Psych Stats Exam 2
In a matched-samples t test, the standard error of the mean of difference scores could be calculated by
dividing the standard deviation of difference scores by the square root of the number of difference scores.
In a matched-samples t test, a difference score is obtained by A. subtracting the Before score from the After score. B. subtracting the After score from the Before score. C. dividing After scores by Before scores. D. either a or b, just so long as you are consistent.
either a or b, just so long as you are consistent.
We are most likely to reject a null hypothesis if the test statistic we compute is
extreme numerically
A Type II error refers to
failing to reject a false null hypothesis.
The basic idea behind hypothesis testing
is largely the same across different statistics tests.
What happens to the standard error of the mean as sample size increases?
it decreases
For a population with µ = 80 and σ = 20, the sampling distribution of the sample mean based on N = 16 will have a mean of 80 and a standard error of ____.
5
Samples of size N = 9 are selected from a population with μ = 80 with σ = 18. What is the standard error of the mean?
6
A sampling distribution of a sample statistic describes
the probability of different values of the sample statistic.
The changes of Type I error concerns
the probability of rejecting a true null hypothesis.
The reason why we need to solve for t instead of z in some situations relates to
the sampling distribution of the variance.
If we were to repeat an experiment a large number of times and calculate a statistic such as the mean for each experiment, the distribution of these statistics would be called
the sampling distribution.
The standard error of the mean is
the standard deviation of the sampling distribution of the sample mean.
In a matched-samples t-test, if sample size and standard error of the mean of difference scores are held constant, as the value of the mean difference score decreases...
the t test statistic decreases.
When using the independent-samples t test with large samples, the results will not be accurate if:
the two sample variances differ substantially, and the sample sizes are far from being equal.
In a matched-samples t-test, the degrees of freedom are equal to
N - 1.
When you are using a one-sample t test, the degrees of freedom are
N-1
The degrees of freedom for independent-samples t test is:
N1 + N2 - 2
what value is expected for the t statistic when the null hypothesis is true?
0
Which of the following can be a statement of H1?
A. H1 : µ > 0 B. H1 : µ < 0 C. H1 : µ ≠ 0 D. all of the above
A researcher conducts a repeated-measures study to evaluate a treatment with a sample of N = 16 participants and obtains a t test statistic of t = 1.94. The treatment is expected to increase scores and the sample mean difference shows an increase. Which of the following is the correct decision for a hypothesis test using α = .05? A. Reject the null hypothesis with a one-tailed test but fail to reject with two tails. (when setting group 1 = after and group 2 = before) B. Reject the null hypothesis with either a one-tailed or a two-tailed test. C. Fail to reject the null hypothesis with either a one-tailed or a two-tailed test. (when setting group 1 = before and group 2 = after) D. Fail to reject the null hypothesis with a one-tailed test but reject with two tails.
A. Reject the null hypothesis with a one-tailed test but fail to reject with two tails. (when setting group 1 = after and group 2 = before) C. Fail to reject the null hypothesis with either a one-tailed or a two-tailed test. (when setting group 1 = before and group 2 = after)
When you state a two-tailed test for an experimental treatment that aims to change behavior, what does the appropriate alternative hypothesis state? A. The experimental treatment has no effect on the behavior B. The experimental treatment increased the behavior C. The experimental treatment decreased the behavior D. Both (a) and (b) are included in the two-tailed alternative hypothesis E. Both (b) and (c) are included in the two-tailed alternative hypothesis
Both (b) and (c) are included in the two-tailed alternative hypothesis
A researcher obtains t = 2.35 for a repeated-measures study using a sample of N = 8 participants. Based on this t value, what is the correct decision for a two-tailed test?
Fail to reject the null hypothesis with either α = .05 or α = .01.
What is a Type II error?
Failing to accept the alternative hypothesis when it is true
Which of the following is most likely to represent a statement of the null hypothesis?
H0 : µ = 0
A researcher wishes to use independent-samples t test to test whether the difference between two population means is zero. If the sample means are 106.4 and 99.2, the standard error of the mean difference is 2.3, and the critical value needed to reject the null hypothesis is 2.09, what should the researcher decide about the difference between the two population means?
It is not equal to 0.0.
In general, if the variance of the difference scores increases, then what will happen to the value of the t-statistic?
It will decrease (move toward 0 at the center of the distribution).
If other factors are held constant, what is the effect of increasing the sample size?
It will decrease the estimated standard error and increase the likelihood of rejecting H0.
If other factors are held constant, what is the effect of increasing the sample variance?
It will increase the estimated standard error and decrease the likelihood of rejecting H0.
A researcher wishes to test the theory that men and women differ on a measure of personality. The researcher draws a sample of 35 men and a sample of 35 women. The sample means on the personality measure are: men, 46.7; women, 51.4. Using the .05 criterion of significance, the critical value needed to reject the null hypothesis is 2.03. If the standard error of the mean difference is 2.0, what should the researcher decide and what error might be made?
Reject the null hypothesis—Type I error.
What is a Type I error?
Rejecting the null hypothesis when it is true
A researcher wishes to test the theory that men and women differ on a measure of personality. The researcher draws a sample of 35 men and a sample of 35 women. The sample means on the personality measure are: men, 46.7; women, 51.4. Using the .05 criterion of significance, the critical value needed to reject the null hypothesis is 2.03. If the standard error of the mean difference is 4.0, what should the researcher decide, and what error might be made?
Retain the null hypothesis—Type II error.
A researcher wishes to test the theory that men and women differ on a measure of personality. The researcher draws a sample of 35 men and a sample of 35 women. The sample means on the personality measure are: men, 46.7; women, 51.4. Why can't the researcher conclude, just by looking at the difference of 4.7 between the two sample means, that the difference between the population means is not zero?
Sampling error may have caused one or both samples to be unrepresentative of the corresponding populations.
When you state a one-tailed test for an experimental treatment that aims to decrease anxiety, what does the appropriate null hypothesis state?
The experimental treatment has the opposite effect what was expected
Which of the following statements is true about t distributions?
The larger the sample size, the more a t distribution resembles a standard normal distribution.
Which of the following does NOT directly affect the magnitude of t?
The population variance (σ2).
An assumption behind the use of a one-sample t test is that
the population is normally distributed.
The central limit theorem tells us that, as sample size increases, the sample mean of a variable is more likely to be equal to its population mean. Besides increasing sample size, which condition is also necessary for this to be true?
There is no other condition necessary for this to be true.
Suppose that we know that the sample mean is 18 and the population standard deviation is 3. We want to test the null hypothesis that the population mean is 20. In this situation we would
We cannot solve this problem without knowing the sample size.
All of the following increase the magnitude of the t-statistic/chances of rejecting H0 EXCEPT: A. a greater difference between the sample mean and the population mean. B. an increase in sample size. C. a decrease in sample variance. D. a smaller significance level (α).
a smaller significance level (α).
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
As the size of the samples increases, the standard error of the mean difference in the independent-samples t test:
becomes smaller
To look at the sampling distribution of the mean we would
calculate many means and plot them.
In one-sample t tests, we
compare one sample mean against a population mean.
The importance of the underlying assumption of normality behind a one-sample means test
depends on the sample size.
The standard deviation of a distribution of means is sometimes called "the standard error of the mean," or the "standard error," because
it represents the degree to which particular sample means are "in error" as estimates of the population mean.
If we set α = .05, we often reject the null hypothesis if the probability of our result, given that the null hypothesis were true, is
less than .05
A researcher wishes to test the theory that men and women differ on a measure of personality. The researcher draws a sample of 35 men and a sample of 35 women. The sample means on the personality measure are: men, 46.7; women, 51.4.If the statistical analysis indicates that the null hypothesis should be rejected, the researcher should conclude that:
men and women are not the same in the population on this personality measure.
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
Most research is undertaken with the hope of
rejecting the null hypothesis
The null hypothesis in a matched-samples t-test (two-tailed test) is:
the population mean difference score is equal to 0.
The sampling distribution of the mean
resembled a normal distribution.
If we have run a t test with 35 observations and have found a t of 3.60, which is significant at the .05 level, we would write
t(34) = 3.60, p < .05.
Sampling distributions help us test hypotheses about means by
telling us what kinds of means to expect if the null hypothesis is true.
The sampling distribution of the mean is
the distribution of sample means over repeated samples.
A researcher wishes to test the theory that men and women differ on a measure of personality. The researcher draws a sample of 35 men and a sample of 35 women. The sample means on the personality measure are: men, 46.7; women, 51.4. Literally, the null hypothesis states that:
the means of the male and female populations are equal.