exam 3 for psych stats
If the null hypothesis is true, what value is expected on average for the repeated-measures t statistic?
0
An independent-measures study has one sample with n=6 and a second sample with n=8 to compare two experimental treatments. What is the df value for the t statistic for this study?
12
A sample of n = 4 scores has SS = 60. What is the variance for this sample?
20
what is the pooled variance for the following two samples? Sample 1: n=8 and SS=168 Sample 2: n=6 and SS=120
24
One sample has n=5 scores and the second has n=10 scores. If the pooled variance for the two samples is 30, what is the value of the estimated standard error for the difference between sample means?
3
For a repeated-measures study comparing two treatment conditions, a researcher obtains a sample of n = 9 difference scores with a mean of MD = 4 and a variance of s2 = 36. What is the value for the repeated-measures t statistic for these data?
4/2
what is the sample variance and the estimates standard error for a sample of n=9 scores with SS=72
9
Which of the following research situations would be most likely to use an independent-measures design?
Compare the mathematics skills for 9th -grade boys versus 9th -grade girls
If two samples are selected from the same population, under what circumstances will the two samples have exactly the same t statistic?
If the samples are the same size and have the same mean and the same variance.
when the population standard deviation is not known, we substitute the estimated standard error for the
actual standard error of the mean
Sm
estimated standard error
degrees of freedom
n-1
two separate samples are being used to estimate the population mean difference between two treatment conditions. Which of the following would produce the widest confidence interval?
n1=n2=10 with a pooled variance of 100
t distribution approximates the shape of
normal distribution
where is the expected value of the sample mean obtained from
null hypothesis
M
sample mean
estimated standard error equation
√s₂ ÷ n
estimated d
M- µ ÷ s
Why are t statistics more variable than z-scores?
The extra variability is caused by variations in the sample variance
when the population standard deviation is known, we construct a 95% confidence interval for the population mean by
adding and subtracting 2 standard errors from sample mean
t distribution
complete set of t-values computed for every possible random sample for a specific sample size (n) of a specific degrees of freedom (df)
Which combination of factors would definitely increase the width of a confidence interval?
large samples and small variances
M-µM÷ σM
ratio that includes one variable
s²= √SS ÷ df
sample standard deviation
for t distributions, the "tails" are heavier, meaning
the distribution is more spread out
Which of the following is a fundamental difference between the t statistic and a z-score?
the t-statistic uses the sample variance in place of the population variance
estimated standard error
used as an estimate of the real standard error when the value of σ is unknown. Computed using the sample variance or sample standard deviation and provides an estimate of the standard distance between a sample mean and the population mean
will the estimate standard error of the sample mean change from sample-to-sample
yes
will the sample mean changes from sample-to-sample
yes
Two samples, each with n=5 scores, have a pooled variance of 40. What is the estimate standard error for the difference between sample means?
4
What is the average value expected for the independent-measures t statistic if the null hypothesis is true?
0
on average, what value is expected for the t statistic when the null hypothesis is true?
0
the difference between the sample mean and its expected value should, in the long run, be equal to
0
z-score is normally distributed with a mean of
0
A sample is selected from a population with m = 46, and a treatment is administered to the sample. After treatment, the sample mean is M = 48 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen's d?
0.50
z-score is normally distributed with a standard deviation of
1
One sample has M=18 and a second sample has M=14. If the pooled variance for the two samples is 16, what is the value of Cohen's d?
1.00
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
Cohen's d
M -µ ÷ s
single sample t statistic
M- µ ÷ Sm
t-statistic formula
M-µ ÷ √s²÷n
Which of the following sets of data would produce the largest value for an independent-measures t-statistic?
The two sample means are 10 and 20 with variances of 20 and 25.
if a researcher is using a t statistic to test a null hypothesis about a population, what information is needed from the population to calculate the t statistic
does not require any information about the population
matched-subject design
each individual in one sample is matched with an individual in the other sample. The matching is done so that 2 individuals are equivalent (or nearly) with respect to a specific variable that the researcher would like to control
which of the following confidence intervals also indicates a significant difference between treatments with a = .05?
estimate that μ1 - μ2 is in an interval between 2 and 10 with 95% confidence
One sample of n=8 scores has a variance of s2=6 and a second sample of n=8 scores has s2=10. If the pooled variance is computed for these two samples, then the value obtained will be _____.
exactly halfway between 6 and 10
When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution?
flatter and more spread out
with heavier the tails in t distributions you will have to go _____ ______ from the mean to find the extreme 5% of score
further away
For an independent-measures t statistic, what is the effect of increasing the number of scores in the samples
increase the likelihood of rejecting H₀ and have little or no effect on measures of effect size
Which of the following would have no effect on the width of a confidence interval?
increase the sample mean
Which of the following describes what a confidence interval does?
it uses a sample mean to estimate the corresponding population mean
Assuming that there is a 5-point difference between the two sample means, which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic?
large samples, small variances
For which of the following situations would a repeated-measures research design be appropriate?
less likely to reject null hypothesis
there will be more sample-to-sample variability for small samples than large samples, so the the distribution of t will be
more variable for fewer degrees of freedom
repeated-measures design
one in which the dependent variable is measure 2 or more times for each individual in a single sample. The same group of subjects is used in all of the treatment conditions
µ
population mean
what is the standard error of the mean determined by
population standard deviation and sample size
M-µM÷ Sm
ratio that includes two variables
independent-measures research study
research design that uses a separate group of participants for each treatment condition
sample means will differ from sample to sample. These differences will tend to be larger in the _____ than the z distribution
t distribution
ratio that contains 2 variables will have a greater variability than one that contains one variable
true
t statistic
used to test hypothesis about an unknown population mean, µ, when the value of σ is unknown
What value is estimated with a confidence interval using the t statistic?
value of unknown population mean
are the critical values always the same
yes
can the sample mean change is we select another sample?
yes
Which of the following is the correct null hypothesis for a repeated-measures t test?
µD = 0
Which of the following is the correct null hypothesis for an independent-measure t test?
µ₁−µ₂=0
A sample of n = 4 scores is selected from a population with an unknown mean. The sample has a mean of M = 40 and a variance of s2 = 16. Which of the following is the correct 90% confidence interval for m?
μ = 40 ± 2.353(2)
