Psych Stats Final-NOT COMPREHENSIVE

A set of X and Y scores has a regression equation with a slope of b = 4. If the mean for the X values is MX = 2 and the mean for the Y values is MY = 6, what is the Y-intercept value for the regression equation?

-2

Which of the following Pearson correlations shows the greatest strength or consistency of relationship?

-0.90

Which of the following would have no effect on the width of a confidence interval?

-if the population standard deviation increases, the confidence interval decreases in width -mean or x-bar would have no effect on width of Confidence Interval

If the null hypothesis is true, what value is expected on average for the repeated-measures t statistic?

0

On average, what value is expected for the t statistic when the null hypothesis is true?

0

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?

1.0

A repeated-measures study and an independent-measures study both produced a t statistic with df = 10. How many individuals participated in each study?

11 for repeated, and 22 for matched

An independent-measures study has one sample with n = 6 and a second sample with n = 8 to compare two experimental treatments. What is the df value for the t statistic for this study?

12

Suppose the correlation between height and weight for adults is +0.40. What proportion (or percent) of the variability in weight can be explained by the relationship with height?

16% As R=0.4 R2 = 0.42 = 0.16.

A repeated-measures study using a sample of n = 20 participants would produce a t statistic with df = ____.

19

A researcher conducts a hypothesis test using a sample of n = 20 from an unknown population. What is the df value for the t statistic?

19

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?

2

Two samples each have n = 4 scores. If the first sample has a variance of 10 and the second sample has a variance of 6, what is the estimated standard error for the difference between sample means?

2

For the linear equation Y = 2X + 4, if X increases by 1 point, how much will Y increase?

2 points

Using an independent-measures t, the 90% confidence interval for the difference between two population means ranges from 19 to 23. Based on this confidence interval, how big is the difference between the two sample means?

21

What is the pooled variance for the following two samples? Sample 1: n = 8 and SS = 168 Sample 2: n = 6 and SS = 120

24

A sample of n = 100 people is classified into four categories. If the results are evaluated with a chi-square test for goodness of fit, what is the df value for the chi-square statistic?

3

The following data were obtained from a repeated-measures research study. What is the value of MD for these data? Subject 1st 2nd #1 10 15 #2 4 8 #3 7 5 #4 6 11

3

A researcher would like to test the claim that 9 out of 10 doctors prefer Brand X. A sample of 60 doctors is obtained and each is asked to compare Brand X with another leading brand. The data show that 48 of the doctors picked Brand X. If these data are evaluated using a chi-square test for goodness of fit, what is the expected frequency for Brand X?

54

The following data were obtained from a repeated-measures research study. What is the value of SS for the difference scores? Subject 1st 2nd #1 10 11 #2 4 6 #3 7 9 #4 6 5

6

For the regression equation Y = 2X - 3, if the mean for X is MX = 5, what is the mean for Y?

7

Which set of characteristics will produce the smallest value for the estimated standard error?

A large sample size and small sample variance

A researcher plans to conduct a research study comparing two treatment conditions with a total of 20 participants. Which of the following designs would produce 20 scores in each treatment?

A repeated measures design

Which of the following is the correct null hypothesis for an independent measure t-test? A. u1-u2=0 B. M1-M2=0 C. u1-u2 0 D. M1-M2 0

A. u1-u2=0

Which of the following research situations would be most likely to use an independent-measures design?

Compare the mathematics skills for 9th grade boys versus 9th grade girls

Which of the following confidence intervals also indicates a significant difference between treatments with a = .05?

Estimate that m1-m2 is an interval between 2 and 10 with 95% confidence

An independent-measures research study uses two samples, each with n = 10 participants. If the data produce a t statistic of t = 2.095, which of the following is the correct decision for a two-tailed hypothesis test?

Fail to reject the null hypothesis with either α = .05 or α = .01

If two samples are selected from the same population, under what circumstances will the two samples have exactly the same t statistic?

If the samples are the same size and have the same mean and the same variance

For the independent-measures t statistic, what is the effect of increasing the difference between sample means?

Increase the likelihood of rejecting H0 and increase measures of effect size.

Which of the following will not increase the width of a confidence interval?

Increase the sample mean from MD = 2 to MD = 4

A sample has a mean of M = 39.5 and a standard deviation of s = 4.3, and produces a t statistic of t = 2.14. For a two-tailed hypothesis test with a = .05, what is the correct statistical decision for this sample?

It is impossible to make a decision about H0 without more information.

Which of the following accurately describes the chi-square test for goodness of fit?

It is similar to a single-sample t test because it uses one sample to test a hypothesis about one population

If other factors are held constant, what is the effect of increasing the sample size? (Hint: Look at the formulas for the estimated standard error and t-test for a single sample to figure out the answer).

It will decrease the estimated standard error and increase the likelihood of rejecting H0.

If other factors are held constant, what is the effect of increasing the sample variance?

It will increase the estimated standard error and decrease the likelihood of rejecting H0.

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 = 5 with s2 = 5 for the difference scores

What happens to the critical value for a chi-square test if the size of the sample is increased?

Nothing! Critical values are determined by categories, not the sample size.

Which of the following accurately describes the chi-square distribution?

Positively skewed with all values greater than or equal to zero

What values are specified by the null hypothesis for the chi-square test for goodness of fit?

Proportions for the entire population

A sample of n = 9 scores has a variance of s2 = 36. What is the estimated standard error for the sample mean?

Sample variance = 36 Sample std deviation = rt of variance = 6 Std error = std dev/rt (sample size) = \frac{6}{\sqrt{9}}=2 Std error for mean = 2

A chi-square test for goodness of fit is used to examine the distribution of individuals across four categories, and a chi-square test for independence is used to examine the distribution of individuals across the six categories in a 2´3 matrix of categories. Which test has the larger value for df?

Test for goodness of fit

What happens to the critical value for a chi-square test if the number of categories is increased?

The critical value also increases.

The data for a chi-square test consist of ___________

The data for a chi-square test consist of frequencies.

What is referred to by the term observed frequencies?

The frequencies found in the sample data

What value is estimated with a confidence interval using the repeated-measures t statistic?

The mean for a population of difference scores

A researcher obtains a negative value for chi-square statistic. What can you conclude because the value is negative?

The researcher made a mistake; the value of Chi2 cannot be negative

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?

The t statistic is t= mean difference / (s/vn) =4/sqrt(12/6) = 2.828 Answer: 2.83

Which of the following is a fundamental difference between the t statistic and a z-score?

The t statistic uses the sample variance in place of the population variance.

What value is estimated with a confidence interval using the t statistic?

The value for an unknown population mean

What conclusion is appropriate if a chi-square test produces a chi-square statistic near zero?

There is a good fit between the sample data and the null hypothesis.

Which of the following describes the effect of increasing sample size?

There is little or no effect on measures of effect size, but the likelihood of rejecting the null hypothesis increases

Which of the following accurately describes the observed frequencies for a chi-square test?

They are always whole numbers

The narrower the confidence interval, the more precise it is. With this in mind, which combination of factors will produce the most precise estimate of the difference between two population means?

Two samples of n = 50 and 80% confidence

A researcher records the odometer reading and price for a group of used Hondas. What kind of correlation is likely to be obtained for these two variables?

a negative correlation

The results from a research study indicate that adolescents who watch more violent content on television also tend to engage in more violent behavior than their peers. The correlation between amount of TV violent content and amount of violent behavior is an example of _______.

a positive correlation

For an independent-measures t statistic, what is the effect of increasing the number of scores in the samples?

an increase in the standard error and a decrease in the value of t

A sample is selected from a population with m = 46, and a treatment is administered to the sample. After treatment, the sample mean is M = 48 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen's d?

d = 0.50

A sample of difference scores has a mean of MD = 5 with a variance of s2 = 100. If effect size is measured using Cohen's d, what is the value of d?

d = 5/10

An independent-measures research study with n = 5 participants in each treatment produces sample variances of 8 and 10, and a 2-point difference between the two treatment means. Given this information, what is the value of Cohen's d?

d=0.67

What is indicated by a positive value for a correlation?

increases in X tend to be accompanied by increase in Y

Assuming that there is 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?

large sample sizes and small sample variances

A researcher reports t(12) = 2.86, p < .05 for a repeated-measures research study. How many individuals participated in the study?

n=13

A researcher is using a chi-square test to determine whether people have any preferences among three brands of televisions. The null hypothesis for this test would state that ______.

one-third of the population prefers each brand

Ten years ago, only 20% of the U.S. population consisted of people more than 65 years old. A researcher plans to use a sample of n = 200 people to determine whether the population distribution has changed during the past ten years. If a chi-square test is used to evaluate the data, what is the expected frequency for the older-than-65 category?

proportion of U.S. population consisted of people more than 65 years old = 0.20 sample size,n = 200 expected frequency for the older-than-65 category = 200*0.20 = 40

What values are specified by the null hypothesis for a chi-square test?

proportions for the entire population The Chi-square test can be used to compare the population proportions from different populations. The data collected is divided into intervals and then the number of poinst that fall into the intervals are compared with the expected number of points in each interval. Thus, the Chi-suqare test for goodness of fit specified by the null hypothesis compares the proportions for the entire population.

A set of n = 25 pairs of scores (X and Y values) has a Pearson correlation of r = 0.80. How much of the variance for the Y scores is predicted by the relationship with X?

r = .80 r^2 = (r)^2 = (.80)^2 = .64 or 64% Answer: .64 or 64% Note: r^2 tells us what percent of the variation in y can be explained (predicted) by x.

A set of n = 15 pairs of scores (X and Y values) produces a correlation of r = 0.40. If each of the X values is multiplied by 2 and the correlation is computed for the new scores, what value will be obtained for the new correlation?

r= 0.40 -multiplying each X simply shifts the location of the scores. the pattern of the relationship (and the correlation) are not changed.

What is the sample variance and the estimated standard error for a sample of n = 9 scores with SS = 72?

s2 = 9 and sM = 1

A set of n = 15 pairs of X and Y scores has SSX = 10, SSY = 40, and SP = 30. What is the slope for the regression equation for predicting Y from X?

slope = SSxy/SSxx = 30/10

What is the average value expected for the independent-measures t statistic if the null hypothesis is true? (i.e., the two samples represent the same population)

t=0

How does the difference between fe and fo influence the outcome of a chi-square test?

the larger the difference, the larger the value of chi-squared, and the greater the likelihood of rejecting the null hypothesis

One sample of n = 8 scores has a variance of s2 = 6 and a second sample of n = 8 scores has s2 = 10. If the pooled variance is computed for these two samples, then the value obtained will be ______.

will be exactly half way between 6 and 10

A linear regression equation has b = 3 and a = - 6. What is the predicted value of Y for X = 4?

y-hat = 6 Y'=3X+(-6) when X=4, Y'=3(4)-6=6

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?

y=2x-3

Which of the following is the correct null hypothesis for a repeated-measures t test?

µD = 0

The regression equation is determined by finding the minimum value for which of the following?

Σ(Y − Ŷ)2