, and a treatment is administered to the sample. After treatment, the sample mean is M = 44. If other factors are held constant, then what would happen if the sample mean were increased to M = 46? a. It increases the size of the z-score (farther from 0) and increases the likelihood of rejecting the null hypothesis. b. It decreases the size of the z-score (closer to 0) and increases the likelihood of rejecting the null hypothesis. c. It increases the size of the z-score (farther from 0) and decreases the likelihood of rejecting the null hypothesis. d. It decreases the size of the z-score (closer to 0) and decreases the likelihood of rejecting the null hypothesis.
a. It increases the size of the z-score (farther from 0) and increases the likelihood of rejecting the null hypothesis.
A sample of n = 36 individuals is selected from a population with µ = 100 and σ = 12, and a treatment is administered to the sample. After treatment, the sample mean is M = 105. How does this sample compare to samples that should be obtained if the treatment has no effect? a. It is an extreme value that would be very unlikely if the treatment has no effect. b. The mean is a little larger than would be expected if the treatment has no effect but it is not an extreme sample. c. There is no way to compare this sample with those that would be obtained if the treatment had no effect. d. It is much the same as samples that would be obtained if the treatment has no effect.
a. It is an extreme value that would be very unlikely if the treatment has no effect.
If a sample is selected from a normal population with µ = 50 and σ = 20, which of the following samples has the lowest probability of being obtained? a. M = 45 for a sample of n = 25 scores. b. M = 45 for a sample of n = 9 scores. c. The three samples are equally likely to be obtained. d. M = 45 for a sample of n = 4 scores.
a. M = 45 for a sample of n = 25 scores.
The distribution of sample mean is the set of means for all of the possible random samples of a specific size selected from a population and the standard deviation of the distribution of sample means is called the standard error of M. How is the standard error of M related to the size of the sample? a. The larger the sample, the smaller the standard error of M. b. The larger the sample, the bigger the standard error of M. c. The standard error of M varies randomly and is not related to the size of the sample. d. The standard error of M is constant and does not depend on the size of the sample.
a. The larger the sample, the smaller the standard error of M.
Under what circumstances can a hypothesis test correctly identify a very small treatment effect? a. With a large sample size and a small value for the population standard deviation b. With a small sample size and a large value for the population standard deviation c. With a large sample size and a large value for the population standard deviation d. With a small sample size and a small value for the population standard deviation
a. With a large sample size and a small value for the population standard deviation
Just as standard deviation measures the standard distance between a score and the population mean, the standard error measures the standard distance between a sample mean and the population mean. For samples selected from a population with µ = 100 and σ = 15, which of the following has the smallest standard error? a. a sample of n = 25 scores b. The three samples all have the same standard error. c. a sample of n = 4 scores d. a sample of n = 16 scores
a. a sample of n = 25 scores
If other factors are held constant, the standard error will ________ as the sample size increases. a. decrease b. stay constant c. increase d. cannot answer with the information given
a. decrease
If sample size (n) is held constant, the standard error will ________ as the population variance increases. a. increase b. stay constant c. Cannot answer with the information given d. decrease
a. increase
A random sample is obtained from a population with μ = 80 and σ = 10 and a treatment is administered to the sample. Which of the following outcomes would be considered noticeably different from a typical sample that did not receive the treatment? a. n = 100 with M = 83 b. n = 25 with M = 83 c. n = 100 with M = 81 d. n = 25 with M = 81
a. n = 100 with M = 83
If the power of a statistical test is p = 0.80, then what is the probability of a Type II error? a. p = 0.20 b. p < 0.20 c. p > 0.80 d. p = 0.80
a. p = 0.20
The critical region for a hypothesis test is defined as sample outcome that are very unlikely to be obtained if the null hypothesis is true. What should a researcher do if the data produce a sample mean that is in the critical region? a. reject the null hypothesis b. reject that alternative hypothesis c. fail to reject the null hypothesis d. fail to reject the alternative hypothesis
a. reject the null hypothesis
A z score that is used for hypothesis testing is also called a ________. a. test statistic b. critical value c. critical region d. level of significance
a. test statistic
When the sample size is greater than n = 30 ________. a. the distribution of sample means will be approximately normal b. the distribution of sample means will be approximately normal and the sample mean will equal the population mean c. the sample mean will be equal to the population mean d. None of the other 3 choices is correct.
a. the distribution of sample means will be approximately normal
When a random sample is selected from a population, the sample mean is not expected to be exactly equal to the population mean. On average, the size of the difference between the sample mean and the population mean is predicted by ________. a. the standard error b. the expected value c. the standard deviation of the population d. the mean of the population
a. the standard error
A researcher is predicting that a treatment will increase scores. If this treatment is evaluated using a directional hypothesis test, then the critical region for the test ________. a. would be entirely in the right-hand tail of the distribution b. cannot answer without knowing the value of the alpha level c. would be entirely in the left-hand tail of the distribution d. would be divided equally between the two tails of the distribution
a. would be entirely in the right-hand tail of the distribution
A normal population has μ = 50 and σ = 8. A random sample of n = 4 scores from this population has a mean of 54. What is the z score for this sample mean? a. +2.00 b. +1.00 c. +0.50 d. +4.00
b. +1.00
A positively skewed population has μ = 50 and σ = 20. A random sample of n = 4 scores obtained from this population has a mean of M = 55. What is the z score corresponding to this sample mean? a. 1.00 b. 0.50 c. 0.25 d. You cannot compute a z-score for a skewed population.
b. 0.50
A sample of n = 25 scores is determined to have a standard error of 2 points. What is the standard deviation for the population from which the sample was obtained? a. 50 b. 10 c. 2/5 d. 2
b. 10
On average, how much difference should there be between the sample mean and the population mean for a sample of n = 25 scores selected from a population with a standard deviation of σ = 20? a. cannot answer without additional information b. 4 points c. 2 points d. 0.80 points
b. 4 points
If random samples, each with n = 25 scores, are selected from a normal population with µ = 80 and σ = 20, and the mean is calculated for each sample, then the average of all the sample means would be _____. a. 4 b. 80 c. 20 d. 0.80
b. 80
If random samples, each with n = 4 scores, are selected from a normal population with μ = 80 and σ = 10, then the distribution of sample means will have an expected value of ________. a. 10 b. 80 c. 4 d. 5
b. 80
A sample of n = 16 individuals is selected from a population with µ = 80 and σ = 5, and a treatment is administered to the sample. If the treatment really does have an effect, then what would be the effect of increasing the standard deviation to σ = 25? a. Increase the chances that the sample will produce an extreme z-score and increase the likelihood that you will conclude that a treatment effect exists. b. Increase the chances that the sample will produce a z-score near zero and increase the likelihood that you will conclude that a treatment effect does not exist. c. Increase the chances that the sample will produce an extreme z-score and increase the likelihood that you will conclude that a treatment effect does not exist. d. Increase the chances that the sample will produce a z-score near zero and increase the likelihood that you will conclude that a treatment effect exists.
b. Increase the chances that the sample will produce a z-score near zero and increase the likelihood that you will conclude that a treatment effect does not exist.
A sample of n = 16 individuals is selected from a population with µ = 40 and σ = 12, and a treatment is administered to the sample. After treatment, the sample mean is M = 42. How does this sample compare to samples that should be obtained if the treatment has no effect? a. It is an extreme value that would be very unlikely if the treatment has no effect. b. It is much the same as samples that would be obtained if the treatment has no effect. c. There is no way to compare this sample with those that would be obtained if the treatment had no effect. d. The mean is noticeably larger than would be expected if the treatment has no effect but it is not quite an extreme sample.
b. It is much the same as samples that would be obtained if the treatment has no effect.
A random sample of n = 36 scores is selected from a population. Which of the following distributions will be normal? a. Neither the sample, the population, nor the distribution of sample means will be normal. b. The distribution of sample means for all samples of size n = 36 will form a normal distribution. c. The scores in the sample will form a normal distribution. d. The scores in the population will form a normal distribution
b. The distribution of sample means for all samples of size n = 36 will form a normal distribution.
The distribution of sample means is the set of means for all of the possible random samples of a specific size selected from a population and the mean of the distribution of sample means is called the expected value of M. How is the expected value of M related to the size of the sample? a. The larger the sample, the bigger the expected value of M. b. The expected value of M is constant and does not depend on the size of the sample. c. The larger the sample, the smaller the expected value of M. d. The expected value of M varies randomly and is not related to the size of the sample.
b. The expected value of M is constant and does not depend on the size of the sample.
In general, how is the distance between a sample mean and the population mean related to the size of the sample? a. The larger the sample, the bigger the difference. b. The larger the sample, the smaller the distance. c. The difference is constant and does not depend on the size of the sample. d. The difference varies randomly and is not related to the size of the sample.
b. The larger the sample, the smaller the distance.
A researcher administers a treatment to a sample of n = 25 participants and uses a hypothesis test to evaluate the effect of the treatment. The hypothesis test produces a z-score of z = 1.77. Assuming that the researcher is using a two-tailed test, a. Cannot answer without additional information. b. The researcher should fail to reject H0 with either α = .05 or α = .01. c. The researcher should reject the null hypothesis with either α = .05 or α = .01. d. The researcher should reject the null hypothesis with α = .05 but not with α = .01.
b. The researcher should fail to reject H0 with either α = .05 or α = .01.
A researcher expects a treatment to produce an increase in the population mean. The treatment is evaluated using a one-tailed hypothesis test, and the test produces z = −1.85. Based on this result, what is the correct statistical decision? a. The researcher should reject the null hypothesis with either α = .05 or α = .01. b. The researcher should fail to reject H0 with either α = .05 or α = .01. c. Cannot answer without additional information d. The researcher should reject the null hypothesis with α = .05 but not with α = .01.
b. The researcher should fail to reject H0 with either α = .05 or α = .01.
A sample of n = 25 individuals is selected from a population with µ = 80 and a treatment is administered to the sample. In a hypothesis test, a researcher uses a z-score to compare the mean for the treated sample with the distribution of means that would be obtained if the treatment had no effect. In this situation, what is the implication of a z-score near zero? a. The sample mean is close to 80 and suggests that the treatment has an effect b. The sample mean is close to 80 and suggests that the treatment has no effect c. The sample mean is far from 80 and suggests that the treatment has no effect
b. The sample mean is close to 80 and suggests that the treatment has no effect
In a hypothesis test, researchers determine which sample means are very unlikely to be obtained if the treatment has no effect by using a very small probability called the alpha level (α level) to define "very unlikely." What is the consequence of decreasing the alpha from α = .05 to α = .01? a. None of the other options is a consequence of decreasing alpha. b. You decrease the likelihood that you will obtain a very unlikely sample and increase the likelihood that you will conclude that the treatment has no effect. c. You increase the likelihood that you will obtain a very unlikely sample and increase the likelihood of concluding that the treatment does not have an effect. d. You increase the likelihood that you will obtain a very unlikely sample and increase the likelihood of concluding that the treatment has an effect.
b. You decrease the likelihood that you will obtain a very unlikely sample and increase the likelihood that you will conclude that the treatment has no effect.
Cohen's d is used to describe the size of a treatment effect by measuring the size of the mean difference divided by the standard deviation. A treatment is administered to a sample selected from a population with a mean of µ = 80 and a standard deviation of σ = 10. After treatment, the sample mean is M = 85. Based on this information, the effect size as measured by Cohen's d is _____. a. impossible to calculate without more information b. d = 0.50 c. d = 5.00 d. d = 2.00
b. d = 0.50
The final step of hypothesis testing is to _____. a. collect the sample data and compute the test statistic b. make a statistical decision about the null hypothesis c. state the hypotheses and select an alpha level d. locate the values associated with the critical region
b. make a statistical decision about the null hypothesis
A random sample is selected from a population with a standard deviation of σ = 20. If the sample mean has a standard error of 2 points, how many scores are in the sample? a. n = 25 A random sample is selected from a population with a standard deviation of σ = 20. If the sample mean has a standard error of 2 points, how many scores are in the sample? a. n = 25 b. n = 100 c. n = 10 d. n = 5
b. n = 100
Which of the following samples would probably have the greatest distance between the sample mean and the population mean? a. n = 100 scores from a population with σ = 10 b. n = 25 scores from a population with σ = 20 c. n = 100 scores from a population with σ = 20 d. n = 25 scores from a population with σ = 10
b. n = 25 scores from a population with σ = 20
By selecting a smaller alpha level, a researcher is ________. a. attempting to make it easier to reject H0 b. reducing the risk of a Type I error c. All of the options are consequences of selecting a smaller alpha level. d. better able to detect a treatment effect
b. reducing the risk of a Type I error
The first step of hypothesis testing is to _____. a. make a statistical decision about the null hypothesis b. state a hypothesis about the unknown population c. locate the values associated with the critical region d. compute the test statistic for the sample
b. state a hypothesis about the unknown population
As sample size increases, the expected value of M ________. a. also increases b. stays constant c. decreases d. The expected value changes but not in any predictable way when sample size increases.
b. stays constant
The critical region for a hypothesis test is defined as sample outcomes that are very unlikely to be obtained if the null hypothesis is true. In a normal distribution, what z-score values would form the boundaries for the critical region if "very unlikely" is defined as a probability of 0.05 or smaller? a. z = +2.58 and z = -2.58 b. z = +1.96 and z = -1.96 c. z = +1.28 and z = -1.28 d. z = +1.65 and z = -1.65
b. z = +1.96 and z = -1.96
A random sample of n = 4 scores is obtained from a population with σ = 10. If the sample mean is 10 points greater than the population mean, what is the z-score for the sample mean? a. +10.00 b. Cannot be determined without knowing the population mean c. +2.00 d. +1.00
c. +2.00
A random sample of n = 4 scores is obtained from a normal population with μ = 20 and σ = 4. What is the probability of obtaining a mean greater than M = 22 for this sample? a. 1.00 b. 0.3085 c. 0.1587 d. 0.50
c. 0.1587
A random sample of n = 9 scores is selected from a normally distributed population with μ = 40 and σ = 18. What is the probability that the sample mean will be greater than 43? a. 0.1587 b. 0.4325 c. 0.3085 d. 0.0668
c. 0.3085
A random sample of n = 25 scores is selected from a normally distributed population with μ = 500 and σ = 100. What is the probability that the sample mean will be greater than 490? a. 0.8413 b. 0.9938 c. 0.6915 d. 0.5398
c. 0.6915
A sample of n = 4 scores is selected from a population with μ = 100 and σ = 20. If the sample mean is M = 110, what is the z-score for this sample mean? a. 4.00 b. 2.00 c. 1.00 d. 0.50
c. 1.00
For a population with μ = 80 and σ = 20, the distribution of sample means based on n = 4 will have a standard error of ________. a. 80 b. 20 c. 10 d. 5
c. 10
For a particular population, the standard distance between a sample mean and the population mean is 5 points for samples of n = 4 scores. What would the standard distance be for samples of n = 25 scores? a. 4 points b. 5 points c. 2 points d. 1 point
c. 2 points
The standard distance between a sample mean and the population mean is 12 points for samples of n = 4 scores selected from a population with a mean of µ = 50. What is the standard deviation for the population? a. 3 b. 6 c. 24 d. 48
c. 24
For a particular population a sample of n = 4 scores has a standard error of 10. For the same population, a sample of n = 16 scores would have a standard error of ________. a. 20 b. 2.5 c. 5 d. 10
c. 5
A treatment is administered to a sample selected from a population with a mean of μ = 80 and a standard deviation of σ = 10. After treatment, the effect size is measured by computing Cohen's d, and a value of d = 0.60 is obtained. Based on this information, what is the mean for the treated sample? a. 60 b. Cannot be determined without additional information c. 86 d. 6
c. 86
If other factors are held constant, then how does the size of the standard deviation affect the likelihood of rejecting the null hypothesis and the value for Cohen's d? a. A larger standard deviation increases the likelihood of rejecting the null hypothesis but decreases the value of Cohen's d. b. A larger standard deviation increases the likelihood of rejecting the null hypothesis and increases the value of Cohen's d. c. A larger standard deviation decreases the likelihood of rejecting the null hypothesis and decreases the value of Cohen's d. d. A larger standard deviation decreases the likelihood of rejecting the null hypothesis but increases the value of Cohen's d
c. A larger standard deviation decreases the likelihood of rejecting the null hypothesis and decreases the value of Cohen's d.
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? a. Fail to reject H1. b. Reject H0. c. Fail to reject H0. d. Reject H1.
c. Fail to reject H0.
If other factors are held constant, what is the effect of increasing the number of scores in the sample? a. It decreases the size of the z-score (closer to 0) and increases the likelihood of rejecting the null hypothesis. b. It decreases the size of the z-score (closer to 0) and decreases the likelihood of rejecting the null hypothesis. c. It increases the size of the z-score (farther from 0) and increases the likelihood of rejecting the null hypothesis. d. It increases the size of the z-score (farther from 0) and decreases the likelihood of rejecting the null hypothesis.
c. It increases the size of the z-score (farther from 0) and increases the likelihood of rejecting the null hypothesis.
For a normal population with µ = 80 and σ = 20 which of the following samples is least likely to be obtained? a. M = 84 for a sample of n = 4 b. M = 84 for a sample of n = 25 c. M = 88 for a sample of n = 25 d. M = 88 for a sample of n = 4
c. M = 88 for a sample of n = 25
For a sample selected from a normal population with µ = 100 and σ = 15, which of the following would be the most extreme and unrepresentative? a. M = 95 for a sample of n = 9 scores. b. M = 90 for a sample of n = 9 scores. c. M = 90 for a sample of n = 25 scores. d. M = 95 for a sample of n = 25 scores.
c. M = 90 for a sample of n = 25 scores.
A sample of n = 25 individuals is selected from a population with µ = 80 and a treatment is administered to the sample. In a hypothesis test, a researcher uses a z-score to compare the mean for the treated sample with the distribution of means that would be obtained if the treatment had no effect. In this situation, what is the implication of an extreme z-score like +3 or z = -3? a. The sample mean is close to 80 and suggests that the treatment has no effect b. The sample mean is far from 80 and suggests that the treatment has no effect c. The sample mean is far from 80 and suggests that the treatment has an effect d. The sample mean is close to 80 and suggests that the treatment has an effect
c. The sample mean is far from 80 and suggests that the treatment has an effect
What is a likely outcome for a hypothesis test if a treatment has a very small effect? a. correctly reject the null hypothesis b. correctly fail to reject the null hypothesis c. a Type II error d. a Type I error
c. a Type II error
Just as standard deviation measures the standard distance between a score and the population mean, the standard error measures the standard distance between a sample mean and the population mean. For samples selected from a population with µ = 100 and σ = 15, which of the following has the smallest standard error? a. a sample of n = 4 scores b. The three samples all have the same standard error. c. a sample of n = 25 scores d. a sample of n = 16 scores
c. a sample of n = 25 scores
Which combination of factors will increase the chances of rejecting the null hypothesis? a. a large standard error and a small alpha level b. a large standard error and a large alpha level c. a small standard error and a large alpha level d. a small standard error and a small alpha level
c. a small standard error and a large alpha level
A hypothesis test is _____. a. a descriptive technique that allows researchers to describe a population b. a descriptive technique that allows researchers to describe a sample c. an inferential technique that uses the data from a sample to draw inferences about a population d. an inferential technique that uses information about a population to make predictions about a sample
c. an inferential technique that uses the data from a sample to draw inferences about a population
As sample size increases, the standard error of M ________. a. also increases b. The standard error changes but not in any predictable way when sample size increases. c. decreases d. stays constant
c. decreases
If two samples of exactly the same size are selected from the same population, then the two sample means will have ________. a. exactly the same expected value b. exactly the same standard error c. exactly the same expected value and exactly the same standard error d. None of the other 3 choices is correct.
c. exactly the same expected value and exactly the same standard error
A Type I error means that a researcher has ________. a. correctly concluded that a treatment has no effect b. correctly concluded that a treatment has an effect c. falsely concluded that a treatment has an effect d. falsely concluded that a treatment has no effect
c. falsely concluded that a treatment has an effect
A random sample is selected from a population with μ = 80 and σ = 10. To ensure a standard error of 2 points or less, the sample size should be at least ________. a. n = 10 b. It is impossible to obtain a standard error less than 2 for any sized sample. c. n = 25 d. n = 5
c. n = 25
The critical region for a hypothesis test consists of ________. a. outcomes that have a very low probability whether or not the null hypothesis is true b. outcomes that have a high probability whether or not the null hypothesis is true c. outcomes that have a very low probability if the null hypothesis is true d. outcomes that have a high probability if the null hypothesis is true
c. outcomes that have a very low probability if the null hypothesis is true
If a sample is selected from a normal population, then the probability that the sample mean will have a z-score greater than z = 2.00 is ________. a. p = .9772 b. p = .0456 c. p = .0228 d. cannot determine without knowing the sample size
c. p = .0228
Which of the following defines the power of a hypothesis test? a. the probability of supporting a false null hypothesis b. the probability of supporting true null hypothesis c. the probability of rejecting a false null hypothesis d. the probability of rejecting a true null hypothesis
c. the probability of rejecting a false null hypothesis
A sample of n = 25 individuals is selected from a population with µ = 80 and a treatment is administered to the sample. If the treatment has a large effect, then _____. a. the sample mean should be close to 80 and should lead you to reject the null hypothesis b. the sample mean should be close 80 and should lead you to fail to reject the null hypothesis c. the sample mean should be very different from 80 and should lead you to reject the null hypothesis d. the sample mean should be very different from 80 and should lead you to fail to reject the null hypothesis
c. the sample mean should be very different from 80 and should lead you to reject the null hypothesis
A random sample of n = 9 scores is obtained from a population with μ = 50 and σ = 9. If the sample mean is M = 53, what is the z-score corresponding to the sample mean? a. Cannot determine without additional information b. z = 3.00 c. z = 1.00 d. z = 0.33
c. z = 1.00
A sample is selected from a population with a mean of µ = 45 and a treatment is administered to the sample. If the treatment is expected to produce a decrease in the scores, then what would be the null hypothesis for a directional hypothesis test? a. M ≥ 45 b. M ≤ 45 c. µ ≥ 45 d. µ ≤ 45
c. µ ≥ 45
A random sample of n = 4 scores is selected from a normally distributed population with μ = 80 and σ = 10. What is the probability that the sample mean will be greater than 90? a. 0.1587 b. 0.9778 c. 0.3085 d. 0.0228
d. 0.0228
A sample of n = 25 scores is selected from a population with a mean of μ = 80 and a standard deviation of σ = 10, and a treatment is administered to the sample. After treatment, the sample mean is found to be M = 84. If effect size is measured by computing Cohen's d, then what value will be obtained for d? a. 4.00 b. 4/2 = 2.00 c. 4/100 = 0.04 d. 4/10 = 0.40
d. 4/10 = 0.40
If random samples, each with n = 16 scores, are selected from a normal population with µ = 80 and σ = 20, and the mean is calculated for each sample, then the average distance between M and µ would be _____. a. 0.80 points b. 100 points c. 20 points d. 5 points
d. 5 points
If all the possible random samples of size n = 4 are selected from a population with µ = 80 and σ = 10 and the mean is computed for each sample, then what value will be obtained for the mean of all the sample means? a. 80/4 = 20 b. 80(4) = 320 c. Around 80 but probably not equal to 80. d. 80
d. 80
A random sample of n = 4 scores is selected from a normally distributed population with μ = 100 and σ = 20. What range of sample means would be expected 80% of the time? a. 93.6 to 106.4 b. 95.8 to 104.2 c. 91.6 to 108.4 d. 87.2 to 112.8
d. 87.2 to 112.8
If other factors are held constant, then how does sample size affect the likelihood of rejecting the null hypothesis and the value for Cohen's d? a. A larger sample decreases the likelihood of rejecting the null hypothesis but has no effect on the value of Cohen's d. b. A larger sample increases the likelihood of rejecting the null hypothesis and increases the value of Cohen's d. c. A larger sample increases the likelihood of rejecting the null hypothesis but decreases the value of Cohen's d. d. A larger sample increases the likelihood of rejecting the null hypothesis but has no effect on the value of Cohen's d.
d. A larger sample increases the likelihood of rejecting the null hypothesis but has no effect on the value of Cohen's d.
In a hypothesis test, a Type I error means that a researcher has decided that the treatment has an effect when, in fact, it does not. What does a Type II error mean? a. A researcher has falsely concluded that a treatment has an effect b. A researcher has correctly concluded that a treatment has an effect c. A researcher has correctly concluded that a treatment has no effect d. A researcher has falsely concluded that a treatment has no effect
d. A researcher has falsely concluded that a treatment has no effect
The null hypothesis _____. a. generally states that there is no effect, no change, or no difference b. concerns a population with an unknown mean c. is denoted by the symbol Ho d. All of the other choices are correct.
d. All of the other choices are correct.
In a hypothesis test, an extreme z-score value, like z = +3 or z = +4, ________. a. means that you should probably reject the null hypothesis b. is strong evidence of a statistically significant effect c. is probably in the critical region d. All of the other options are correct.
d. All of the other options are correct
A sample of n = 4 individuals is selected from a population with µ = 80 and σ = 5, and a treatment is administered to the sample. If the treatment really does have an effect, then what would be the effect of increasing the sample size to n = 25? a. Increase the chances that the sample will produce an extreme z-score and increase the likelihood that you will conclude that a treatment effect does not exist. b. Increase the chances that the sample will produce a z-score near zero and increase the likelihood that you will conclude that a treatment effect exists. c. Increase the chances that the sample will produce a z-score near zero and increase the likelihood that you will conclude that a treatment effect does not exist. d. Increase the chances that the sample will produce an extreme z-score and increase the likelihood that you will conclude that a treatment effect exists.
d. Increase the chances that the sample will produce an extreme z-score and increase the likelihood that you will conclude that a treatment effect exists.
Under what circumstances is the distribution of sample means normal? a. It is always normal. b. It is normal only if the population distribution is normal. c. It is normal only if the sample size is greater than 30. d. It is normal if the population distribution is normal or if the sample size is greater than 30.
d. It is normal if the population distribution is normal or if the sample size is greater than 30.
The standard error of M provides a measure of ________. a. the maximum possible discrepancy between M and μ b. the minimum possible discrepancy between M and μ c. the exact amount of discrepancy between each specific M and μ d. None of the other 3 choices is correct.
d. None of the other 3 choices is correct.
In a hypothesis test, a z-score value near zero ________. a. is probably in the critical region b. is strong evidence of a statistically significant effect c. means that you should probably reject the null hypothesis d. None of the other options are correct
d. None of the other options are correct
A research report summarizes the results of the hypothesis test by stating, "z = 2.13, p < .05." Which of the following is a correct interpretation of this report? a. The null hypothesis was rejected and the probability of a Type II error is less than .05. b. The null hypothesis was not rejected and the probability of a Type II error is less than .05. c. The null hypothesis was not rejected and the probability of a Type I error is less than .05. d. The null hypothesis was rejected and the probability of a Type I error is less than .05.
d. The null hypothesis was rejected and the probability of a Type I error is less than .05.
A researcher administers a treatment to a sample of n = 25 participants and uses a hypothesis test to evaluate the effect of the treatment. The hypothesis test produces a z-score of z = 2.37. Assuming that the researcher is using a two-tailed test, a. The researcher should fail to reject H0 with either α = .05 or α = .01. b. The researcher should reject the null hypothesis with either α = .05 or α = .01. c. Cannot answer without additional information. d. The researcher should reject the null hypothesis with α = .05 but not with α = .01.
d. The researcher should reject the null hypothesis with α = .05 but not with α = .01.
If all the possible random samples of size n = 4 are selected from a population with µ = 80 and σ = 10 and the mean is computed for each sample, then how will the variance for the set of sample means compare with the variance for the scores in the population? a. The variance for the means will be larger than the variance for the scores. b. The variance for the means will be four times larger than the variance for the scores. c. The two variances will be equal. d. The variance for the means will be smaller than the variance for the scores.
d. The variance for the means will be smaller than the variance for the scores.
When does a researcher risk a Type I error? a. anytime H1 is rejected b. anytime the decision is "fail to reject H0" c. All of the other options are correct. d. anytime H0 is rejected
d. anytime H0 is rejected
The probability of committing a Type I error ________. a. is determined solely by the size of the treatment effect b. cannot be controlled by the experimenter c. is determined by the value for beta (β) that one selects d. is determined by the level of significance (α) that one chooses
d. is determined by the level of significance (α) that one chooses
Which of the following samples would produce a standard error of 2 points? a. n = 100 scores from a population with σ = 10 b. n = 5 scores from a population with σ = 20 c. n = 5 scores from a population with σ = 10 d. n = 100 scores from a population with σ = 20
d. n = 100 scores from a population with σ = 20
For samples selected from a population with µ = 40 and σ = 10, what sample size is necessary to make the standard distance between the sample mean and the population mean equal to 2 points? a. n = 5 b. n = 2 c. n = 100 d. n = 25
d. n = 25
Which of the following samples would have the largest standard error? a. n = 25 scores from a population with σ = 10 b. n = 100 scores from a population with σ = 10 c. n = 100 scores from a population with σ = 20 d. n = 25 scores from a population with σ = 20
d. n = 25 scores from a population with σ = 20
In hypothesis tests, what is measured by the standard error in the denominator of the z-score? a. variability among population means b. the size of the critical region c. the size of the treatment effect d. the amount of difference between the sample mean and the population mean that is reasonable to expect just by chance
d. the amount of difference between the sample mean and the population mean that is reasonable to expect just by chance
A sample of n = 25 individuals is selected from a population with μ = 80 and a treatment is administered to the sample. If the treatment has no effect, then a. the sample mean should be very different from 80 and should lead you to fail to reject the null hypothesis. b. the sample mean should be very different from 80 and should lead you to reject the null hypothesis. c. the sample mean should be close to 80 and should lead you to reject the null hypothesis. d. the sample mean should be close to 80 and should lead you to fail to reject the null hypothesis.
d. the sample mean should be close to 80 and should lead you to fail to reject the null hypothesis.
A sample is selected from a population with a mean of μ = 60 and a treatment is administered to the individuals in the sample. For this situation, what is the correct statement of the null hypothesis concerning the effect of the treatment on the population? a. M = 60 b. M ≠ 60 c. μ ≠ 60 d. μ = 60
d. μ = 60
A population is known to have a mean of μ = 50. A treatment is expected to increase scores for individuals in this population. If the treatment is evaluated using a one tailed hypothesis, then the null hypothesis would state ________. a. μ ≥ 50 b. μ < 50 c. μ > 50 d. μ ≤ 50
d. μ ≤ 50
sampling error
discrepancy that occurs naturally between a statistic and its corresponding population parameter
standard error of M
formula provides a measure of the average distance between sample mean and population mean
alpha level
level of significance
expected value of M
population's mean is equal to the mean of the sample means
law of large numbers
rule states that bigger sizes yield closer approximations of the population mean
sampling distribution
the distribution of values taken by the statistic in all possible samples of the same size from the same population
critical region
the area in the tails of the comparison distribution in which the null hypothesis can be rejected
distribution of sample means
the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population
Type 2 error
the mistake occurs when a researcher falls to reject a null hypothesis that's really false
type 1 error
the mistake occurs when a researcher rejects a null hypothesis that is actually true
mode
the most frequently occurring score(s) in a distribution
power
the probability that a test will correctly reject a false null hypothesis
alternative hypothesis
the supposition Staes there's a change, difference, or relationship in the general population
null hypothesis
the supposition states that in the general population there's no change, difference, or relationship
