PSY 418 Final
on average, what value is expected for the t-statisitc when the null hypothesis is true?
0
a "two-factor" experimental study means that the study has:
two independent variables
assuming that the null hypothesis is true, what is the probability of obtaining a sample that generates a z-value of at least as extreme as z= -1.19?
.234
assuming that the null hypothesis is true, what is the probability of obtaining a sample that generates a z-value of at least as extreme as z=-1.19?
.234
assuming that the null hypothesis is true, what is the likelihood of obtaining a sample mean at least as extreme as one that produces a z-score of 2.58?
.98%
the binomial distribution shows the probability associated with each value of X, where X is the number of occurrences of outcome A in a series of n trials. What is the range of possible values for X?
0 to n
for an experiment involving 2 levels of factor A and 3 levels of factor B, with a sample of n = 10 in each treatment condition, what are the df values for the F-ratio for factor A?
1, 54
for a binomial test, p + q =
1.00
for binomial data, what is the value of p + q?
1.00
the results of a repeated-measures ANOVA are reported as follows, F(3, 27)=1.12, p > .05. How many subjects participated in the study?
10
on a multiple-choice exam for which each question has four possible answers, the probability of guessing the correct answer is p = 1/4. What is the mean of the binomial distribution for the number of correct guesses for a series of 48 questions?
12
a two-factor analysis of variance produces SSA = 20, SSB = 40 and SSAxB = 90. For this analysis, what is the value for SSbetween treatments?
150
a repeated-measures study uses a sample of n = 8 participants to evaluate the mean differences among three treatment conditions. In the analysis of variance for this study, what is the value for dftotal?
23
a chi-square test for goodness of fit has df = 2. How many categories were used to classify the individuals in the sample?
3
a sample of 100 people is classified by gender (male/female) and by whether or not they are registered voters. The sample consists of 60 females, of whom 50 are registered voters, and 40 males, of whom 25 are registered voters. If these data were used for a chi-square test for independence, the expected frequency for registered males would be ________.
30
a binomial distribution has p = 3/4. How large a sample (n) would be necessary to satisfy the criterion for using the normal approximation to the binomial distribution?
40
a chi-square test for independence has df = 2. What is the total number of categories (cells in the matrix) that were used to classify individuals in the sample?
6
the results of a two-factor analysis of variance produce df = 1, 28 for the F-ratio for factor A, df = 2, 28 for the F-ratio for factor B, and df = 2, 28 for the AxB interaction. Based on this information, how many different treatment conditions were compared in the study?
6
assuming that all other factors are held constant, which confidence level will produce the smallest width for a confidence interval?
60%
a researcher obtains an F-ratio with df = 2, 12 from an ANOVA for a repeated-measures research study. How many subjects participated in the research study?
7
for an experiment comparing more than two treatment conditions you should use analysis of variance rather than separate t tests because:
ANOVA has less risk of a Type I Error because several means are compared in one test
a sample of n = 25 individuals is selected from a population with μ = 80, and a treatment is administered to the sample. Which set of sample characteristics is most likely to lead to a decision that there is a significant treatment effect?
M=90 and a small sample variance
which of the following samples will produce the largest value for a t statistic? Assume each sample has n = 10 scores
MD = 10 with SS = 20
what does it mean to obtain a negative value for the chi-square statistic?
The chi-square statistic can never be negative
Assuming that a treatment has an effect on the population, it is still possible to obtain a sample mean that doesn't result in rejection of the null hypothesis. What can be concluded
Type II Error
under what conditions can the phi-coefficient be used to measure effect size for a chi-square test for independence?
When both variables consist of exactly two categories
in the sign test, how are the difference scores coded?
as increases (+) or decreases (-)
a z-score of -2.00 indicates a position in a distribution that is:
below the mean by a distance of 2 standard deviations
in a repeated-measures ANOVA the SSwithin treatments is divided into two components. What are they?
between subjects and error
in a chi-square test for independence or goodness of fit:
both Σfe = n and Σfe = Σfo
he expected frequencies:
can contain fractions or decimal values
what will always change the value of the mean?
changing the values of one score
for which of the following situations would a repeated-measures study be appropriate?
compare reaction times before and after taking a pain medication
If it is theoretically possible to divide the existing categories of a variable into an infinite number of values, then it is an example of a _____ variable.
continuous
in general, if the variance of the difference scores increases, then the value of the t statistic will:
decrease (move toward 0 at the center of the distribution)
in general, decreasing the alpha level (for example: from .05 to .01) will:
decrease the likelihood of rejecting Ho and decrease the risk of type I error
for the independent-measures t statistic, if other factors are held constant, increasing sample variance will ________ the chances of a significant t statistic and ________ measures of effect size
decrease, decrease
the purpose of a post hoc test is to:
determine which treatments are different
a two-factor, independent-measures research study is evaluated using an analysis of variance. The F-ratio for factor A has df = 2, 36 and the F-ratio for factor B has df = 3, 36. Based on this information, what are the df values for the AxB interaction?
df = 6, 36
which of the following research situations is most likely to use and independent-measures design?
evaluate the verbal skills between 3 year old girls and 3 year old boys
If other factors are held constant, then decreasing the sample size will increase statistical power.
false
in a repeated-measures ANOVA, a P value is obtained by:
finding the sum of the scores for a participant in the study
in general, increasing the sample size (for example, from n = 4 to n = 50) will ________ the risk of Type-I error (assuming α is held constant at .05).
have no influence on
the estimated standard error, Sm, provides a measure of:
how much difference is reasonable to expect between the sample mean and the population mean
for an independent-measures research study, the value of Cohen's d or r2 helps to describe:
how much difference there is between the two treatments
what does it mean to say that the sample variance is an unbiased statistic?
if many samples are selected, the average of the sample variances will be equal to the population variance
with α = .01 and df = 25, the critical value for a one-tailed t test is t = 2.485. Assuming all other factors are held constant, if the df value were decreased, the critical value of t would:
increase
for a fixed level of significance, the critical value for chi-square will:
increase as df increases
in the F-ratio for a repeated-measures ANOVA, variability due to individual differences:
is automatically eliminated from the numerator but must be computed and subtracted out of the denominator
what happens to the standard error of M as sample size increases?
it decreases
Which combination of factors is most likely to produce a large value for the F-ratio and a large value for η2?
large mean differences and small sample variances
assuming that the null hypothesis is true, what is the likelihood of obtaining a sample mean as least as extreme as one that produces a t(30) score of -2.58?
lower than 2%, but greater than 1%
in a two-factor analysis of variance, the F-ratios for factor A, factor B, and the AxB interaction:
may have different df values but they all have the same denominator
if a binomial distribution satisfies the criterion for using the normal approximation with p = 0.2, then what can be concluded about the value of n?
n ≥ 50
which os the following is an advantage of transforming x-values into z-scores: all negative numbers are eliminated, all scores are moved closer to the mean, the distribution is transformed to a normal distribution, none of the other options is an advantage
none of the other options is an advantage
the critical region for a hypothesis test consists of:
outcomes that have a very low probability if the null hypothesis is true
What accurately describes the critical region
outcomes with very low probabilities if the null hypothesis is true
in any normal distribution, the middle 50% is bounded by z-scores of:
plus or minus .67
in general the distribution of F-ratios is:
positively skewed with all values greater than or equal to zero
the chi-square distribution is:
positively skewed with all values greater than or equal to zero
which of the following accurately describes the chi-square distribution?
positively skewed with all values greater than or equal to zero
a researcher obtains a t statistic of t = 2.00 from a repeated measures study using n = 17 participants. If the effect size is measured using r2 then the value of r2 for the study would be:
r^2 = 4/20 = 0.20
the power of a statistical test is the probability of:
rejecting a false null hypothesis
a type 1 error is defined as:
rejecting a true null hypothesis
the appropriate denominator for the F-ratio for a repeated-measures ANOVA is:
remaining variance when the variance between subjects is subtracted from the variance within treatments
what is s^2
sample variance
although samples are usually representative of the populations from which they are selected, you should not expect a sample statistic to be exactly equal to the corresponding population parameter. The natural differences that exist between statistics and their parameters are known as:
sampling error
a distribution of N=3 scores consists of 5,7, and 50. The best way to present these data would be to:
simply list the three scores
in general, what is the relationship between the standard deviation and variance?
standard deviation is the square root of variance
the null hypothesis:
states that the treatment has no effect
what is the shape of the distribution for the following set of data: 1,1,1,2,3,3,3?
symmetrical
what value for t would be best for a point estimate of a population mean using a single-sample t-statistic
t=0
with α = .01, what is the critical t value for a one-tailed test with n = 30?
t=2.462
what happens to the critical value for a chi-square test if the number of categories is increased?
the critical value also increases
for a repeated-measures ANOVA, which of the following is computed differently, compared to an independent-measures ANOVA?
the denominator of the F-ratio
the term expected frequencies refers to:
the frequencies computed from the null hypothesis
the term observed frequency refers to:
the frequencies found in the sample data
how does the difference between fe and fo influence the outcome of a chi-square test?
the larger the difference, the larger the value of chi-square and the greater the likelihood of rejecting the null hypothesis.
if the results of a two-factor experiment are presented in a line graph, then an interaction can be seen whenever:
the lines move toward each other or cross
in a two-factor analysis of variance a main effect is defined as:
the mean differences among the levels of one factor
for an extremely skewed distribution of scores, the best measure of central tendency would be:
the median
in a typical hypothesis testing situation, the null hypothesis makes a statement about:
the population after treatment
a one-tailed, directional test has a critical value (value needed to reject the null hypothesis) of 1.645 (alpha=.05). Based on this information, it is probably safe to assume that:
the population standard deviation is known
what is an accurate definition for the power of a statistical test?
the probability of rejecting a false null hypothesis
the chi-square test for goodness of fit evaluates:
the shape or proportions for a population distribution
in a repeated-measures ANOVA, a P value corresponds to:
the total of all the scores for an individual person
what conclusion is appropriate if a chi-square test produces a chi-square statistic near zero?
there is a good fit between the sample data and the null hypothesis
the null hypothesis for the chi-square test for independence states that:
there is no relationship between the two variables
The analysis of variance for a two-factor experiment produces:
three separate F-ratios
which of the following are sources of variability that contribute to SSbetween treatments in a repeated ANOVA?
treatment effect and chance/error
for a repeated-measures hypothesis test, the null hypothesis states:
ud=0
the purpose of a confidence interval is to:
use a sample mean or mean difference to estimate the corresponding population mean or mean difference
what is an example of measurement on an ordinal scale of measurement?
using letter grades A,B,C,D, and E to classify student performance on an exam
when testing a hypothesis with the binomial distribution, the null hypothesis specifies the
values for p and q
in analysis of variance, the F-ratio is a ratio of:
variances
under what circumstances can the binomial test be used as an alternative to the chi-square test for goodness of fit?
when the chi-square test involves exactly two categories
under what circumstance is a score that is 15 points above the mean an extreme score relatively far from the mean?
when the population standard deviation is much smaller than 15
under what circumstances are post tests necessary?
when you reject the null hypothesis with more than 2 treatment conditions
for the binomial test, what is the relationship between chi-square and z?
x^2=z^2
the 95% confidence interval for mu is computed from sample data and the interval estimate ranges fro 115-120. This indicates:
you can be 95% confident that this interval contains the population mean
the results from a two-factor analysis of variance show a significant main effect for factor A and a significant main effect for factor B. Based on this information, you can conclude that:
you cannot make any conclusion about the significance of the interaction
a population of scores has µ=50 and σ =5. If every score in the population is multiplied by three then what are the new values for the mean and standard deviation?
µ = 150 and σ = 15
the null hypothesis for the independent-measures t-test states:
μ1 - μ2 = 0
the null hypothesis for an independent-measures states:
μ1-μ2=0
for a repeated-measures hypothesis test, the null hypothesis states
μD = 0
a researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population which is known to have a mean of μ = 80. The results will be examined using a one-tailed hypothesis test. Which of the following is the correct statement of the null hypothesis?
μ≤ 80
if the null hypothesis is true, what value is expected on average for the related-samples t-test?
0
which proportion of a normal distribution falls between z=-1.96 and z=+1.96?
0.9500
for an independent-measures experiment comparing two treatment conditions with a sample of n = 10 in each treatment, the F-ratio would have df equal to:
1, 18
if the null hypothesis is true and there is no treatment effect, what value is expected on average for the F-ratio?
1.00
when the null hypothesis is true for an ANOVA, what is the expected value for the F-ratio?
1.00
a research report describing the results from a repeated-measures study includes the following: "The data show no significant difference between the two treatments, t(10) = 1.65, p > .05." Based on this report, you can conclude that a total of ________ individuals participated in the research study
11
a researcher uses a repeated-measures study to compare two treatment conditions with a set of 20 scores in each treatment. What would be the value of df for the repeated-measures t statistic?
19
a researcher reports an F-ratio with df = 2, 36 for an independent-measures experiment. How many treatment conditions were compared in this experiment?
3
an analysis of variance produces SStotal = 90 and SSwithin treatments = 40. For this analysis, what is SSbetween treatments?
50
What cannot be true for a distribution of scores?
80% of the scores are above the median
a researcher obtains t = 3.00 for a repeated-measures study using a sample of n = 10 participants. If the researcher measures effect size using the percentage of variance accounted for, what value will be obtained for r2?
9/18 = 0.50
If a treatment has a very small, but nevertheless legitimate effect on the population, then
a Type II error
a researcher wants to conduct an experiment comparing two treatment conditions and obtains 30 scores in each treatment. Which design would require the smallest number of participants?
a repeated-measure design
what is not a continuous variable
number of kids in a family
In a distribution with negative skew, scores with the highest frequencies are _____.
on the right side of the distribution
in hypothesis tests, standard error measures:
the size of the treatment effect
as sample variance increases, what happens to measures of effect size such as r2 and Cohen's d?
they tend to decrease
what is the goal of a binomial distribution?
to estimate population proportion
Adding a new score to a distribution will not change the value of the mean, as long as the new score has the same value as the mean.
true
For a positively skewed distribution, the mean usually has a larger value than either the median or the mode
true
It is possible for the value of the mode to be greater than the value of the mean.
true
true or false: as df increases, the student's t distribution approaches a normal distribution
true
true or false: as sample size decreases, the estimated standard error increases
true
true or false: for a hypothesis test using a t statistic, the boundaries for the critical region will change if the sample size is changed (assume that the alpha level is held constant)
true
true or false: in general, an increase in the sample variance makes it less likely that the t statistic will be large enough to reject the null hypothesis
true
true or false: within any normal or symmetrical distribution of scores, the location specified by z=+.1 and the location specified by z=-.1 are exactly the same distance from the mean
true
What accurately describes the effect of increasing the sample size?
decreases the standard error, increases statistical power, and has no effect on the risk of a Type I error
in a hypothesis test, a z-score value near zero:
does not mean: you should probably reject the null hypothesis, means the z-score is in the critical region, or that there is strong evidence of a statistically significant effect
The alpha level is one of a group of factors that determine the risk of a Type I error.
false
true of false: it is impossible for fewer than half of the scores in a distribution to have values greater than the mean
false
true or false: a score with a value higher than the mean will have a negative z-score
false
true or false: distributions of sample means (sampling distributions) are normal when they are based on samples of at least n=30
false
true or false: you are more likely to make a type I error with a sample of n=4,000 than with a sample of n=100,000,000 even if you use an alpha level of .05 for both tests
false
which of the following sets of sample data would produce the largest value for an independent-measures t statistic? Assume that n = 10 for all samples. Note: You should not need to do any serious calculations to answer this question.
first sample: M = 30 and SS = 10, second sample: M = 50 and SS = 10.
under what circumstances will the distribution of sample means be normal?
if the population is normal or if the sample size is greater than 30
under what circumstances will a very small treatment effect most likely be statistically significant?
if the sample size is big and the sample variance is small
if two samples are selected from the same population and are testing the same null hypothesis, under what circumstances will the two samples have exactly the same t statistic?
if the samples are the same size, have the same sample mean, and have the same sample variance
If sample size (n) is held constant, the standard error will ________ as the population variance increases
increase
with an alpha level of .01 and df=25, the critical value for a one-tailed t test is t=2.485. Assuming all other factors are held constant, if the df value were decreased, the critical value of t would:
increase
assuming the other factors are held constance, which of the following would tend to decreases the value of the calculated t-statistic?
increase the sample variance
an advantage of a repeated-measured design (compared to an independent-measures design) is that it reduces the contribution of error variability due to
individual differences
a researcher is predicting that a treatment will decrease scores. If this treatment is evaluated using a directional hypothesis test, then the critical region for the test:
is in the left-hand tail of the distribution
what cannot be an accurate depiction of scores?
majority of the scores are above the median
the z-score boundaries for the critical regions in a hypothesis test are determined by:
the alpha level
when the sample size is greater than n=30:
the distribution of sample means will be approximately normal
a teacher gave a reading test to a class of 5th grade students and computed the mean, median, and mode for the test scores. Which of the following cannot be an accurate description of the scores?
the majority of the students had scores above the mean
the value of one score in a distribution is changed from X=20 to X=30. Which measures of central tendency is certain to be changed
the mean
the width of the bars in a histogram is determined by:
the real limits of a score or interval
a sample has a mean of M=25. If a new score with a value of X=25 is added to the sample, what effect will it have on the sample mean?
the sample mean will remain the same
what is major difference between a hypothesis test with the t-statistic formula and the test with a z-score?
you must know the population variance (or standard deviation) for the z-score but not for the t statistic, you use the unit normal table to find critical values for the z-score test but not for the t test, and you must calculate the sample variance (or standard deviation) for the t statistic but not for the z-score