Statistics Final

The variance of a set of z scores is equal to

+1.00

Which of the following indicates the strongest relationship between two variables

-.54

The 95% confidence interval for the difference between two means is -3.7 to 8.5. Which of the following CANNOT be the 99% confidence interval for the difference between the same 2 means?

-3.2 to 7.9

What is the inflated Type I error for doing multiple independent samples-tests with 4 groups, an alpha of 0.05?

0.26 alpha* = 1 (1-alpha)^c c = [k x (k-1)] / 2 c = [4 x [4-1)] / 2 c = 6 alpha* = 1 (1-0.05)^6

What is the inflated Type I error for doing multiple independent samples-tests with ten groups, an alpha of 0.01?

0.36

If an individual with a z score on X of 2.0 is predicted by the linear regression line to have a z score on Y of 1.0, the predicted score on Y for an individual with a z score on X of 1.0 would be

0.5

Given the following regression equation Y = 16X + 5, for what value of X would 29 be predicted?

1.5 29 = 16X + 5

If the standard deviation is 10, the variance is

100 (variance is SD squared)

If the r between X and Y is .40, what percentage of the variability in X is explained by the variability in Y?

16% r = .40 r squared = .16 (so 16%)

If the correlation is calculated from a sample of N=21 individuals, what value for the df should be used to determine whether or not the correlation is significant?

19 df = N-2, (21-2) = 19

In a grouped frequency distribution, the lower real limit of the 24-26 interval is

23.5

The 95% confidence interval for the mean of a population is 25.8 to 40.1. Which of the following CANNOT be the 99% confidence interval for the same population mean?

27.0 to 38.9 this is a smaller range, and when you increase the percentage the range is supposed to get LARGER

How many groups were in this experiment?

3

If EX=60 and N=20, the sum of X is equal to

3.0 (60/20)

If the variance is 81, the standard deviation is

9

How man subjects were in this experiment altogether? (example)

93 dfbetween = df numerator = k-1 2=k-1 3=k dfwithin = NT-k 90=NT-3 93=NT

What are the practical consequences of Type I error?

A false positive - erroneously concluding that the researcher's theory has been supported

Which of the following is a raw score?

A score of 7 on a 10-point quiz

What is a Type II Error?

Failing to accept the alternative hypothesis when it is true (false -)

Which of the following can be a statement of H1?

H1: mu>0 H1: mu<0 H1: Mu does not = 0

Which of the following is most likely to represent a statement of the null hypothesis?

Ho: mu = 0

In general, if the variance of the difference scores increases, then what will happen to the value of the t statistic?

It will decrease (move toward 0 at the center of the distribution)

A set of scores has a mean of 23.8 and a standard deviation of 4.2. If 3 points are subtracted from each score, what are the new mean and standard deviation?

Mean = 20.8, SD= 4.2 (standard deviation of old = standard deviation of new) (new mean = old mean minus 3)

For the matched samples t test, the degrees of freedom are

N-1, where N = the number of pairs

When using the Pearson r as an inferential statistic, the degrees of freedom are equal to

N-2, where N=number of pairs

When testing hypotheses about the difference between the means of two populations, the degrees of freedom are

N1 + N2 - 2 Independent Samples t-test

Which result(s) seem(s) the LEAST consistent with the researcher's hypothesis?

Neither result 3 nor result 4 contradicts the researcher's hypothesis

The 95% confidence interval for the mean of a population is 87.5 to 113.4. Using hypothesis testing and the 0.05 criterion for significance, which of the following null hypotheses should be REJECTED?

Population mean = 115.6 Outside the range so reject

The 95% confidence interval for the mean of a population is 23.4 to 38.6. Using hypothesis testing and the 0.05 criterion for significance, which of the following null hypotheses should be RETAINED?

Population mean = 25.7 Population mean = 34.2 Population mean = 38.1 All within the range so retain

What is a Type I Error?

Rejecting the null hypothesis when it is true (false +)

For which result(s) should the researcher reject the null hypothesis that the difference between the two population means is zero?

Results 1 and 2 (because these ranges DO NOT include 0)

For which result(s) should the researcher retain the null hypothesis that the difference between the two population means is zero?

Results 3 and 4 (because these ranges DO include 0)

If we are testing a hypothesis about the difference between two population means and we switch from the 0.01 criterion of significance to the 0.05 criterion of significance, what happens to the probabilities of a Type I and Type II error?

The probability of a Type I error becomes LARGER and the probability of a Type II error becomes SMALLER as criterion level INCREASES, Type I error INCREASES (so Type II decreases)

Why is it useful to convert a raw score to a percentile rank?

We can show how the raw score compares to the scores of a specific group

What would you conclude about the differences between the groups?

We don't have enough information to draw a conclusion (we need the critical value)

In linear regression, which symbol stands for the predicted scores on Y?

Y'

In linear regression, the error in predicting Y is often written as

Y-Y'

Even if your data consists of numbers, it is not valid to perform arithmetic operations on those numbers if your data were derived from

a nominal scale

As used in statistics, the term sample refers to

a relatively small number of people drawn from a specified population

A distribution that is skewed to the right would have

a small number of very high scores

A researcher finds that the Pearson r between two variables is +1.17. This indicates that

an error in the computation was made (never should be above +1 or below -1)

If we draw 1,000 samples of size 100 from a population and compute the mean of each sample, the distribution of sample means will tend to be

approximately normal in shape

A histogram displays data using

bars

As the size of the sample increases, the standard error of the difference

becomes smaller

As the size of the sample increases, the standard error of the mean

becomes smaller

In the equation Y' = byxX + ayx, the slope of the regression line is denoted by

byx

A researcher conducts a repeated measures (matched samples) study to evaluate a treatment with a sample of N=16 participants and obtains t test statistics of t=1.94. The treatment is expected to increase scores and the sample mean difference shows an increase. Which of the following is the correct decision for a hypothesis test using 0.05 level of significance?

df = 16-1 = 15 c.v. = 1.753, one-tailed c.v = 2.13, two-tailed Reject the null hypothesis with a one-tailed test but fail to reject with two tails

When we speak about "within" variance in the analysis of variance we are speaking about

differences between subjects in the same group

The purpose of inferential statistics is to

draw conclusions about a group that is too large to measure

The null hypothesis states that the population mean is

equal to 100 (the mean IQ in this ex)

A Type II error refers to

failing to reject a false null hypothesis

Positive regression coefficients imply

for every unit increase in X, Y goes up

If we compute the correlation between scores on an intelligence test and grades in school, the correlation will be closest to zero for which of the following samples?

gifted children with IQs of at least 130

A frequency distribution is unimodal if it:

has only one peak

The standard deviation and variance are measures of

how spread out the scores in a set of data are from one another

Assumptions of a two-sample t test

independent observations within and across each group ; a normally distributed dependent variable ; equal population variances

When drawing inferences about the raw scores in a population, the total area under the normal curve

is defined as 100%

All of the following are advantages of using the mean EXCEPT

it is NOT affected by extreme scores at the high or low end of the distribution (IT IS!)

When the distribution is symmetric and unimodal, which of the following are always equal?

mean, median, and mode

The alternative hypothesis states that the population mean is

not equal to 100

If the statistical analysis indicates that the null hypothesis should be rejected, the researcher should conclude that the population mean is

not exactly equal to 100.0

The purpose of a frequency distribution is

only descriptive - to conveniently summarize and describe large quantities of data

If a subject's attitude toward the death penalty is assessed on a scale that consists of: strongly opposed, somewhat opposed, slightly opposed, neutral, slightly for, somewhat for, strongly for, which of the following types of scales is being used?

ordinal scale

What would the scatter plot show for data that produce a Pearson correlation of r = -.79?

points clustered close to a line that slopes down to the right

If every increase of one point on a test-anxiety scale is associated with a decrease of 2 points on predicted performance on a test, the value 2 is the

regression coefficient (b)

If we convert a set of raw scores to z scores, the shape of the distribution will

remain the same

The situation in which you figure a correlation but only a limited range of the possible values on one of the variables is included in the group studied is called

restriction in range

What is the standard error of the difference a weighted average of?

sample variance (s) standard error = square root of [s2 pooled (1/N1 + 1/N2)] s means SAMPLE

A graph that shows the pattern of the relation of two variables is a

scatter plot

A researcher is interested in studying gifted children who have an IQ of 130 or more. As compared to the general population, the variability of the IQ scores for the group of gifted children is

small

What is the interpretation of an effect size?

standardized difference of means

The purpose of descriptive statistics is to

summarize important characteristics of a set of data

If we have run a t-test with 35 observations and have found a t of 3.60, which is significant at the .05 level, we would write

t(34) = 3.60, p>.05

In the analysis of variance, MSbetween measures how different group means are from the grand mean, and MSwithin measures how different subjects in the same group are from the corresponding group mean. If the null hypothesis were false, what would we expect to find?

that MSbetween would be larger than MSwithin

When drawing inferences about the mean of one population, the correct statistical model to use is

the normal curve if the population standard deviation IS known and the t distributions of the population standard deviation is NOT know (z test vs. t test)

In hypothesis testing, which of the following is assumed to be true in order to find the p value?

the null hypothesis

One major difference between independent-samples t tests and analysis of variance is in

the number of groups that can be analyzed

Using a sample of 10,000 cases, a researcher obtains a Pearson r of .11 that is statistically significant using the .01 criterion. The researcher should conclude that

the population correlation coefficient is not zero

The changes of Type 1 error concerns

the probability of rejecting a true null hypothesis

The t distribution that you use to find your critical values closely resembles the normal distribution when

the sample size is LARGE

The median is equal to

the second quartile; the fifth decile; the 50th percentile

A researcher wishes to use scores on X to predict scores on Y as accurately as possible. The researcher wants

the sum of the squared Y-Y' values to be small

A researcher wishes to test the hypothesis that a persuasive message about our government will change people's attitudes toward politicians. Each of 20 participants' attitudes is measured before and after receiving the message. The correct procedure to use is

the t-test with matched samples

In the analysis of variance with 3 groups, the null hypothesis is

the three population means are equal to each other

The Y-intercept is defined as

the value of Y when X equals zero

In the analysis of variance, F test statistic compares

the variance between group means with the variance within groups

If we switch from the 95% confidence interval to the 99% confidence interval

we can be more sure that the population mean falls within the confidence interval (wider range)

On a midterm exam, your score expressed as a z score is +0.50. The mean of the exam is 65, and the standard deviation is 10. Your raw score is:

x = z(standard deviation)+mean x = (0.50)(10) + 65 x = 70

Given the critical vale of z is + or - 2.58 for a two-tailed test at the 0.01 level, what should the researcher decide, and what error might the researcher make?

z = 2.40, 2.40 < 2.58 Retain the null hypothesis - Type II Error

Given that the critical value of z is + or - 1.96 for a two-tailed test at the 0.05 level, was should the researcher decide, and what error might the researcher make?

z = x-mu/pop.standard deviation/square root of N z = 2.40, 2.40 > 1.96 reject the null hypothesis - Type I Error