Stats 221...
Which of the following statements about the comparison between effect size and power is correct?
As effect size increases, power also increases.
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
A researcher is interested in having as much ability as possible to identify a treatment effect if one really exists. Which of the following strategies should they employ?
change the sample size from n = 25 to n = 100
A researcher is performing an experiment to determine whether eating chocolate can improve memory. Measurements of memory in this experiment would be the ____ variable.
dependent
A confounding variable is a variable that influences the ____.
dependent variable and varies systematically with the independent variable.
In an experiment, the purpose for manipulating the independent variable is to help ____.
establish the direction of the relationship and help eliminate the third variable problem
A researcher conducts a hypothesis test using a sample from an unknown population. If df = 30 for the t-statistic and M = 46 and s 2 = 10, how many individuals were in the sample?
n = 31
A sample obtained from a population with σ = 48 has a standard error of σM = 6. How many scores are in the sample?
n = 64
Dr. Sian varies the amount of a new sedative given to three groups of participants (0, 1, and 2 mg) and then observes the reaction for each group. The 0-mg condition represents the ____ condition.
no-treatment control
A random sample of n = 64 scores is obtained from a normal population with µ = 30 and σ = 10. What is the probability that the sample mean will be greater than M = 31?
p = 0.2119
A sample of n = 4 scores is selected from a normal population with a mean of µ = 50 and a standard deviation of σ = 20. What is the probability of obtaining a sample mean less than M = 52?
p = 0.5793
A random sample of n = 25 scores is obtained from a normal population with µ = 30 and σ = 6. What is the probability that the sample mean will be within 2 points of the population mean?
p = 0.9050
For the distribution of sample means for all random samples of a certain size from a population depicted below, what is the probability that a randomly selected sample will have a sample mean less than M = 6?
p = 2/13
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. Which outcome is likely if this happens?
reject H0 and make a Type I error
If a hypothesis test produces a z-score in the critical region, which decision should be made?
reject the null hypothesis
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, which is the correct statistical decision?
reject the null hypothesis with either α = .05 or α = .01
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, which is the correct statistical decision?
reject the null hypothesis with α = .05 but not with α = .01
A hypothesis test involves a comparison of which two elements?
research results from a sample and a hypothesis about a population
A sample of n = 4 scores has SS = 60. Which is the variance for this sample?
s2 = 20
A sample of n = 7 scores has a mean of M = 65 and an estimated standard error of 2 points. What is the sample variance?
s2 = 28
A sample of n = 25 scores has a mean of M = 40 and a standard deviation of s = 10. What is the estimated standard error for the sample mean?
sM = 2
Which of the following accurately describes the critical region?
sample means that are very unlikely to be obtained if the null hypothesis is true
A sample is obtained from a normal population with µ = 100 and σ = 20. Which of the following samples would produce the most extreme z-score?
sample of n = 100 scores with M = 104 (big m)
Consider a researcher who is exploring new potential treatments for specific forms of cancer. This researcher is extremely focused on avoiding mistakes in concluding that treatments that may very well be effective are ineffective when conducting their research. What should this researcher do?
set a higher alpha level
Consider a researcher who is conducting final clinical trials to validate that a new treatment for anxiety is effective. This researcher is extremely focused on avoiding mistakes in concluding that this new treatment is effective when it really is not when conducting their research. What should this researcher do?
set a low alpha level
A researcher attempts to recreate the real world in the laboratory. This type of research is called a ____.
simulation study
It is expected that a treatment will reduce scores on a variable. If α = .05, what is the critical t value for a one-tailed hypothesis test with n = 15?
t = -1.761
Which of the following results from a hypothesis test involving the computation of a t-statistic is structured correctly based on standards for presenting hypothesis tests in scientific reports?
t(19) = 2.30, p < .05, r2 = 0.42
Dr. Ramos is interested in studying how indoor temperature can influence people's sleep quality during the summer. A sample of 100 households is selected in which the residents keep their houses at 76 degrees during the summer. The residents wear a monitoring device that measures their sleep cycles for several nights to get baseline readings. Then, 50 of the homes are randomly assigned to the warm temperature condition in which the residents agree to keep their houses at 82 degrees Fahrenheit. In the other 50 houses, the residents agree to keep their houses at 70 degrees. For several nights, Dr. Ramos collects the sleep data for the people living in the houses to see how the residents' sleep patterns have changed. In this study, the independent variable is the ____.
temperature of the houses
What is measured by the numerator of the z-score test statistic?
the distance between the sample mean and hypothesized population mean
Which is the expected value of M?
the mean of the distribution of sample means
A researcher has observed that adults who are more optimistic tend to have a higher level of life satisfaction than adults who are less optimistic. However, the researcher suspects that the apparent relationship may be explained by the fact that some people have positive things happen in their lives, which causes them to be more optimistic and satisfied with their lives compared to people who have bad things happen in their lives and therefore have a more negative outlook on things. This is an example of the ____.
third-variable problem
In an experiment, participants are usually assigned to treatments using random assignment. The reason for using random assignment is ____.
to help control extraneous variables
In an experiment, participants are randomly assigned to treatment conditions ____.
to help protect the internal validity of the study
Larry wants to do everything possible to be in a position to detect that a treatment he has designed is effective given that it is actually effective. Which of the following should he do?
use an alpha (α) of .05 instead of .01
When is a researcher at risk of making a Type II error?
whenever H0 fails to be rejected
When is a researcher at risk of making a Type I error?
whenever H0 is rejected
If a sample of n = 4 scores is obtained from a normal population with µ = 70 and σ = 12, what is the z-score corresponding to a sample mean of M = 69?
z = -0.17
A sample of n = 64 scores is selected from a population with µ = 60 and σ = 10. If the sample mean is M = 57, what is the z-score for this sample mean?
z = -2.40
A sample of n = 16 scores is selected from a normal population with σ = 32. If the sample mean of M = 81 produces a z-score of z = -1.75, then what is the population mean?
µ = 95
For a normal population with µ = 60 and σ = 50, the distribution of sample means based on n = 25 will have an expected value of ____ and a standard error of ____.
µM = 60; σM = 10.
Samples of size n = 9 are selected from a normal population with µ = 80 with σ = 18. What is the expected value for the mean of the distribution of sample means?
µM = 80
An instructor is interested in whether frequent feedback in their course to a small sample of students influences student performance. The instructor knows that final class scores are normally distributed with µ = 85 and σ = 6. Which is the alternative hypothesis for this research study?
µfrequent feedback ≠ 85
A researcher is interested in whether a new teaching method influences the public speaking skills of students in an introductory to communications class. The researcher knows that public speaking skills in the class are normally distributed with µ = 10 and σ = 2. Which is the null hypothesis for this research study?
µteaching method = 10
If a treatment is expected to increase scores on a variable for which the mean is expected to be µ = 100, what is the null hypothesis?
µwith treatment < 100
A sample of n = 16 scores has a standard error of σM = 4. What is the standard deviation of the normally distributed population from which the sample was obtained?
σ = 16
A researcher administers a new treatment to a sample of participants selected from a population with µ = 80. If the researcher obtains a sample mean of M = 88, which combination of factors is most likely to result in rejecting the null hypothesis?
σ = 5 and α = .05
Which symbol is used to identify the standard error of M?
σM
A sample of n = 49 scores with M = 43 is selected from a population with µ = 40 with σ = 21. What is the standard error for the sample mean?
σM = 3
Samples of size n = 9 are selected from a normal population with µ = 80 with σ = 18. What is the standard error for the distribution of sample means?
σM = 6
For a normal population, a sample of n = 9 scores has a standard error of 10. For the same population, a sample of n = 25 scores would have a standard error of _____.
σM = 6.
Which statement below is not consistent with the distribution of sample means.
. The distribution of sample means tends to pile up around the population standard deviation.
A sample of n = 9 individuals is selected from a population with µ = 60 and σ = 6, and a treatment is administered to the sample. After treatment, the sample mean is M = 63. What is the value of Cohen's d for this sample?
0.50
Consider that a population is normally distributed with µ= 100 and σ = 6. What is the power of a α = .05, two-tailed hypothesis test with an expected treatment of 2 points and sample size of n = 64?
0.7611
A sample of n = 64 scores is selected from a population with µ = 80 with σ = 24. On average, how much error is expected between the sample mean and the population mean?
3 points
If random samples, each with n = 16 scores, are selected from a normal population with µ = 100 and σ = 20, how much difference, on average, should there be between a sample mean and the population mean?
5 points
Which of the following statements comparing one-tailed with two-tailed hypothesis tests is correct?
All else equal, a less extreme z-score is needed to obtain statistical significance for a one-tailed than two-tailed hypothesis test.
A researcher designs a study to determine whether female preschoolers prefer sweetened or unsweetened cereal. The researcher uses a box of sweetened colorful cereal and a box of unsweetened tan colored cereal. The research finds that the group of preschoolers ate more of the sweetened colorful cereal and therefore prefers the sweetened cereal. Which two variables are confounded in this experiment?
Color of the cereal and sweetness of the cereal
A sample is selected from a normal population with µ = 54 and σ = 8. Which of the following samples would be considered extreme and unrepresentative for this population?
M = 52 and n = 81
A researcher decides to use only participants that weigh between 150 and 160 pounds in an experiment comparing two treatment conditions. For this study, what method is being used to control participant weight?
Holding constant
Which characteristic is necessary for an extraneous variable to become a confounding variable?
It must change systematically when the independent variable is changed.
How does sample variance influence the estimated standard error and measures of effect size such as r 2 and Cohen's d?
Larger sample variance increases the estimated standard error but decreases measures of effect size.
Researchers know that excessively low or high exposure to stress during early childhood can become problematic when individuals are exposed to stress as adults. The measurement of exposure to stress during childhood using a well-validated questionnaire forms a normal distribution with µ= 70 and σ = 6. Researchers know that individuals that score in the middle 65% of exposure to stress during childhood tend to respond the best to exposure to stress as adults. Based on this information, for a sample size of n = 16, which range of sample mean values on the stress questionnaire would be expected 65% of the time?
M = 68.605 to M = 71.395
Which technique provides useful information when there are small changes from one treatment condition to another, when simulations are used or when a placebo is used?
Manipulation checks
In an experiment comparing two treatments, the researcher assigns participants to treatment conditions so that each condition has 10 adults with college degrees and 10 adults with high-school diplomas only. For this study, what method is being used to control participant education level?
Matching
An experiment includes a treatment condition, a no-treatment control, and a placebo control. Which two conditions should be compared to determine the size of the effect that is actually caused by the treatment?
Placebo versus treatment
Assuming all other factors are held constant, if the df value for a two-tailed t-test with α = .05 were increased from df = 6 to df = 20, what would happen to the critical values for t?
The critical values would move closer to t = 0.
Which of the following statements is consistent with hypothesis testing?
The edges of the distribution of sample means are consistent with the alternative hypothesis.
A researcher chooses to collect data from a large sample that represents a population instead of a smaller sample. Which of the following is not a likely consequence of choosing to collect data from a large sample relative to a smaller sample?
The expected value of M will decrease.
Why are t statistics more variable than z-scores?
The extra variability is caused by variations in the sample variance.
An educational specialist develops a new teaching technique for a nutrition course. The educational specialist knows that typically scores on a well-validated measure of nutrition knowledge are normally distributed with µ = 20 and σ = 8. The educational specialist administers their new teaching technique to a sample of n = 25 students who subsequently score M = 22.5 on the measure of nutrition knowledge. Which conclusion can the educational specialist make based on the results of this research study?
The new teaching technique does not have an effect on nutrition knowledge because the computed z-score does not reach the z = ±1.96 threshold.
A sample of n = 25 individuals is selected from a population with µ = 80, and a treatment is administered to the sample. Which outcome is expected if the treatment has no effect?
The sample mean after the treatment should be close to 80, leading a researcher to fail to reject the null hypothesis.
Dr. Jones systematically varies the brightness in the laboratory (400, 800, and 1600 lumens) while holding other variables constant, and observes that the participants' activity level decreases as the brightness decreases. This illustrates ____.
a causal relationship between brightness and activity level
A sample is selected from a normal 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
Two samples from the same population both have n = 10 scores with M = 45. If the t statistic is computed for each sample, then what is the relationship between the two t values?
The sample with the smaller variance will produce the larger t statistic.
Which of the following is a fundamental difference between a t statistic and a z-score?
The t statistic uses the sample variance in place of the population variance
In New York State, the winter months produce higher heating bills and higher levels of depression. Although the numbers show that higher heating bills are related to higher levels of depression, what most likely explains this relationship?
The third-variable problem
A researcher selects a sample and administers a treatment for anxiety to the individuals in the sample. If the sample is used for a hypothesis test, what does the alternative hypothesis ( H 1) put forth about the treatment?
The treatment has an effect on anxiety.
A researcher selects a sample and administers a treatment for anxiety to the individuals in the sample. If the sample is used for a hypothesis test, what does the null hypothesis ( H 0) put forth about the treatment?
The treatment has no effect on anxiety.
What is the effect of decreasing the alpha level (for example, from α = .05 to α = .01)?
This action increases the likelihood of failing to reject H0 and increases the risk of a Type II error.
Which of the following statements correctly describes the effect of increasing the alpha level (for example, from a = .01 to a = .05)?
This action increases the likelihood of rejecting H0 and increases the risk of a Type I error.
A sample has a mean of M = 39.50, a standard deviation of s = 4.30, and produces a t statistic of t = +2.14. For a two-tailed hypothesis test, which of the following is the correct statistical decision for this sample?
This is impossible to determine based on the provided information.
A researcher selects a sample from a population with µ = 30 and uses the sample to evaluate the effect of a treatment. After treatment, the sample has a mean of M = 32 and a variance of s 2 = 6. If Cohen's d is used to measure the size of the treatment effect, which of the following would have no effect on the value of Cohen's d?
an increased sample size
Dr. Ramos is interested in studying how indoor temperature can influence people's sleep quality during the summer. A sample of 100 households is selected in which the residents keep their houses at 76 degrees during the summer. The residents wear a monitoring device that measures their sleep cycles for several nights to get baseline readings. Then, 50 of the homes are randomly assigned to the warm temperature condition in which the residents agree to keep their houses at 82 degrees Fahrenheit. In the other 50 houses, the residents agree to keep their houses at 70 degrees. For several nights, Dr. Ramos collects the sleep data for the people living in the houses to see how the residents' sleep patterns have changed. Assuming that the study allows people to use as many or as few blankets as they like, number of blankets would be a(n) ____ variable in the experiment.
extraneous
The critical boundaries for a hypothesis test are z = +1.96 and z = -1.96. If the z-score for the sample data is z = -1.90, which is the correct statistical decision?
fail to reject H0
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. Which outcome is likely if this happens?
fail to reject H0 and make a Type II error
A researcher moves an experiment out of the laboratory and into the real world. This type of research is called a ____.
field study
Under which circumstance can a very small treatment effect still be statistically significant?
if the sample size (n) is very large
Under what circumstances can a very small treatment effect be statistically significant?
if the sample size is large and the sample variance is small
A researcher is forced to collect data from a smaller sample of individuals to test their research hypotheses than originally anticipated. This will have the effect of ______.
increasing the expected distance between M and µ.
Researchers often use simulation experiments in an attempt to obtain the ____ of an experiment and still keep much of the ____ of research conducted in the real world.
internal validity; external validity
The specific treatment conditions that are used in an experiment are called the ____.
levels of the independent variable
A researcher exposes people to a stressful situation (such as public speaking) to examine the effect of stress on depressed mood. The researcher includes a measure of stress as a ____.
manipulation check
If other factors are held constant, which set of sample characteristics is most likely to produce a statistically significant t statistic?
n = 100 with s2 = 100
The results of a hypothesis test are reported as follows in a scientific report: t(15) = 2.70, p < .05. Based on this report, how many individuals were in the sample?
n = 16
Which of the following samples will have the smallest value for the estimated standard error?
n = 16 with s2 = 16
A researcher is using a two-tailed hypothesis test with α = .05 to evaluate the effect of a treatment. If the boundaries for the critical region are t = ± 2.080, then how many individuals are in the sample?
n = 22
A sample is selected from a normal population with µ = 40 σ = 10. If the sample mean of M = 46 produces a z-score of z = +3.00, then how many scores are in the sample?
n = 25
Consider a normal population with µ = 75 and σ = 10. A sample of at least which size needs to be obtained in order to achieve a standard error of σM = 2.00 or less?
n = 25
A sample with a mean of M = 40 and a variance of s 2 = 12 has an estimated standard error of 2 points. How many scores are in the sample?
n = 3
