Stats Midterm
For the scores in the following frequency distribution table, the mean is M = 3. (T/F) X f 4 1 3 4 2 2
False
If the sample size is increased, then the standard error for sample means will also increase. (T/F)
False
If two samples from the same population are the same size and have the same mean, then they will have the same t statistic. (T/F)
False
A sample of n = 4 scores is selected from a population with μ = 40 with σ = 8, and the sample mean is M = 43. What is the expected value for the sample mean? A. 40 B. 10 C. 8 D. 2
40
A normal distribution has a mean of µ = 40 with σ = 10. If a vertical line is drawn through the distribution at X = 55, what proportion of the scores are on the right side of the line? A. 0.3085 B. 0.6915 C. 0.0668 D. 0.9332
0.0668
What is the probability of randomly selecting a z-score greater than z = 0.75 from a normal distribution? A. 0.7734 B. 0.2266 C. 0.2734 D. 0.4532
0.2266
For a repeated-measures study comparing two treatments with a sample of n = 9 participants, the difference scores have a mean of MD = 4.90 with SS = 72. What is the estimated standard error for the sample mean difference? A. 9 B. 3 C. 1 D. √8/3
1
A linear regression equation is computed for a sample of n = 13 pairs of X and Y scores. For the analysis of regression testing the significance of the equation, what are the df values for the F-ratio? A. 1, 11 B. 1, 12 C. 2, 10 D. 2, 11
1, 11
The results of a hypothesis test are reported as follows: t(15) = 2.70, p < .05. Based on this report, how many individuals were in the sample? A. 14 B. 15 C. 16 D. Cannot be determined from the information provided
16 type of test (df) = sample's t score, p [significant or not] [alpha level]
A repeated-measures study using a sample of n = 20 participants would produce a t statistic with df = ____. A. 9 B. 19 C. 20 D. 39
19
A skewed distribution typically has _____ tail(s) and a normal distribution has ____ tail(s). A. 1; 1 B. 1; 2 C. 2; 1 D. 2; 2
1; 2
What is the value of ΣX2 for the scores 1, 0, 2, 4? A. 14 B. 21 C. 28 D. 49
1^2=1 0^2=0 2^2=4 4^2=16 1+0+4+16=21 21
An independent-measures study with n = 6 in each sample produces a sample mean difference of 4 points and a pooled variance of 12. What is the value for the t statistic? A. 1 B. 2 C. 4 D. 4
2
An analysis of variances produces dftotal = 29 and dfwithin = 27. For this analysis, what is dfbetween? A. 1 B. 2 C. 3 D. Cannot be determined without additional information
2
The following table shows the results of an analysis of variance comparing two treatment conditions with a sample of n = 11 participants in each treatment. Note that several values are missing in the table. What is the missing value for the F-ratio? Source SS df MS Between xx xx 14 F = xx Within xx xx xx Total 154 xx A. 2 B. 7 C. 14 D. 28
2
For the linear equation Y = 2X + 4, if X increases by 1 point, how much will Y increase? A. 1 points B. 2 points C. 3 points D. 4 points
2 points
A sample of n = 4 scores has SS = 60. What is the variance for this sample? A. 30 B. 20 C. 60 D. 15
20
For the following frequency distribution of quiz scores, how many individuals took the quiz? X f 5 6 4 5 3 5 2 3 1 2 A. 5 B. 15 C. 21 D. Cannot be determined
21
A matched-subjects study and an independent-measures study both produced a t statistic with df = 10. How many individuals participated in each study? A. 11 for matched-subjects and 11 for independent-measures B. 11 for matched-subjects and 12 for independent-measures C. 12 for matched-subjects and 12 for independent-measures D. 22 for matched-subjects and 12 for independent-measures
22 for matched-subjects and 12 for independent-measures
An independent-measures study uses n = 15 participants in each group to compare two treatment conditions. What is the df value for the t statistic for this study? A. 14 B. 15 C. 28 D. 29
28
For a particular population, a sample of n = 4 scores has a standard error of 6. For the same population, a sample of n = 16 scores would have a standard error of _____. A. 8 B. 6 C. 3 D. 2
3
For an independent-measures ANOVA comparing three treatments with a sample of n = 5 in each treatment, what is the critical value for the F-ratio using α = .05? A. 3.88 B. 3.49 C. 3.74 D. 3.34
3.88
In a population with a standard deviation of σ = 5, a score of X = 44 corresponds to a z-score of z = 2.00. What is the population mean? A. 49 B. 54 C. 39 D. 34
34
An independent-measures study produces sample means of M1 = 20 and M2 = 17. If both samples have n = 18 scores and Cohen's d = 0.50, what is the value for the pooled variance? A. 2 B. 4 C. 6 D. 36
36
An independent-measures research study uses a total of 40 participants to compare two treatment conditions. What is the df value for the t statistic for this study? A. 18 B. 19 C. 38 D. 39
38
A sample is selected from a population with μ = 50 and σ = 12. If the sample mean of M = 56 produces a z-score of z = +1.00, then how many scores are in the sample? A. 2 B. 4 C. 9 D. 16
4
What is the mean for the following sample of scores? Scores: 1, 4, 5, 6 A. 16 B. 8 C. 4.5 D. 4
4
A sample has a mean of M = 90. If each score in the sample is multiplied by 5, then what is the mean for the new distribution? A. 18 B. 85 C. 95 D. 450
450
A chi-square test for independence is being used to evaluate the relationship between two variables, one of which is classified into 3 categories and the second of which is classified into 4 categories. What is the df value for the chi-square statistic? A. 6 B. 4 C. 10 D. 11
6
For the following distribution, how many people have scores greater than X = 14? X f 20-24 2 15-19 5 10-14 4 5-9 1 A. 2 B. 5 C. 7 D. 11
7
An analysis of variances produces dfbetween = 3 and dfwithin = 24. If each treatment has the same number of participants, then how many participants are in each treatment? A. 6 B. 7 C. 8 D. 9
7
If random samples, each with n = 9 scores, are selected from a normal population with µ = 80 and σ = 36, what is the expected value for the distribution of sample means? A. 4 B. 12 C. 16 D. 80
80
When the data form a 2×2 matrix, the phi-coefficient is used to measure effect size for the chi-square test for independence. If other factors are held constant, how does sample size influence the values for phi and chi-square? A. A larger sample increases both phi and chi-square. B. A larger sample increases phi but has no effect on chi-square. C. A larger sample increases chi-square but has no effect on phi. D. Sample size does not influence either phi or chi-square.
A larger sample increases chi-square but has no effect on phi.
Which combination of factors will produce the largest value for the standard error? A. A large sample and a large standard deviation B. A small sample and a large standard deviation C. A large sample and a small standard deviation D. A small sample and a small standard deviation
A small sample and a large standard deviation
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 s2 = 6. Which of the following would definitely increase the likelihood of rejecting the null hypothesis? A. Increase the sample size B. Increase the sample mean C. Decrease the sample variance D. All of the other options will increase the likelihood of rejecting the null hypothesis
All of the other options will increase the likelihood of rejecting the null hypothesis
Dependent vs. Independent
An independent variable is the variable that is changed or controlled in a scientific experiment to test the effects on the dependent variable. A dependent variable is the variable being tested and measured in a scientific experiment.
Which of the following is true for most distributions? A. Around 30% of the scores will be located within one standard deviation of the mean. B. Around 50% of the scores will be located within one standard deviation of the mean. C. Around 70% of the scores will be located within one standard deviation of the mean. D. Around 90% of the scores will be located within one standard deviation of the mean.
Around 70% of the scores will be located within one standard deviation of the mean.
What is the relationship between the alpha level, the size of the critical region, and the risk of a Type I error? A. As the alpha level increases, the size of the critical region increases, and the risk of a Type I error increases. B. As the alpha level increases, the size of the critical region increases, and the risk of a Type I error decreases. C. As the alpha level increases, the size of the critical region decreases, and the risk of a Type I error increases. D. As the alpha level increases, the size of the critical region decreases, and the risk of a Type I error decreases.
As the alpha level increases, the size of the critical region increases, and the risk of a Type I error increases.
What kind of variable requires the use of real limits? A. Independent B. Dependent C. Discrete D. Continuous
Continuous
Continuous vs. Discrete
Continuous: Changing. (ex. age) Discrete: You either are or aren't. Categories. (ex. Married/Not married)
For the independent-measures t statistic, what is the effect of increasing the sample variances? A. Increase the likelihood of rejecting H0 and increase measures of effect size B. Increase the likelihood of rejecting H0 and decrease measures of effect size C. Decrease the likelihood of rejecting H0 and increase measures of effect size D. Decrease the likelihood of rejecting H0 and decrease measures of effect size
Decrease the likelihood of rejecting H0 and decrease measures of effect size
A researcher collects a sample of n = 20 Introductory Psychology textbooks and records the number of pages in each book. The results are then placed in a grouped frequency distribution table using intervals of 0-99 pages, 100-199 pages, 200-299 pages, and so on. If the results were converted into a frequency distribution graph, what kind of graph should be used? A. A bar graph B. A histogram C. A polygon D. Either a histogram or a polygon
Either a histogram or a polygon
The critical boundaries for a hypothesis test are z = +1.96 and -1.96. If the z-score for the sample data is z = -1.90, what is the correct statistical decision? (beginning of ch.8 quiz) A. Fail to reject H1 B. Fail to reject H0 C. Reject H1 D. Reject H0 (beginning of ch.8 quiz)
Fail to reject H0
A jar contains 10 red marbles and 20 blue marbles. If you take a random sample of two marbles from this jar, and the first marble is blue, then the probability that the second marble is blue is p = 19/29. (T/F)
False
A professor records the number of students who are absent each day for the semester. Because this is a discrete variable, a bar graph should be used to show the frequency distribution. (T/F)
False
A recent report concluded that children with siblings have better social skills than children who grow up as an only child. This is an example of an experimental study. (T/F)
False
A repeated-measures study and an independent-measures study both produce a t statistic with df = 20. The repeated-measures study used more subjects than the independent-measures study. (T/F)
False
A sample has a mean of M = 40. If a new score of X = 35 is added to the sample, then the sample mean would increase. (T/F)
False
A sample is obtained from a population with σ = 20. If the sample mean has a standard error of 5 points, then the sample size is n = 4. (T/F)
False
A sample of n = 10 scores has a mean of 50. A second sample has n = 5 scores and M= 60. If the two samples are combined, the combined sample mean will be greater than 55. (T/F)
False
A vertical line drawn through a normal distribution at z = -0.75 separates the distribution into two sections. The proportion in the smaller section is 0.2734. (T/F)
False
After a researcher adds 5 points to every score in a sample, the standard deviation is found to be s = 10. The original sample had a standard deviation of s = 5. (T/F)
False
For the following distribution of scores, 20% of the individuals have scores of X = 1. (T/F) X f 5 2 4 8 3 5 2 3 1 2
False
It is possible to have a distribution of scores where no individual has a score exactly equal to the mode. (T/F)
False
A negative correlation means that decreases in the X variable tend to be accompanied by decreases in the Y variable. (T/F)
False
A research report presents the results of an independent-measures ANOVA as follows: F(3, 28) = 5.36, p < .01. If all the samples were the same size, then each sample had n = 7 participants. (T/F)
False
If other factors are held constant, lowering the alpha level will increase the power of a hypothesis test. (T/F)
False
In a repeated measures study, the null hypothesis says that the mean for the sample of difference scores is equal to zero. (T/F)
False
One concern for a repeated-measures study is that the participants in one treatment may have different characteristics than the participants in the other treatment. (T/F)
False
The observed frequencies for a chi-square test can be fractions or decimal values. (T/F)
False
The phi-coefficient is used to measure relationships for data that would also be appropriate for an independent-measures t test. (T/F)
False
The null hypothesis states that the sample mean (after treatment) is equal to the original population mean (before treatment). (T/F)
False (?) -> emailed professor with question on 3/22
For a population of exam scores, a score of X = 83 corresponds to z = +0.50 and a score of X = 89 corresponds to z = +1.50. The population mean is μ = 80. (T/F)
Given info: x=83 z=.50 x=89 z=1.50 1. Find standard deviation by finding the difference between x values/difference between z values. Difference between x values = 6 Difference between z values = 1 σ = 6/1 2. Find mean with x = μ+zσ formula. Use formula x = μ+zσ 83 = μ + (.5)(6) 83 = μ + 3 80 = μ Answer: True
A sample of n = 4 scores has a mean of M = 8. If one new score with a value of X = 3 is added to the sample, what will be the value for the new mean? A. M = 7 B. M = 8 C. M = 8.75 D. Cannot be determined with the information provided
Given info: M=8 Step 1. M=ΣX/N= unknown ΣX/4= 8 Step 2. 34/4=8, so ΣX is 32 Step 3. Add ΣX (ΣX=32) + new x value (x=3) = 35 Step 4: M= ΣX/N = 35/5 = 7 Answer: The new M = 7
Students in an introductory art class are classified as art majors and non-art majors. What scale of measurement is being used to classify the students? A. Nominal B. Ordinal C. Interval D. Ratio
Nominal
Scales of Measurement
Nominal: Things you can name (ex. name, gender, race) Ordinal: Order (ex. 1st, 2nd, 3rd; small, med, large) Interval: Equal spacing/sizing between categories. Zero doesn't mean absence (ex. Zero in golf just means above/below par) Ratio: Ordered categories. Equal interval between categories. Absolute zero point. (Note: This is almost everything.)
Positive vs. Negative Skew
If mean - median > 0, the distribution is positively skewed. Tail points right, toward larger numbers. If mean - median < 0, the distribution is negatively skewed. Tail points left, toward smaller numbers.
Under what circumstances can a very small treatment effect be statistically significant? A. If the sample size big and the sample variance is small B. If the sample size and the sample variance are both big C. If the sample size is small and the sample variance is big D. If the sample size and the sample variance are both small
If the sample size big and the sample variance is small
For an independent-measures t statistic, what is the effect of increasing the number of scores in the samples? A. Increase the likelihood of rejecting H0 and increase measures of effect size B. Increase the likelihood of rejecting H0 and decrease measures of effect size C. Increase the likelihood of rejecting H0 and have little or no effect on measures of effect size D. Decrease the likelihood of rejecting H0 and have little or no effect on measures of effect size
Increase the likelihood of rejecting H0 and have little or no effect on measures of effect size
What happens to the expected value of M as sample size increases? A. It increases. B. It decreases. C. It stays constant. D. The expected value does not change in a predictable manner when sample size increases.
It stays constant.
Which of the following describes what a confidence interval does? A. It uses a sample mean to estimate the corresponding population mean. B. It uses a population mean to predict a sample mean. C. It uses a level of confidence to estimate a sample mean. D. It uses the sample mean to determine a level of confidence.
It uses a sample mean to estimate the corresponding population mean.
The Pearson and the Spearman correlations are both computed for the same set of data. If the Spearman correlation is rS = +1.00, what can you conclude about the Pearson correlation? A. It will be positive. B. It will have a value of 1.00. C. It will be positive and have a value of 1.00. D. There is no predictable relationship between the Pearson and the Spearman correlations.
It will be positive.
In the observed frequencies for a chi-square test for independence, how often is each participant counted? A. Just once B. Once in each row C. Once in each column D. Once in each row and once in each column
Just once
Assuming 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? A. Large sample sizes and small sample variances B. Large sample sizes and large sample variances C. Small sample sizes and small sample variances D. Small sample sizes and large sample variances
Large sample sizes and small sample variances
If other factors are held constant, which set of sample characteristics is most likely to reject a null hypothesis stating that μ = 80? A. M = 85 for a sample of n = 25 B. M = 85 for a sample of n = 100 C. M = 90 for a sample of n = 25 D. M = 90 for a sample of n = 100
M = 90 for a sample of n = 100
Which of the following is expected if the null hypothesis is true for an analysis of variance? A. SSbetween should be about the same size as SStotal B. SSbetween should be about the same size as SSwithin C. MSbetween should be about the same size as MStotal D. MSbetween should be about the same size as MSwithin
MSbetween should be about the same size as MSwithin
descriptive statistics
Numerical data used to measure and describe characteristics of groups. Includes measures of central tendency (mean, median, mode) and measures of variation (the range, interquartile range, variance, and standard deviation). Includes mean and graphs.
In a distribution with positive skew, scores with the highest frequencies are _____. A. on the right side of the distribution B. on the left side of the distribution C. in the middle of the distribution D. represented at two distinct peaks
On the left side of the distribution
Using letter grades (A, B, C, D, and F) to classify student performance on an exam is an example of measurement on a(n) _______ scale of measurement. A. nominal B. ordinal C. interval D. ratio
Ordinal
Which of the following accurately describes the proportions in the tails of a normal distribution? A. Proportions in the right-hand tail are greater than 0.50, and proportions in the left-hand tail are less than 0.50. B. Proportions in the right-hand tail are less than 0.50, and proportions in the left-hand tail are greater than 0.50. C. Proportions in both tails are less than 0.50. D. Proportions in both tails are greater than 0.50.
Proportions in both tails are less than 0.50.
A researcher uses an anonymous survey to investigate the television-viewing habits of American adolescents. Based on the set of 356 surveys that were completed and returned, the researcher finds that these students spend an average of 3.1 hours each day watching television. For this study, the set of 356 students who returned surveys is an example of a _______. A. Parameter B. Statistic C. Population D. Sample
Sample
What is the first step to be performed in the following mathematical expression, ΣX2? A. Square each score B. Add the scores C. Add the squared scores D. Square the sum of the scores
Square each score
For the following scores, which of the following actions will increase the range? Scores: 3, 7, 10, 15 A. Subtract 3 points from the score X = 3 B. Subtract 3 points from the score X = 7 C. Subtract 3 points from the score X = 10 D. Subtract 3 points from the score X = 15
Subtract 3 points from the score X = 3
What is referred to by the term observed frequencies? A. The frequencies found in the sample data B. The frequencies found in the population being examined C. The frequencies computed from the null hypothesis D. The frequencies that are hypothesized for the population being examined
The frequencies found in the sample data
Which of the following is an accurate definition for the power of a statistical test? A. The probability of rejecting a true null hypothesis B. The probability of supporting true null hypothesis C. The probability of rejecting a false null hypothesis D. The probability of supporting a false null hypothesis
The probability of rejecting a false null hypothesis
A high school gym teacher records how much time each student requires to complete a one-mile run. This is an example of measuring a continuous variable. (T/F)
True
A professor standardizes exam scores so that all exams have μ = 50 and σ = 10. If the original scores from an exam have μ = 42 and σ = 6, then a student with an original exam score of X = 45 would receive a standardized score of X = 55. (T/F)
True
A researcher is interested in the average income for registered voters in the United States. The entire group of registered voters is an example of a population. (T/F)
True
If an analysis of variance produces a value of F = 0, then all the samples have the same mean. (T/F)
True
A sample of n = 7 scores has a mean of M = 5. After one new score is added to the sample, the new mean is calculated to be M = 6. The new score was X = 13. (T/F)
True
For a normal distribution with µ = 80 and σ = 10, the score that separates the bottom 10% of the distribution from the rest is 67.2 (T/F)
True
For a severely skewed distribution, the median often provides a better measure of central tendency than the mean. (T/F)
True
For any normal distribution, the probability of randomly selecting a z-score less than z = 1.40 is p = 0.9192. (T/F)
True
If an entire population of N = 20 scores is transformed into z-scores, the set of 20 z-scores will have SS = 20. (T/F)
True
If you have a score of X = 66 on an exam with m = 70, you should expect a better grade if σ = 10 than if σ = 5. (T/F)
True
It is customary to list the score categories in a frequency distribution from the highest down to the lowest. (T/F)
True
A Pearson correlation of r = -0.90 indicates that the data points are clustered close to a line that slopes down to the right. (T/F)
True
A repeated-measures research study uses a total of 20 participants to compare two treatment conditions. If the results are used to construct a 90% confidence interval for the population mean difference, then the t values will be ±1.729. (T/F) [Ch.11]
True
A researcher obtains SSX = 20, SSY = 5, and SP = 7 for a set of n = 25 pairs of scores. The Pearson correlation for these scores is r = 7/10 = 0.70. (T/F)
True
After an ANOVA, a researcher computes n2 to evaluate effect size and obtains n2 = 0.50. If the ANOVA had SStotal = 100, then SSwithin = SSbetween = 50. (T/F)
True
Chi-square values are always greater than or equal to zero. (T/F)
True
For a fixed level of significance, the critical value for chi-square increases as the degrees of freedom increase. (T/F)
True
For a regression equation with a positive slope, if the X value is above the mean for the X scores, then the predicted Y value will be above the mean for the Y scores. (T/F)
True
For the expected frequencies in a chi-square test for independence, the proportions for any row are the same as the proportions in every other row. (T/F)
True
If a sample has an odd number of scores, at least one individual will have a score exactly equal to the median. (T/F)
True
If a set of n = 9 difference scores has a mean of MD = 3.5 and a variance of s2 = 36, then the sample will produce a repeated-measures t statistic of t = 3.5/2. (T/F)
True
If other factors are held constant, the larger the two sample sizes, the greater the likelihood that the independent-measures t test will find a significant difference. (T/F)
True
One sample has s2 = 12, and a second sample has s2 = 15. The pooled variance for these two samples will be between 12 and 15. (T/F)
True
Posttests are only needed if H0 is rejected in an ANOVA comparing more than two treatments. (T/F)
True
The 95% confidence interval for the difference between two treatment means extends from 2.50 to +5.50. Based on this information, you can conclude that there is no significant difference between the treatments at the .05 level of significance. (T/F)
True
The alpha level determines the risk of a Type I error. (T/F)
True
The chi-square test for goodness of fit evaluates the distribution for one variable, and the test for independence evaluates the relationship between two variables. (T/F)
True
The chi-square test for independence is similar to an independent-measures t test because it can be used to evaluate the difference between two populations or two treatment conditions. (T/F)
True
There is always a possibility that the decision reached in a hypothesis test is incorrect. (T/F)
True
To calculate the variance for a population, SS is divided by N. (T/F)
True
To estimate a population mean with a confidence interval, you first must estimate a range of values for t. (T/F)
True
A sample of n = 9 scores is selected from a population with μ = 50 and σ = 12. The probability of obtaining a sample mean greater than 46 is p = 0.8413. (T/F)
True (according to quiz, but this seems false...? Ask professor)
When comparing more than two treatment means, why should you use an analysis of variance instead of using multiple t tests? A. Using multiple t tests increases the risk of a Type I error. B. Using multiple t tests increases the risk of a Type II error. C. The analysis of variance is more likely to detect a treatment effect. D. There is no advantage to using an analysis of variance instead of multiple t tests.
Using multiple t tests increases the risk of a Type I error.
The sum of the squared deviation scores is SS = 20 for a sample of n = 5 scores. What is the variance for this sample? A. 4 B. 5 C. 80 D. 100
Variance of sample = SS/N-1 = 20/5-1 = 20/4 = 5 Answer: 5
Under what circumstances is a score that is located 5 points above the mean a central value, relatively close to the mean? A. When the population mean is much less than 5 B. When the population mean is much greater than 5 C. When the population standard deviation is much less than 5 D. When the population standard deviation is much greater than 5
When the population standard deviation is much greater than 5
Under what circumstances is the computational formula preferred over the definitional formula when computing SS, the sum of the squared deviations, for a sample? A. When the sample mean is a whole number B. When the sample mean is not a whole number C. When the sample variance is a whole number D. When the sample variance is not a whole number
When the sample mean is not a whole number
When is there a risk of a Type II error? A. Whenever H0 is rejected B. Whenever H1 is rejected C. Whenever the decision is "fail to reject H0" D. The risk of a Type II error is independent of the decision from a hypothesis test.
Whenever the decision is "fail to reject H0"
If the following distribution were shown in a histogram, the width of the bar above the 15-19 interval would reach from _____ to _____. X f 20-24 2 15-19 5 10-14 4 5-9 1 A. X = 14.5 to X = 19.5 B. X = 15.5 to X = 18.5 C. X = 15.5 to X = 19.5 D. X = 15.0 to X = 19.0
X = 14.5 to X = 19.5
You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis. If the treatment actually does have an effect, which of the following is true? A. You have made a Type I error. B. You have made a Type II error. C. You might have made a Type I error, but the probability is only 5% at most. D. You have made the correct decision.
You have made the correct decision.
A sample of n = 20 scores has a mean of M = 45 and a standard deviation of s = 8. In this sample, what is the z-score corresponding to X = 57? A. z = 12/20 = 0.60 B. z = 1.00 C. z = 1.50 D. z = 2.00
z = 1.50
mean, median, mode
measures of central tendency Mean: add all the scores and divide by number of scores Median: middle number in the ordered scores Mode: most frequent score
A researcher reports t(12) = 2.86, p < .05 for a repeated-measures research study. How many individuals participated in the study? A. n = 11 B. n = 13 C. n = 24 D. n = 25
n = 13
inferential statistics
numerical data that allow one to generalize- to infer from sample data the probability of something being true of a population procedures used to draw conclusions about larger populations from small samples of data Sample to population
Formulas
proportion = f/N (frequency/size of population) M = Σx/n deviance (from mean) = x-μ Variance (population) = SS/N Standard deviation (population) = √SS/N Variance (sample) = SS/N-1 Standard deviation (sample) = √SS/N-1 Comparing individual to population = z = M-μ/σ --- Comparing sample to a population = z = M-μ/σM Standard error of the mean = σM = σ/√n --- x = μ + zσ --- μM (distribution of sample means) = μ (population mean)
A set of n = 5 pairs of X and Y values has SSX = 16, SSY = 4 and SP = 2. For these data, what is the Pearson correlation? A. r = 2/64 B. r = 2/8 C. r = √2/8 D. r = 64/64
r = 2/8
For a population with a mean of μ = 80 and σ = 10, only 2.28% of the scores are greater than X = 100. (T/F)
z= x-μ/σ = 100-80/10 = 20/10 = 2 z=2.00 -> .0228 on z-table -> 2.28% Answer: True
A sample of n = 9 scores is obtained from a population with μ = 70 and σ = 18. If the sample mean is M = 76, what is the z-score for the sample mean? A. z = 0.33 B. z = 0.50 C. z = 1.00 D. z = 3.00
z=1.00
A set of X and Y scores has MX = 4, SSX = 10, MY = 5, SSY = 40, and SP = 20. What is the regression equation for predicting Y from X? A. Ŷ = 0.25X + 4 B. Ŷ = 4X - 9 C. Ŷ = 0.5X + 3 D. Ŷ = 2X - 3
Ŷ = 2X - 3
You are instructed to subtract 4 points from each score, square the resulting value, and find the sum of the squared numbers. How would this set of instructions be expressed in summation notation? A.ΣX - 42 B. (ΣX - 4)2 C. Σ(X - 4)2 D. ΣX2 - 4
Σ(X - 4)2
In a population with σ = 8, a score of X = 44 corresponds to a z-score of z = -0.50. What is the population mean? A. μ = 36 B. μ = 40 C. μ = 48 D. μ = 52
μ = 48
A population has μ = 50. What value of σ would make X = 55 an extreme value out in the tail of the distribution? A. σ = 1 B. σ = 5 C. σ = 10 D. Cannot determine with the information given
σ = 1
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? A. σ = 12 B. σ = 1.00 C. σ = 0 D. Cannot be determined from the information given
σ = 1.00
Symbols
σ = population standard deviation σ^2 = population variance μ = population mean N = population size s = sample standard deviation s^2 = sample variance σM = standard error of the mean (S.E.M.) M = sample mean n = sample size μM = distribution of sample means n-1 = degrees of freedom
IQ scores form a normal distribution with µ = 100 and σ = 15. Individuals with IQs above 140 are classified in the genius category. What proportion of the population consists of geniuses? A. 0.9962 B. 0.5038 C. 0.4962 D. 0.0038
0.0038
What proportion of a normal distribution is located between the mean and z = 1.40? A. 0.9192 B. 0.0808 C. 0.4192 D. 0.8384
0.4192
Which set of scores has the smallest standard deviation? A. 11, 17, 31, 53 B. 5, 11, 42, 22 C. 145, 143, 145, 147 D. 27, 105, 10, 80
145, 143, 145, 147
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. What outcome is likely if this happens? A. Reject H0 and make a Type I error B. Correctly reject H0 C. Fail to reject H0 and make a Type II error D. Correctly fail to reject H0
Fail to reject H0 and make a Type II error
Which of the following will not increase the width of a confidence interval? A. Increase the percentage of confidence from 80% to 90% B. Reduce the sample size from n = 25 to n = 16 C. Increase the sample mean from MD = 2 to MD = 4 D. All of the other options will increase the width of a confidence interval.
Increase the sample mean from MD = 2 to MD = 4
If a set of scores is displayed in a frequency distribution polygon, what scale of measurement was used to measure the scores? A. Nominal or ordinal B. Interval C. Ratio D. Interval or ratio
Interval or ratio
What are the values for SS and variance for the following sample of n = 4 scores? Sample: 1, 1, 0, 4 A. SS = 9 and variance = 3 B. SS = 9 and variance = 2.25 C. SS = 18 and variance = 6 D. SS = 18 and variance = 9
SS = 9 and variance = 3
A distribution with µ = 35 and σ = 8 is being standardized so that the new mean and standard deviation will be µ = 50 and σ = 10. In the new, standardized distribution, your score is X = 45. What was your score in the original distribution? A. X = 30 B. X = 31 C. X = 39 D. X = 45
X = 31
A sample of n = 16 scores produces a t statistic of t = 2.00. If the sample is used to measure effect size with r^2, what value will be obtained for r^2? A. r^2 = 2/20 B. r^2 = 4/20 C. r^2 = 2/19 D. r^2 = 4/19
r^2 = 4/19 r^2 = t^2/t^2+df r^2 = 2^2/2^2+15 =4/4+15 =4/19
A sample is selected from a population with μ = 70, and a treatment is administered to the sample. After treatment, the sample mean is M = 74, and Cohen's d is d = 1.00. What is the value of the sample variance? A. s^2 = 2 B. s^2 = 4 C. s^2 = 16 D. It is impossible to determine the sample variance without more information.
s^2 = 16 d = M - μ/s So... 1 = 74-70/s 1=4/s s=4 So s^2 = 16
There is a 6-point difference between two sample means. If the two samples have the same variance, which of the following values would make the mean difference easiest to see in a graph showing the two distributions? A. s^2 = 2 B. s^2 = 8 C. s^2 = 16 D. s^2 = 64
s^2 = 2