Experimental Exam 1
You would rather have a z score of +1, -1, 0, or -2 on your exam.
+1
For a population with m = 70 and s = 8, what is the z-score corresponding to X = 82?
+1.50
What z-score corresponds to a score that is above the mean by 2 standard deviations?
+2
For a population with m = 80 and s = 6, what is the z-score corresponding to X = 68?
-2.00
A sample of n = 20 scores is transformed into z-scores. What is the mean for the set of 20 z-scores?
0
For any distribution, what is the z-score corresponding to the mean?
0
The mean and the standard deviation of a z distribution.
0, 1
A random sample of n = 4 scores is obtained from a normal population with µ = 30 and σ = 8. What is the probability that the sample mean will be smaller than M = 22?
0.0228
A normal distribution has a mean of µ = 40 with σ = 10. If a vertical line is drawn through the distribution at X = 55, what proportion of the scores are on the right side of the line?
0.0668
What proportion of a normal distribution is located in the tail beyond z = 1.50?
0.0668
What proportion of a normal distribution is located in the tail beyond z = -1.00?
0.1587
A normal distribution has a mean of µ = 40 with σ = 10. If a vertical line is drawn through the distribution at X = 35, what proportion of the scores are on the left side of the line?
0.3085
A random sample of n = 9 scores is obtained from a normal population with µ = 40 and σ = 18. What is the probability that the sample mean will be greater than M = 43?
0.3085
What proportion of a normal distribution is located between the mean and z = 1.40?
0.4192
What is the mode for the following sample of n = 8 scores? Scores: 0, 1, 1, 1, 2, 2, 3, 3
1
z score for a one-tailed test when alpha = .05
1.645
A population of N = 100 scores has m = 30 and s = 4. What is the population variance?
16
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?
2 points
z score for a one-tailed test when alpha = .01
2.3
Percentage of the distribution in each critical region when alpha = .05 when using a two-tail test.
2.5%
A sample of n = 4 scores is selected from a population with μ = 40 with σ = 8, and the sample mean is M = 43. What is the standard error for the sample mean?
4
What is the mean for the following sample of scores? Scores: 1, 4, 5, 6
4
A sample of n = 4 scores is selected from a population with μ = 40 with σ = 8, and the sample mean is M = 43. What is the expected value for the sample mean?
40
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?
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?
6
What is the median for the following set of scores? Scores: 1, 2, 6, 11, 17
6
What is the value of (SX)2 for the scores 1, 5, 2?
64
What is the value of SX + 1 for the scores 1, 0, 2, 4?
8
If random samples, each with n = 9 scores, are selected from a normal population with µ = 80 and σ = 36, what is the expected value for the distribution of sample means?
80
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 ____.
80;5
For a population with m = 100 and s = 20, what is the X value corresponding to z = -0.75?
85
Percent chance that we will get a score in the likely range when alpha = .05
95%
A sample is selected from a population with a mean of µ = 40. If the sample mean is M = 45, which of the following combinations would make the sample mean an extreme, unrepresentative value for the population?
A large sample and a small population standard deviation
What is measured by the denominator of the z-score test statistic?
A likely distance between M and µ that would be expected if H0 was true
A sample is obtained from a population with μ = 100 and σ = 20. Which of the following samples would produce the most extreme z-score?
A sample of n = 100 scores with M = 104
What is the effect of decreasing the alpha level (for example, from α = .05 to α = .01)?
All of the other options are results of decreasing alpha.
Which of the following accurately describes a hypothesis test?
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
With a = .05, how are the boundaries for the critical region determined?
Boundaries are drawn so there is 2.5% (.025) in each tail of the distribution.
Which of the following will increase the power of a statistical test?
Change the sample size from n = 25 to n = 100
What is the consequence of a Type I error?
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 no effect when it really does
Distribution of scores on the DV has to have this shape.
DV normally distributed
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, what is the correct statistical decision?
Fail to reject H0
Which of the following is an accurate definition of a Type II error?
Failing to reject a false null hypothesis
Under what circumstances can a very small treatment effect still be significant?
If the sample size (n) is very large
For a hypothesis test evaluating the effect of a treatment on a population mean, what basic assumption is made concerning the treatment effect?
If there is a treatment effect, it will add (or subtract) a constant to each score.
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
For a normal population with µ = 40 and σ = 10 which of the following samples is least likely to be obtained?
M is less than 36 for a sample of n = 100
A random sample of n = 6 scores is selected from a population. Which of the following distributions will definitely be normal?
None of the distributions (the sample, population, or distribution of sample means) will definitely be normal.
What symbol is used to identify the standard error of M?
O(theta)m
Which of the following accurately describes the critical region?
Outcomes with a very low probability if the null hypothesis is true
Which of the following accurately describes the proportions in the tails of a normal distribution?
Proportions in both tails are less than 0.50.
Which of the following accurately describes the proportions in the tails of a normal distribution?
Proportions in both tails are positive.
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
Which of the following is an accurate definition of a Type I error?
Rejecting a true null hypothesis
When you reject H0, even though it is true, you are saying the IV had/didn't have an effect when in reality it really did/didn't.
The IV had an effect, but it really didn't
What is measured by the numerator of the z-score test statistic?
The actual distance between M and µ
Which of the following is a consequence of increasing variability?
The distance from one score to another tends to increase, and a single score tends to provide a less accurate representation of the entire distribution.
What is the expected value of M?
The mean of the distribution of sample means
Which of the following is directly addressed by the null hypothesis?
The population after treatment
Which of the following is an accurate definition for the power of a statistical test?
The probability of rejecting a false null hypothesis
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.
What is the standard error of M?
The standard deviation of the distribution of sample mean
A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a hypothesis test, what does the alternative hypothesis (H1) say about the treatment?
The treatment causes a change in the scores.
A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a hypothesis test, what does the null hypothesis (H0) say about the treatment?
The treatment has no effect on the scores
A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a hypothesis test, what does the null hypothesis (H0) say about the treatment?
The treatment has no effect on the scores.
For a population, a deviation score is computed as X - m.
True
When is there a risk of a Type I error?
Whenever H0 is rejected
When is there a risk of a Type II error?
Whenever the decision is "fail to reject H0"
You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis. If the treatment actually has no effect, which of the following is true?
You have made a Type I error.
You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to fail to reject the null hypothesis. If the treatment actually does have an effect, which of the following is true?
You have made a Type II error.
You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis. If the treatment actually does have an effect, which of the following is true?
You have made the correct decision.
You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis. Which of the following is true?
You might have made a Type I error, but the probability is less than 5%
For any population of scores, regardless of form, the sampling distribution of the mean will approach this shape as N (sample size) gets larger.
a normal distribution
What is the first step to be performed when computing S(X + 2)2?
add 2 points to each score
The probability of making a type I error.
alpha (a)
The probability of obtaining an unlikely sample mean when H0 is true.
alpha level (level of significance, p value)
says there is a relationship between the IV and DV.
alternative hypothesis
mexperimental group ¹ mpopulation / control group
alternative hypothesis for a two-tailed test
What position in the distribution corresponds to a z-score of z = -1.00?
below the mean by a distance equal to 1 standard deviation
A variable that affects the results of a study, but is *not* a variable of interest in the study.
confound
The area in the tails of the sample distribution where sample values are very unlikely to occur if the H0 is true
critical region (rejection region)
The variable that is being measured to determine whether it changes across levels of the IV
dependent variable
The collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population.
distribution of sample means
A tentative statement about the relationship between your IV and DV.
hypothesis
After measuring two individuals, a researcher can say that Tom's score is 4 points higher than Bill's. The measurements must come from a(n) _______ scale.
interval or ratio
What happens to the standard error of M as sample size increases?
it decreases
u
mean of the population
The mean of the sampling distribution of means will be equal to this.
mean of the population (u)
M
mean of the sample
Two types of hypotheses.
null and alternative
symbolized by H0
null hypothesis
mexperimental group ¬< mpopulation / control group
null hypothesis for a one-tailed test
Determining the class standing (1st, 2nd, and so on) for the graduating seniors at a high school would involve measurement on a(n) _____ scale of measurement.
ordinal
Using letter grades (A, B, C, D, and E) to classify student performance on an exam is an example of measurement on a(n) _______ scale of measurement.
ordinal
z score for a two-tailed test when alpha = .05
plus or minus 1.96
z score for a two-tailed test when alpha = .01
plus or minus 2.575
z score for a two-tailed test when alpha = .001
plus or minus 3.30
What kind of measurement scale is necessary to conclude that one score is twice a big as another?
ratio
DV has to be measured on one of these two scales.
ratio or interval scale
Decision made about H0 when the absolute value of zobtained > the absolute value of zcritical
reject
Decision made about H0 when zobt is in the critical region.
reject
Decision made about H0 when mexperimental group = mpopulation / control group
retain
The average verbal SAT score for the entire class of entering freshmen is 530. However, if you select a sample of 20 freshmen and compute their average verbal SAT score you probably will not get exactly 530. What statistical concept is used to explain the natural difference that exists between a sample mean and the corresponding population mean?
sampling error
Two assumptions for all parametric tests.
scores on the DV are normally distributed scores in the DV are measured on a ration or interval scale
What is the final step to be performed in the mathematical expression, (SX)2?
square the sum of the scores
sigma
standard deviation of the population
Measures the average distance between a sample mean and the population mean (m).
standard error of the mean
theta x bar
standard error of the mean
capital sigma
sum of
What is the final step to be performed when computing S(X - 2)2?
sun the squared values
For an experiment comparing two methods of teaching social skills training to autistic children, the independent variable is _______ and the dependent variable is _______.
teaching methods; the social skills that are learned
One piece of information that has to be known about the population.
the SD of the population in that other condition is known
What additional information is obtained by measuring two individuals on an ordinal scale compared to a nominal scale?
the direction of the difference
A recent study reports that students who just finished playing a prosocial video game were more likely to help others than students who had played a neutral or antisocial game. For this study, what is the independent variable?
the kind of game given to the students
One piece of information that has to be known about the population.
the mean of the population in some other condition if the IV (e/no mental activity) is known
The standard deviation of the sampling distribution of means is called this.
the standard error of the mean
A distribution based on a mathematical model.
theoretical distribution
Which of the following symbols identifies the population standard deviation?
theta
Rejecting the H0 when the H0 is true.
type I error
Retaining the H0 when the H0 is false.
type II error
Under what circumstances is the computational formula preferred over the definitional formula when computing SS, the sum of the squared deviations, for a sample?
when the sample mean is not a whole number
Also called standardized scores.
z score
For a population with a standard deviation of s = 10, what is the z-score corresponding to a score that is 5 points below the mean?
z= -0.50
For a population with a standard deviation of s = 6, what is the z-score corresponding to a score that is 12 points above the mean?
z= 2
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= 2.00
A sample of n = 9 scores is obtained from a population with μ = 70 and σ = 18. If the sample mean is M = 76, what is the z-score for the sample mean?
z=1.00
For a normal population with a mean of µ = 80 and a standard deviation of σ = 10, what is the probability of obtaining a sample mean greater than M = 75 for a sample of n = 25 scores?
0.9938
Which combination of factors will produce the largest value for the standard error?
A small sample and a large standard deviation
Even if a treatment has an effect, it is still possible to obtain a sample mean after the treatment that is very similar to the original population mean. What outcome is likely if this happens?
Fail to reject H0 and make a Type II error
What happens to the expected value of M as sample size increases?
It stays constant.
For a normal population with µ = 40 and σ = 10, which of the following samples has the highest probability of being obtained?
M is less than 38 for a sample of n = 4
If a hypothesis test produces a z-score in the critical region, what decision should be made?
Reject the null hypothesis
A researcher conducts a hypothesis test to evaluate the effect of a treatment that is expected to increase scores. The hypothesis test produces a z-score of z = 2.27. If the researcher is using a one-tailed test, what is the correct statistical decision?
Reject the null hypothesis with α = .05 but not with α = .01.
A random sample of n = 60 scores is selected from a population. Which of the following distributions will definitely be normal?
The distribution of sample means will definitely form a normal distribution.
A researcher expects a treatment to increase the scores for individuals in a population. The treatment is evaluated using a one-tailed hypothesis test, and the test produces z = +2.40. Based on this result, what is the correct statistical decision?
The researcher should reject the null hypothesis with either α = .05 or α = .01.
Samples of n = 16 scores are selected from a population. If the distribution of sample means has an expected value of 40 and a standard error of 2, what is the mean and the standard deviation for the population?
µ = 40 and σ = 8
