Final Practice Stats

Professor Juarez thinks the students she has in her statistics class this term are more creative than most students at this university. A previous study found that students at this university had a mean score of 35 on a standard creativity test. Professor Juarez finds that her class scores an average of 40 on this scale, with an estimated population standard deviation of 7. The standard deviation of the distribution of means comes out to 1.63.What is the t score? -(40-35)/7 = .71 -(40-35)/1.63 = 3.07 -(40-35)/72 = 5/49 = .10 -(40-35)/1.632 = 5/2.66 = 1.88

(40-35)/1.63 = 3.07

A social psychologist interested in cultural differences, compared women of two ethnic groups on a Role Approval Index (high scores mean high degrees of approval of ones own social role). The results were as follows. Ethnic Group A: N=15 M=55 S2=6.5 Ethnic Group B: N=23 M=51 S2=4.5If the standard deviation of the distribution of the difference between means is .76, what is the t score? (15-23)/.76 = -10.53. (.76)(15-23) = -8.00. [(6.5+4.5)/2][.76] = 4.18. (55-51)/.76 = 5.26.

(55-51)/.76 = 5.26.

When conducting a t test for independent means, a typical research hypothesis might be -the mean of Population 1 is greater than the mean of Population 2. -the mean of Sample 1 is greater than the mean of Sample 2. -the mean of Sample 1 is the same as the mean of Sample 2. -the mean of Population 1 is the same as the mean of Population 2.

-the mean of Population 1 is greater than the mean of Population 2.

In psychology, a moderate correlation coefficient is considered to be about .7 .5 .3 .1

.3

A school counselor claims that he has developed a technique to reduce pre-studying procrastination in students. He has students time their procrastination for a week and uses this as a pretest (before) measure of procrastination. Students then attend a workshop in which they are instructed to do a specific warming up exercise for studying by focusing on a pleasant activity. For the next week, students again time their procrastination. The counselor then uses the time from this week as the posttest (after) measure.Suppose the counselor found the sum of squared deviations from the mean (of the change scores) of the sample to be 135. Given that he tested 10 people, what would the estimated population variance be? 135/10 = 13.5 135/9 = 15.0 10/135 = .074 9/135 = .067

135/9 = 15.0

In a chi-square test, the variables are -rank-order (ordinal). -ratio-scale. -continuous (quantitative). -categorical (nominal).

categorical (nominal).

One advantage of the chi-square test over most other inferential statistical procedures is that it -can use the comparison distribution of any other statistical procedure. -does not require as many participants. -can be easily applied to repeated-measures designs. -has minimal assumptions.

has minimal assumptions.

Which of the following is the most likely way for results of a t test to be presented in a research article for a study with 25 participants? -t test(25) < significant. -t test(25) = 3.01, p < .05. -t(24) = 2.94, p < .01. -t(24) < significant.

t(24) = 2.94, p < .01.

A school counselor claims that he has developed a technique to reduce pre-studying procrastination in students. He has students time their procrastination for a week and uses this as a pretest (before) measure of procrastination. Students then attend a workshop in which they are instructed to do a specific warming up exercise for studying by focusing on a pleasant activity. For the next week, students again time their procrastination. The counselor then uses the time from this week as the posttest (after) measure.Presume the counselor wants to examine whether there is a change (either an increase or decrease) in procrastination after attending his workshop. The counselor tests 10 students using the 0.05 level. What cut-off t score(s) will he use? (You should be able to figure this out without a table.) -2.62, 0, +2.62 +2.262 -2.262, 0 -2.262, +2.262

-2.262, +2.262

Which of the following is different for a t test for a single sample compared to a Z test for a single sample (hypothesis testing with a population with a known μ and σ2)? -The way you restate the problem as a research hypothesis and a null hypothesis about the populations. -The way you determine the mean of the known population. -The way you determine the variance of the known population. -The way you decide whether to reject the null hypothesis (once you have the cutoff and your sample's score on the comparison distribution).

-The way you determine the variance of the known population.

A researcher hypothesizes that biology majors score better than literature majors on an intelligence test. The SDifference turned out to be .9. The mean score of biology majors was 18.8 and the mean score for literature majors was 21.3. What is the t score? -t = (18.8-21.3)/.92 = -3.09. -t = (18.8-21.3)(.9) = -2.25. -t = (18.8-21.3)/.9 = -2.78. -t = (18.8-21.3)/[(2)(.9)] = -1.39.

-t = (18.8-21.3)/.9 = -2.78.

When making a scatter diagram, the lowest value on the horizontal axis is usually 0 1 -1 the Zscore for the highest value of the critierion variable

0

A sample has three individuals, with scores of 2, 3, and 4. What is the estimated population variance? 1 1.33 2 3.67

1

Fifteen participants take a pretest and a posttest and have a mean change score of 1.5. The standard deviation of the comparison distribution is .5. What is the t score? 1.5/(15-1) = .11 1.5/15 = .10 1.5/.5 = 3.00 15/1.5 = 10

1.5/.5 = 3.00

Which of the following is an example of a situation in which you could conduct a t test for independent means? -A comparison of the SAT scores of a group of 10 students who completed a special SAT preparation course compared to how people do on the SAT in general. -A comparison of scores of participants in a memory study in which one group is assigned to learn the words in alphabetical order and another group is assigned to read the words in order of length of the word. -A comparison of participants' scores on a skills test before and after attending a training session suspected to improve the skill. -None of the above are suitable for a t test for independent means.

A comparison of the SAT scores of a group of 10 students who completed a special SAT preparation course compared to how people do on the SAT in general.

When figuring a correlation coefficient, for each individual, you multiply the person's deviation scores on one variable times the person's deviation score on the other variable. This is because, -the result will always be positive if you have a high score with a high score. -the result will always be positive if you have a low score with a low score. -the result will always be negative if you have a high score with a low score. -All of the above

All of the above

A school counselor tests whether the level of depression in fourth graders in a particular class of 20 students differs from that of fourth graders in general at her school. On the test, a score of 10 indicates severe depression, while a score of 0 indicates no depression. From reports she is able to find about past testing, fourth graders at her school usually score 5 on the scale, but the variation is not known. Her sample of 20 fourth graders has a mean depression score of 4.4. The counselor tests the null hypothesis that fourth graders in this class do not differ from fourth graders in general at the school in level of depression. She figured a t score of -0.20. What decision should she make regarding the null hypothesis? -Reject it. -Fail to reject it -Accept it. -There is not enough information given to make a decision

Fail to reject it.

What is the difference between a positive correlation and a negative correlation? -In a negative correlation, high scores go with high scores and low with low; in a positive correlation, high scores go with low scores and low with high. -In a negative correlation, high scores go with low scores and low with high; in a positive correlation, high scores go with high scores and low with low. -Negative correlations are curvilinear; positive correlations are straight lines. -Negative correlations represent a weak relationship; positive correlations represent a strong relationship.

In a negative correlation, high scores go with high scores and low with low; in a positive correlation, high scores go with low scores and low with high.

Which of the alternatives below best describes the pattern of scores on this scatter diagram? -No correlation -Curvilinear correlation -Positive linear correlation -Negative linear correlation

No correlation

To figure the t score for the significance test of a correlation coefficient between X and Y, you only need two numbers. What are they? -Sum of squared deviations of X and sum of squared deviations of Y. -Sum of the product of deviation scores and the correction number. -Estimated variance of the null hypothesis population and the degrees of freedom. -Number of individuals and the correlation coefficient.

Number of individuals and the correlation coefficient.

Which of the alternatives below best describes the pattern of scores on this scatter diagram? -No correlation. -Curvilinear correlation. -Positive linear correlation. -Negative linear correlation.

Positive linear correlation

When figuring the correlation coefficient, you use a correction number that involves the sum of squared deviation scores for the X variable (SSX) and the sum of squared deviations on the Y variable (SSY ). Which of the following is the formula for the correction number? -SSX + SSY -The square root of (SSX + SSY ) -(SSX)(SSY ) -The square root of (SSX)(SSY )

The square root of (SSX)(SSY )

In which of the following situations is the t test for dependent means least robust? -When the population is highly skewed. -When the population is normal -When there are more than 30 participants -When the population variance is small

When the population is highly skewed.

When is the correlation coefficient zero? -It is never zero. -When there is no linear correlation. -When there is a perfect positive linear correlation. -When there is a perfect negative linear correlation.

When there is no linear correlation.

A social psychologist interested in cultural differences, compared women of two ethnic groups on a Role Approval Index (high scores mean high degrees of approval of ones own social role). The results were as follows. Ethnic Group A: N=15 M=55 S2=6.5 Ethnic Group B: N=23 M=51 S2=4.5What is the pooled estimate of the population variance? [(14/36)(6.5)] + [(22/36)(4.5)] = 5.28. [(15/38)(6.5)] + [(23/38)(4.5)] = 5.29. [(15/23)(6.5)] + [(23/15)(4.5)] = 11.14 [(14/22)(6.5)] + [(22/14)(4.5)] = 11.21

[(14/36)(6.5)] + [(22/36)(4.5)] = 5.28.

Suppose that in general it turned out that when eating a certain fruit before a test, the more fruit eaten, the better people do on the test. However, beyond a certain point, the more fruit eaten, the worse people do on the test. The relation between amount of fruit eaten and how well people do on the test is an example of -a positive linear correlation. -a curvilinear correlation. -a negative linear correlation. -no correlation.

a curvilinear correlation.

If you were conducting a study, and you found a correlation coefficient of .33, this would be considered -too small to care about. -a small but important correlation. -a moderate correlation coefficient. -a large correlation coefficient.

a moderate correlation coefficient.

The dots on a scatter diagram seem to form a straight line that goes upward to the right. This situation is called -a positive linear correlation. -a negative linear correlation. -a curvilinear correlation. -no correlation.

a positive linear correlation

Difference scores are usually used with -t test for a single sample. -a t test for dependent means. -a t test for independent means. -all of the above.

a t test for a single sample

The comparison distribution for a t test for independent means is a -distribution of differences between means. -Z distribution (that is, a normal curve) -poisson distribution. -distribution of proportional variance scores.

distribution of differences between means.

When estimating the population's variance from the scores in the sample, you should: -look on a special table to find the estimated variance. -proceed normally, but interpret the results with caution. -divide the sum of squared deviations by N-1 instead of N. -multiply the sample's variance by the degrees of freedom.

divide the sum of squared deviations by N-1 instead of N.

All of the following are part of figuring the chi-square statistic, EXCEPT -figure the overall F ratio, by figuring, for each category or cell, the observed minus expected, and squaring this difference. -determine the actual, observed frequencies in each category or cell. -divide each squared difference between observed and expected frequencies by the expected frequency for its category or cell. -determine the expected frequencies in each category or cell.

figure the overall F ratio, by figuring, for each category or cell, the observed minus expected, and squaring this difference

When testing the significance of the correlation coefficient, the null hypothesis is usually that in the population, the true correlation -is less than 1. -is zero. -is greater than the actual correlation. -is less than the actual correlation.

is zero.

When estimating the variance of a population from the sample, you cannot use the sample's variance directly because -it is based on using absolute deviations. -it is based on using squared deviations. -it tends to be slightly too large. -it tends to be slightly too small.

it tends to be slightly too small.

A research article reports a significant correlation using the .01 significance level. How would this be presented in the article if the correlation coefficient was .43? -r = .43, p < .01. -r = .43, significant. -r(.43) = significant. -p = .01, r = .43.

r = .43, p < .01.

What is the main difference between a Z score and a t score? -t scores are used when a study is analyzed with a one-tailed test. -t scores are used when the population variance is unknown -t scores are used only when the sample size is greater than 30. -t scores are only used when inferences are made about other samples.

t scores are used when the population variance is unknown

The main idea of a chi-square test is that you -test the estimated degree of fit (proportion of variance accounted for) of one variable to the other variable. -compare the estimated population means, to see if they vary from each other more than by chance. -compare estimated population variances, to see if they vary from each other more than by chance. -test how well the pattern of observed frequencies fits some expected pattern of frequencies.

test how well the pattern of observed frequencies fits some expected pattern of frequencies.

In a chi-square test of independence, the term "expected frequency" generally refers to -the distribution of people over categories on the measured variables under the assumption of equal numbers of people in all cells. -the distribution of people over categories on one variable expected if the distribution of people over categories on the other variable is completely unrelated to it. -the spread of the grouping variable, to see if it is a truly an independent variable. -the population's distribution of the scores on the measured variable, as estimated by the sample data.

the distribution of people over categories on one variable expected if the distribution of people over categories on the other variable is completely unrelated to it.

The degrees of freedom for the chi-square test for goodness of fit is -the number of categories minus one -the mean number of individuals per category, minus the number of categories. -the mean number of individuals per category, minus one. -the total number of individuals, minus the number of categories.

the number of categories minus one

The degrees of freedom for the chi-square test for independence is -the number of categories minus one. -the number of columns minus one, times the number of rows minus one. -the total number of category levels minus one. -the number of people minus the number of cells.

the number of columns minus one, times the number of rows minus one.

In the formula for estimating the population variance from the sample, the sum of squared deviations is divided by -the number of participants in the sample. -the number of participants in the sample minus one. -the number of participants in the population. -the number of participants in the population minus one.

the number of participants in the sample minus one.

A research article reports results of a study using a t test for dependent means as "t(38) = 3.11, p < .01." This means -the result is significant. -the result is not significant. -you can assume a one-tailed test was used. -there were 39 degrees of freedom.

the result is significant.

In the formula t = (M1 - M2)/SDifference, "SDifference" is -the sum of the standard deviations of the distribution of means. -the pooled estimate of the populations' standard deviation. -the standard deviation of the distribution of differences between means.

the standard deviation of the distribution of differences between means.

The variance of a distribution of differences between means equals -the difference between the variances of the two distributions of means. -the sum of the variances of the two distributions of means. -the difference between the two estimated population variances. -the sum of the two estimated population variances.

the sum of the variances of the two distributions of means.

An assumption for a significance test of the correlation coefficient is that in the populations, -the variance of each variable is the same. -the variance of the deviation scores for each variable is the same. -the variance of each variable is the same at each point of the other variable. -the variance of the squared deviations of each variable is the same at each point of the distribution of the squared deviations of the other variable.

the variance of each variable is the same at each point of the other variable.

You carry out a study in which you measure two personality traits and find a correlation of +.07. This is considered a: -weak positive linear correlation. -weak negative linear correlation. -strong positive linear correlation. -strong negative linear correlation.

weak positive linear correlation.

When carrying out a chi-square test for independence, a good check on your arithmetic in figuring the expected frequencies is to make sure that -the expected frequency of each cell is no larger than the observed frequency. -the sum of all the expected frequencies times the degrees of freedom equals the sum of all the observed frequencies. -within any one row or column, the sum of the observed frequencies and the sum of the expected frequencies come out to be the same. -for each row, the sum of all the expected frequencies equals the observed frequencies, minus 1, for each column.

within any one row or column, the sum of the observed frequencies and the sum of the expected frequencies come out to be the same.

The formula for the chi-squared statistic is -Σ[(O-E)2/E]. -[Σ(O-E) 2]/E. -O/[Σ(O-E) 2]. -E/[Σ(O-E) 2].

Σ[(O-E)2/E].