Stats Final
For a population with µ = 80 and σ = 10, what is the z-score corresponding to X = 95?
+1.50
A random sample of n = 16 scores is obtained from a parent population with
+2.00
In a population of scores, X = 83 corresponds to z = -0.50 and X = 93 corresponds to z = +2.00. What are the values for the population mean and standard deviation?
. µ = 85 and σ = 4
For any distribution, what is the z-score corresponding to the mean?
0
On average, what value is expected for the t statistic when the null hypothesis is true?
0
If an entire population with μ = 60 and σ = 8 is transformed into z-scores, then the distribution of zscores will have a mean of ____ and a standard deviation of ____.
0 and 1
A random sample of n = 16 scores is selected from a parent population with μ = 100 and σ = 32. If the sample mean is M = 104, what is the z-score for this sample mean?
0.50
The data from an independent-measures research study produce a sample mean difference of 4 points, and each sample has a variance of 10. If there are n = 20 scores in each sample, then what is the estimated standard error of the difference between means?
1
A sample of n = 4 scores is selected from a parent population with μ = 50 and σ = 12. If the sample mean is M = 56, what is the z-score for this sample mean?
1.00
Two samples, each with n = 8 scores, each have a standard deviation of 20. What is the estimated standard error of the difference between means?
10
An independent-measures study comparing two treatment conditions produces a t statistic with df = 18. If the two samples are the same size, how many participants were in each of the samples?
10 each
What is the value of SS (sum of squared deviations) for the following sample? Sample: 2, 3, 4, 7
14
A sampling distribution composed of samples of n = 9 has a standard error of 6. What is the standard deviation of the population from which the sample was obtained?
18
An independent-measures study uses two samples, each with n = 10, to compare two treatment conditions. What is the df value for the t statistic for this study?
18
If random samples, each with n = 4 scores, are selected from a normal population with µ = 80 and σ = 36, then what is the standard error for the sampling distribution?
18
An independent-measures study has one sample with n = 10 and a second sample with n = 15 to compare two experimental treatments. What is the df value for the t statistic for this study?
23
A researcher reports a two-sample t-test for an independent-measures experiment as follows: t(22) = 5.30, p < .01. How many individuals participated in the entire experiment?
24
An independent-measures study with n = 8 in each sample, produces a sample mean difference of 6 points, and each sample has a standard deviation of 4. What is the value for the t statistic?
3
A sampling distribution composed of samples of n = 4 has a standard error of 10 points. Using the same parent population, what is the standard error for a sampling distribution composed of samples of n = 16?
5
Of a hundred randomly sampled 50% confidence intervals, how many would you expect to contain the population parameter?
50
For a particular population, a sampling distribution composed of samples of n = 9 has a standard error of 8. For the same population, a sampling distribution composed of samples of n = 16 would have a standard error of _____.
6
The data from an independent-measures research study produce a sample mean difference of 6 points and an estimated standard error of the difference between means of 2 points. The value for the t statistic is _____.
6/2
For a population with µ = 80 and σ = 10, what is the X value corresponding to z = -0.50?
75
If a near-infinite (i.e., very large) number of random samples with n = 36 scores are selected from a parent distribution with µ = 80 and σ = 18, and the mean is calculated for each sample, then what is the average of the sample means?
80
For a population with µ = 100 and σ = 20, what is the X value corresponding to z = -0.75?
85
A researcher administers a treatment to a sample of participants selected from a population with µ = 80. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis?
A sample mean much different than 80 for a large sample
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
In a 95% confidence interval, what is the likelihood that the same mean precisely and accurately estimates the population mean?
Extremely low
Last week Sarah had exams in Math, Spanish and English. On the Math exam, the mean was µ = 40 with σ = 5 and Sarah had a score of X = 45. On the Spanish exam, the mean was µ = 60 with s = 8 and Sarah had a score of X = 68. On the English exam, the mean was µ = 70 with s = 8 and Sarah had a score of X = 78. For which class should Sara expect the better grade?
Grades are the same.
What happens to the standard error of M as sample size increases?
It decreases.
Which of the following accurately describes an independent-measures study?
It uses a different group of participants for each of the two conditions being compared
A sample of n = 4 scores is obtained from a parent population with μ = 70 and σ = 8. If the sample mean corresponds to a z-score of 2.00, then what is the value of the sample mean?
M = 78
If other factors are held constant, which set of sample characteristics is will obtain the smallest p-value when testing a null hypothesis stating that µ = 80?
M = 90 and small sample variance
If other factors are held constant, which set of sample characteristics will obtain the largest t-statistic when testing a null hypothesis stating that µ = 80?
M = 90 for a sample of n = 100
For a normal parent population with µ = 40 and σ = 10 which of the following samples is least likely to be obtained?
M ≤ 42 for a sample of n = 4
For a normal parent population with µ = 40 and σ = 10 which of the following samples has the highest probability of being obtained?
M ≤ 44 for a sample of n = 100
If the sample size is held constant, which of the following will produce the widest 90% confidence interval for the population mean difference for a repeated-measures study?
MD = 3 with s2 = 20 for the difference scores
Last week, Sarah had exams in Math, Spanish, and English. On the Math exam, the mean was µ = 30 with s = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was µ = 60 with s = 8 and Sarah had a score of X = 68. On the English exam, the mean was µ = 70 with s = 8 and Sarah had a score of X = 70. For which class should Sara expect the better grade?
Math
A random sample of n = 36 scores is selected from a population. Which of the following distributions definitely will be normal?
Neither the sample, the parent distribution, nor the distribution of sample means will definitely be normal.
A random sample of n = 4 scores is selected from a parent distribution. Which of the following distributions definitely will be normal?
Neither the sample, the parent distribution, nor the distribution of sample means will definitely be normal.
What is measured by the numerator of the z-score test statistic?
The actual distance between M and µ
A sample of n = 25 individuals is selected from a population with µ = 80 and a treatment is administered to the sample. What is expected if the treatment has no effect?
The sample mean should be close 80 and should lead you to fail to reject the null hypothesis
If other factors are held constant, 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 sample variances of 20 and 25.
In an independent-measures hypothesis test, what must be true if our computed t-statistic is 0?
The two sample means must be equal.
If other factors are held constant, which of the following sets of data would produce the largest value for an independent-measures t statistic (assuming the difference in sample means is not zero)?
The two samples both have n = 30 with sample variances of 20 and 25.
What is measured by the denominator of the z-score test statistic?
The variability of a sampling distribution
What is the likelihood that a 95% CI contains 95% of the scores (e.g., sample means, etc.) in the sampling distribution?
Very low
Which set of sample characteristics is most likely to produce a small p-value for the independent-measures t statistic?
a large mean difference and small sample variances
Which combination of factors will produce the smallest value for the standard error?
a large sample and a small population standard deviation
Which set of characteristics will produce the smallest value for the estimated standard error?
a large sample size and a small sample variance
. If n = 15 for each sample, which of the following sets of data provides the clearest most evidence that the population means may be different?
a sample mean difference of 10 points with s2 = 5 for both samples
A random sample is obtained from a parent pop
a sample of n = 100 scores with M = 104
A sample of n = 25 scores is selected from a parent population with a mean of µ = 80 and a standard deviation of σ = 20. The standard error for the sampling distribution is 20.
false
A sample of n = 25 scores is selected from a parent population with μ = 70 and σ = 20. It is very unlikely that the sample mean will be smaller than 72.
false
A sample of n = 4 scores is selected from a parent population with μ = 30 and σ = 8. The probability of obtaining a sample mean greater than 34 is equal to the probability of obtaining a z-score greater than z = 2.00 from a normal distribution
false
As the sample size increases, the distribution of t statistics becomes flatter and more spread out
false
As the size of the samples comprising the sampling distribution increases, the standard error of mean also increases.
false
In order for the sampling distribution to be normal, it must be composed of samples of at least n = 30
false
The mean for a sample of n = 4 scores has a standard error �!̅= 5 points. This sample was selected from a parent population with a standard deviation of σ = 20.
false
The null hypothesis for the independent-measures t test states that there is no difference between the two sample means.
false
Two separate samples, each with n = 10 scores, will produce an independent-measures t statistic with df = 19
false
Under what circumstances can a very small difference obtain a small p-value?
if the sample size is big and the sample variance is very small
Which combination of factors is most likely to produce a small p-value for an independent-measures t statistic?
large samples and small variance
Decreasing the sample size, while holding the confidence level the same will do what to the width of your confidence interval?
make it bigger
A researcher reports an independent-measures t statistic with df = 30. If the two samples are the same size (n1 = n2), then how many individuals are in each sample?
n = 16 for each
A sample from a population with μ = 40 and σ = 10 has a mean of M = 44. If the sample mean corresponds to a z = 2.00, then how many scores are in the sample?
n = 25
A sampling distribution obtained from a population with σ = 12 has a standard error of 2 points. How many scores are in each sample comprising the sampling distribution?
n = 36
Under what circumstances will the distribution of sample means be normal?
only if the parent distribution is normal
What term is used to identify the variability of the distribution of sample means?
the standard error of M
A sample of n = 16 scores is selected from a parent population with μ = 70 and σ = 8. It is very unlikely that the sample mean will be greater than 78.
true
A sample of n = 4 scores is selected from a parent population with μ = 70 and σ = 10. The probability of obtaining a sample mean greater than 65 is p = 0.8413
true
A sample of n = 9 scores is selected from a normal parent population with a mean of µ = 80 and a standard deviation of σ = 12. The probability that the sample mean will be greater than M = 86 is equal to the probability of obtaining a z-score greater than z = 1.50
true
A sample of n = 9 scores is selected from a parent population with μ = 50 and σ = 12. The probability of obtaining a sample mean greater than 46 is p = 0.8413.
true
As the standard deviation of the parent population increases, the standard error of the sampling distribution will also increase
true
If both samples have the same number of scores (n), then the independent-measures t statistic will have df = 2n - 2.
true
If other factors are held constant, as the sample size increases, the estimated standard error decreases
true
If other factors are held constant, as the sample standard deviation increases, the estimated standard error also increases.
true
If samples are selected from a normal parent population, the resulting sampling distributions will also be normal
true
If the two samples are the same size, the independent measures t statistic will have an even number for degrees of freedom.
true
If two samples, each with n = 20 scores, are selected from the same population and both have the same mean (M = 53) and the same variance (s2 = 12), then they will also have the same t statistic.
true
In general, the null hypothesis states that the treatment has no effect on the population mean.
true
The null hypothesis is stated in terms of the population, even though the data come from a sample
true
The t distribution for df = 4 is flatter and more spread out than the t distribution for df = 20
true
Two samples randomly selected from the same parent population will probably have different means even if they are both the same size.
true
When the population variance or standard deviation is not known (i.e., must be estimated from data), we use a t statistic instead of a z-score for a hypothesis test.
true
The distribution of sample means ____ .
will be normal only if the parent distribution is normal
You take a random sample from some population and form a 96% confidence interval for the population mean, µ. Which quantity is guaranteed to be in the interval?
x-bar
Which of the following z-score values represents the location closest to the mean?
z = +0.50
A sample of n = 16 scores is obtained from a parent population with μ = 50 and σ = 16. If the sample mean is M = 54, then what is the z-score for the sample mean?
z = 1.00
A sample of n = 9 scores is obtained from a parent population with μ = 70 and σ = 18. If the sample mean is M = 76, then what is the z-score for the sample mean?
z = 1.00
If a sample of n = 4 scores is obtained from a parent population with μ = 70 and σ = 12, then what is the z-score corresponding to a sample mean of M = 76?
z = 1.00
For a population with a standard deviation of σ = 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 parent 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
You have a score of X = 65 on an exam. Which set of parameters would give you the best grade on the exam?
μ = 60 and σ = 5
Which of the following is the correct null hypothesis for an independent-measures t test?
μ1 - μ2 = 0 (or μ1 = μ2 )
A population with µ = 85 and σ = 12 is transformed into z-scores. After the transformation, what is the standard deviation for the population of z-scores?
σ = 1.00
On an exam with μ = 52, you have a score of X = 44. Which of the following values for the standard deviation would give you the highest position in the class distribution?
σ = 10
On an exam with μ = 52, you have a score of X = 56. Which of the following values for the standard deviation would give you the highest position in the class distribution?
σ = 2
A population has μ = 50. What value of σ would make X = 55 a more central, representative score in the population?
σ = 20
What symbol is used to identify the standard error of M?
σM
