PSY 3000 Exam 2
Which of the following is the correct equation for calculation z-scores for a sample?
(Y - M)/SD
Z scores =
(Y - M)/SD
Z Scores=
(Y - u)/o
Consider the follwoing data and acalculate their z-scores based on M = 5 and SD = .5. What is the largest z-score in these data? Y = 1 Y = 3 Y = 5 Y = 6
-8
When expressed as a proportion probability will always be a value between _____ and ____.
0 and 1.00
Given u = 5 and o = 1.5, calculate z-scores for the following data: 5, 6,3 ,5, 2, 7
0, .67, -1.33, 0, -2, 133
Consider the following information: u = 40 and o^2 = 16. Compute the standardized score for Y = 45. Remember, this score should keep the score of Y = 45 relative to the other scores in the population.
1.25
About what percentage of scores would you expect to find at lease 2 standard deviations greater than the mean of the population?
2.15%
You repeatedly draw samples (n = 500) from a population that is normally distributed with u = 230 and o = 50. What will be the standard deviation of the sample means (assuming you draw an infinite number of samples)?
2.236
How large does n need to be to count on the SDM being normally distributed? n is equal to or greater than _________________.
30
Effect sizes provide a measure of _______________.
Magnitude
Lets say a population has a large amount of variability. How might a large amount of variability in the population impact the probability of getting a non representative sample?
Makes it more likely
Complete the sentence: One-tailed tests provide ____________ two-tailed tests.
More power than
Which of the following options correctly completes the sentence. The two hypotheses (H0 and H2) are....
Mutually exclusive and exhaustive
What type of significance test would you use if you do not have a specific theory, previous research, or a rationale to base your hypothesis on and you simply want to know if there is a difference between population values from two groups.
Nondirectional hypothesis; two-tailed test
What type of signifigance test would you use if you do not have a specific theory, previous research, or a rationale to base you hypothesis on and you simply want to know if there is a difference between population values from two groups?
Nondirectional hypothesis; two-tailed test
Which of the follwoing situations would occur, if in reality H0 is false and your anaylsis of your data leads you to not reject H0?
A type 2 error
All statistically significant results are meaningful.
False
Statistical analysis can account for poorly designed studies, biased data, and low response rates from potential study participants.
False
A group of researchers is studying the use of specific theraputic modalities when working with children who experience anxiety. After conducting a randomized control trial testing a new modality, the researchers share their results but do not include an effect size. Which of the following is true?
If researchers do not present enough other specific statistics about their data, other researchers will be unable to compare their results to the new resluts presented by the researchers; Other researchers can compute effect sizes if other spefific statistics are also reported
Given a normal distribution about what percentage of sample means would you expect to be +/- SE from the mean of the sample distribution?
Not 2.35, possibly 1.175, 4.70, 5
________-____________ should be used when you have a specific theory, previous research, or a rationale to base your hypothesis on that a specific group will have a larger/smaller population value than another group.
One-tailed
____________ ______________ should be used when you have a specific theory, previous research, or a rationale to base your hypothesis on that a specific group will have a larger/smaller population value than another group.
One-tailed
A group of researchers is conducting an experiment. Which of the following choices would be sufficient justification for using a one-tailed test instead of a two-tailed test?
Some previous, similar, experiment found that M1 < M2; You are testing a theory which specifically predicts that M1 should be less than M2
If the mean of sampling distribution is the mean of all sample means, which is the mean of the population, what is the standard deviation of the sample means?
Standard Error
The standard deviation of the SDM is also known as the ________________ _____________.
Standard error
Consider the following situations: A two-tailed test t(6) = 2.04, p = .0874 A one-tailed test t(6) = 2.04, p = .0437 Which approach had more power (assuming alpha = .05 and IF really did have an effect)? Hint: I have provided you with more information than you need (and know what to do with at this point) to decide which type of significance test offers more power.
The one-tail test
What happens to the probability of getting Y = 5 when M = 3 and SD decreases (e.g. .75 or .25)?
The probability gets smaller (p becomes smaller).
Consider the following hypothesis. Which hypothesis is the null hypothesis? Which hypothesis is the hypothesis?
There are not differences in depression scores based on treatment mobility; There are differences in depression scores based on treatment mobility.
A group of researchers concludes that because they did not find a significant result in their expirement there is not a difference between the treatment and control group. They have asked you to advise them about what could be going on. Which of the following statements would be an accurate statement to share with them?
They did not have enough power to detect the size difference they thought may have existed If in fact difference existed in the population.
Effect sizes are important to advancing scientific knowledge
True
Standardized effect sized provide researchers the ability to compare the magnitude of effects across studies.
True
The size of an effect can be related to whether or not the results of an analysis are statistically significant.
True
Which of the following situations would occur if in reality H0 is true and your analysis of your data leads you to reject H0?
Type 1 error
One study measured the ages of infants in weeks and another study of the very same infants used months. Would the two studies arrive at different values for the standard deviation?
Yes
Rejecting the null hypothesis when you have a confounding variable means.....
You do not know whether the independent variable, the confounding variable or both caused the result.
Power is the probability that....
You will be able to reject the null hypothesis is actually false.
Increasing the power in an experiment will inerase the likelihood of correctly rejecting the null hypothesis....
only if the null hypothesis is actually false
SD =
square root of variance
Consider the following: You are conducting a study about social awareness development among children. Social awareness scores in a population of scores is normally distributed with a mean of u = 350 and a standard deviation of o = 20. What proportion of the scores are with in +/- 17 of the mean (i.e. 333 is less than or equal to Y is less than or equal to 367)? Consider drawing the population and shading in the regions. Please provide your answer to four decimal places. Hint: Consider drawing the population and shading in the regions. Think about how you might leverage Z-score and the Oak Software Tool.
0.6047
For this question think about the area under the curve. What values of z give a two-tail p-value of .05 (.025 on each tail). z = +/- _______? Hint: You will need to use the Oak Software tool. Make sure to select the area with 'p' and 'z' to the left and right of the curve.
1.96
You sample 15 scores from a population that is normally distributed with u = 230 and o = 50. State the value of the standard error of the SDM. oM = ?
12.91
Which of the following situations would occur, if in reality H0 is false and your analysis of the data leads you to reject H0?
A correct decision
If H0 is true, what is the probability that your analysis of the data will lead you to incorrectly decide to reject H0?
Alpha
Consider the following description of majors at a university with 40,000 students. There are 15,000 students who have not yet decided their major. There are 5,000 students who have a major in the social and behavioral sciences. 9,000 students who have a health related major; and 3,000 students in a physical science major. You are conducting a study at this university and want to draw a representative sample of majors. If each major has an equal chance of being selected, what is the probability you will draw a student with a social and behavioral sciences major?
Between 0.12 and 0.131
For this question, think about the area under the curve. What value of z gives a one-tail p-value of .05 on the upper tail? z = ? Hint: You will need to use the Oak Software tool. Make sure to select the area with 'p' and 'z' on the right side of the curve.
Between 1.6 and 1.7
A variable (something other than random error and the independent variable) that could account for why you get a certain result is called a _____________ variable.
Confounding
Which of the following will increase the power of the experiment?
Decrease variability within groups; Increasing the effect of the independent variable; Increase the sample size (n)
Consider the following information for a study participant: Happiness = 90, z = 3.5 Depression = 5, z = .5 Empathy = 3.5, z = 2 Compared to other study participants, for which measure is the current participant most similar the mean of the measure? Hint: Think about how to compare participants to one another.
Depression
Consider the following information M1=50, M2 = 61, a = 0.05, p = 6. If using a two-tailed test, what would you decide about the null hypothesis?
Do not reject the null hypothesis
Raw effect sizes can be compared across studies using different measures of the same construct
False
Which of the following statements is true about one-tailed compared to two-tailed significance tests?
Increased Power
Find the Z Scores for the following data: 5,6,3, 5,2,7
M=4.67 SS=11.97 S^2=2 SD=1.41 .23, .94, -.24, .23,-.94, 1.65
Probability is necessary in statistics to make generalizations about ______________ using data from _______________.
Populations; Samples
A group of researchers is conducting an experiment. Which of the following choices would be sufficiant justification for using a one-tailed test instead of a two-tailed test?
Some previous, similar, experiment found that M1 < M2; You are testing a theory which specifically predicts that M1 should be less than M2
Using the Oak Software, determine if the probability of obtaining a z-score of 1.98 (using a two tailed test) is below p = .05. Hint: Make sure this option is selected when answering this question. Two tailed option.
Answer is not Yes, p is less than .05
Consider the following infromation. M1= 50, M2 = 61, a = .05, p = .06. If using a two-tailed test, what would you decide about the null hypothesis?
Do not reject the null hypothesis
You are conducting a study about young adult perspective-taking. You are using a measure of perspective-taking that provides scores indicating the depth of perspective-taking. The score has possible values of 1-100. you draw a sample from a population of young adults that is normally distributed with u = 65 and o = 9. If you sample one score from the population, what is the probability that it will have a score of at least 4 below the population mean? Consider drawing a curve while working this out. Hint: You will need to use the Oak Software tool. Make sure to select the area with 'p' and 'z' on the left of the curve.
0.33
Given the following information, which set of data has the largest standard error? Set 1: M = 5, SD = 1.5, n = 150 Set 2: M = 5, SD = .75, n = 75 Set 3: M = 5, SD = 1.25, n = 500
Set 1
The standard deviation of the sample means is the ________________.
Standard error
Consider the following situation: A group of researchers conducted a quasi-experimental study examing the effects of spending time outside on people's mental health. After collecting and analyzing their data, they stated they found a statistically significant small effect suggesting that spending time outside was related to mental health. The standardized effet size was very small and the associated significance test resulted in p = .053 Prior to conducting the study, the researchers set o = .05. Based on these results, which of the following are true?
The researches committed a type 2 error. The researchers did not have enough power to detect the size of relationship they through they could between mental health and spending time outside if there was a relationship in the population. There is less than a 10% chance they incorrectly concluded that there was a relationship between spending time outside and mental health when, in fact, there was not a relationship between mental health and spending time outside.
Consider the following: A researcher conducts an experiment to understand if repeating back sentences after hearing them improves a person's memory of the sentence content. Given and alpha = 0.05, do results with an associated p = .01 suggest that the researcher had sufficient power to make a conclusion about the null hypothesis (H0 = Repeating back sentences after hearing them does not improve a person's memory of the sentence content)? Choose the answer below that correct answers this question.
Yes. A significance test with a p = .01 and an alpha = .05 suggests that the test was sufficiently powered to detect the effect because p is less than or equal to .05 would be considered statistically significant, thus leading to the decision to reject the null hypothesis.
Z-scores related to the sampling distribution of the mean.....
provide information about how likely a sample value is to have occurred if a sample value was recalculated from a new sample drawn from the same population an infinite number of times.
