Statistics Exam 2

A test statistic is associated with a p value less then .05. What is the decision?

Reject the null hypothesis

A mean square is the same as what descriptive statistic?

Variance

What is a type II error (β) ?

Probability of retaining a null hypothesis that is actually false

A researcher conducts a one-sample z test. The z statistic for the upper tail critical test at a .05 level of significance is zobt = 2.00. What is the decision?

Reject the HO

True or false: The mean of a sampling distribution is equal to the population mean from which samples are selected.

True

True or false: The standard error of the mean is the standard deviation of a sampling distribution of sample means.

True

True or false: Researchers select a sample from a population to learn more about characteristics in that sample.

False: Researchers select a sample from a population to learn more about the population.

How does computing difference scores increase the power of a related-samples t test compared to a two-independent-samples t test?

It eliminates between-persons error, thereby reducing the estimate for standard error in the denominator

What is the main limitation of the z test in behavioral research?

It requires that the population variance is known and researchers usually don't have access to the population

What type of error is associated with decisions to retain the null hypothesis?

Type II error

The closer the value of a sample mean is to the value stated by the null hypothesis, the likelihood that we reject H0 _____

decreases

State the degrees of freedom and the type of test for the following examples of measures for a related-samples t test: --The difference in coping ability in a sample of 20 brothers and sisters paired based on their relatedness.

df = 19 matched pairs--natural occurrence

State the degrees of freedom and the type of test for the following examples of measures for a related-samples t test: --The difference in a comprehension before and after an experimental training seminar in a sample 30 students

df = 29 repeated measures--pre-post

States the degrees of freedom for the t test for the following situation: --A study in which researchers compare the standardized test scores between a class of 20 psychology students and a class of 26 biology students

df = 44

Distinguish between the repeated-measures design and the matched-pairs design

--Repeated-measures: Each participants is observed at least two times --Matched-pairs: Each pair of participants is matched and observed one time

State whether the following situations describe a between-subjects design or a within-subjects design. --A college professor compares the average class grade for students in each of three sections of a statistic course.

Between subjects

Suppose a population consists of a positively skewed distribution of scores. If we select all possible samples of size 10 from this population, then what will be the approximate shape of the sampling distribution of sample means?

Normal distribution

What are the assumptions for a related-samples t test?

Normality and independence within groups

The decision in hypothesis testing is to retain or reject which hypothesis?

Null hypothesis

Which type of test, one-tailed or two-tailed, is susceptible to the possibility of committing a type II error?

One tailed test

True or false: The effect size, power, and sample size of a study can affect the decisions we make in hypothesis testing?

True

If the null hypothesis is rejected, did we reach significance?

Yes

State the degrees of freedom and the type of test for the following examples of measures for a related-samples t test: --The difference in athletic performance at the beginning and end of an athletic season for 12 athletes.

df = 11 repeated measures--pre-post

A researcher uses a sample ______ to make inferences about the value of a population ________ of interest.

statistic; parameter

How do related samples differ from independent samples?

--Related samples: participants are related because they are either observed more than once or matched on common traits --Independent samples: participants are not related because different participants are observed in each group

Assuming α=0.5, what are the critical values in each of the following t distributions? 1) df = 10, two tailed test 2) df = 30, one-tailed test (lower) 3) df = ∞, two tailed test 4) df = 15, one-tailed test (upper)

1) +/- 2.228 2) -1.697 3) +/- 1.960 4) 1.753

What is the standard error of the mean (σM) when the variance of the sampling distribution of sample means (σ²M) is equal to: 1) 4 2) 144 3) 1,225

1) 2 2) 12 3) 35

What is the test statistic for a related-samples t test with a mean difference equal to 5 and an estimated standard error for difference scores equal to each of the following? a. 2.5 b. 5.0 c. 10.0

1) 5/2.5 = 2.000 2) 5/5 = 1.000 3) 5/10 = 0.500

The number of left-handed people in a hypothetical population of 25 students is 8. What is the probability of selecting two left-handed people from this population when: 1) Sample with replacement 2) Sample without replacement

1) 8/25 * 8/25 = .10 2) 8/25 * 7/24 = .09

A researcher compares the GPA of college students with a full time job to the mean GPA of the general population of college students. Identify: 1) DV 2) Treatment

1) GPA 2) Job or not

Name two types of repeated-measures designs.

1) Pre-post design 2) Within-subjects design

State the two correct decisions that a researcher can make

1) Reject the null hypothesis if the statement is false 2) Retain the null hypothesis if the statement is true

A population is normally distributed with a mean of -30 and a standard deviation of 4. 1) Find µM 2) If a sample of 16 participants is selected from this population, what is the standard error of the mean (σM) 3) Sketch the shape

1) µM = µ = -30 2) σM = 4/4 = 1

Name two sources of variation in the one-way between-subjects ANOVA

1. Between groups variation 2. Within groups variation

State the two criteria for experimental sampling.

1. Sample without replacement 2. Order doesn't matter

State the four steps of hypothesis testing

1. State the hypotheses 2. Set the criterion 3. Compute the t statistic 4. Make a decision

State the two ways for matching pairs of participants using the matched-pairs research design.

1. experimental manipulation 2. natural occurrence

A psychologist selects a sample of 36 children from a population with a standard deviation of 12. Compute the standard error.

12/6 = 2

If a random sample is selected from a population with a mean equal to 15, what can we expect the value of the sample mean to be on average?

15

Compute a z transformation to find the z score, given the following: µ = 5 σM = 1.5 M = 8

2.0

A researcher selects a sample of 49 students to test the null hypothesis that the average student exercises 90 minutes per week. What is the mean for the sampling distribution for the population of interest if the null hypothesis is true.

90

What is a between subjects design?

A research design in which different participants are observed one time in each group or at each level of one factor

The ____ is a statistical procedure used to test hypotheses for one or more factors concerning the variance among two or more group means (k≥2) where the variance in one or more populations is unknown.

ANOVA

Name the source of variation in the numerator and the source of variation in the denominator of the test statistic for the one-way between-subjects ANOVA

Between-groups variation is in the numerator Within groups variation is in the denominator

The ______ states that regardless of the distribution of scores in a population, the sampling distribution of sample means selected from that population will approach the shape of a normal distribution, as the number of samples in the sampling distribution increases.

Central limit theorem

Why do we find difference between pairs of scores before computing the test statistic for a related-samples t test?

Computing difference scores eliminates the between-persons error, thereby increasing the power of the test

When an independent sample is selected, are the same or different participants observed in each group?

Different participants are independently observed one time in each group

What is a sampling distribution?

Distribution of all sample means that could be obtained in samples of a given size from the sample population

True or false: The central limit theorem explains why the mean is always at the center of the distribution

False

Is the following set of hypotheses appropriate for a directional or nondirectional hypothesis test? HO: µ = 35 H1: µ ≠ 35

Nondirectional hypothesis test

Decreasing the ____ will decrease the standard error.

Population standard deviation

A researcher rejects the null hypothesis for a one-way between-subjects ANOVA, where k=4. What is the next step in the analysis?

Post hoc test

As effect size decreases, what happens to the power?

Power decreases

As effect size increases, what happens to the power?

Power increases

What is a type I error (α) ?

Probability of rejecting a null hypothesis that is actually true

A researcher conducts a hypothesis test and finds that p = .0689. What is the decision for a hypothesis test at .05 level of significance?

Retain HO

Increasing the ____ will decrease the standard error.

Sample size

An estimated Cohen's d substitutes which value in the formula to estimate the population standard deviation?

Sample standard deviation

Which method for sampling is associated with equal probabilities for each selection, even with small sample sizes?

Sampling with replacement

Which sampling method is the most commonly used in behavioral research?

Sampling without replacement

Distinguish between the significance and the effect size of a result

Significance is whether an effect exits or not. Effect size measures how big the effect is in the population.

What are the sizes of Cohen's d?

Small: d < 0.2 Medium: 0.2 < d < 0.8 Large: d > 0.8

A researcher conducts two studies. Study 1 uses a one-way between-subjects ANOVA and the Study 2 uses a within-subjects ANOVA. If the number of groups and participants per group are the same in each study, then in which study was the total number of participants larger?

Study 1 because different participants were observed in each group

Explain how overlap in scores between two groups can help to identify whether a difference observed is likely to be significant.

The less that scores in two groups overlap, the more likely we are to decide that two groups are different.

What is the power in hypothesis testing?

The likelihood of detecting an effect

Explain the following statement in words. µ = µM

The mean of the population is equal to the mean of the sampling distribution of sample means

The sample variance is used in the formula for standard error when the population variance is not known. Why is it appropriate to substitute the sample variance for the population variance?

The sample variance is an unbiased estimator of the population variance. Therefore, on average the sample variance equals the population variance.

What type of error do we directly control?

Type I error

What type of error is associated with decisions to reject the null hypothesis?

Type I error

An _____ is any sample statistic obtained from a randomly selected sample that equals the value of its respective population parameter on average.

Unbiased estimator

State whether the following situations describe a between-subjects design or a within-subjects design. --A behavioral psychologist allows a sample of children to play with four toys of various colors and has them rate how much they like playing with each toy. The psychologist compares mean ratings for each toy.

Within subjects

State whether the following situations describe a between-subjects design or a within-subjects design. --A biopsychologist tests the time course for the release of a neurohormone before, during, and following a task thought to cause its release.

Within subjects

What is the difference between z tests and t tests?

You know the population variance and population standard deviation for a z test. You don't for a t test.

A researcher conducts a one-way ANOVA in which one independent variable has four levels: a. how many different groups are in this study b, how many different factors are in this study

a. 4 b. 1

What is the total sample size for each example, assuming that n is equal in each group? a. k=4, n=12 b. k=3, n=8 c. N=28

a. 4 X 12 = 48 b. 3 X 8 = 24 c. 28

The mean difference between two related samples is 4.00. What is the value for an estimated Cohen's d if a sample standard deviation for the difference scores in this example is equal to (a) 4 and (b) 40?

a. 4/4 = 1.00 b. 4/40 = .10

State the degrees of freedom and the type of test for the following examples of measures for a related-samples t test: --The difference in relationship satisfaction in a sample of 25 pairs of married couples.

df = 24 matched pairs--natural occurrence

States the degrees of freedom for the t test for the following situation: --A study in which 12 participants are assigned to one group and 15 participants are assigned to a second group

df = 25

States the degrees of freedom for the t test for the following situation: --A study in which 30 participants are selected, then half are observed in Group 1 and half in Group 2

df = 28

The farther the value of a sample mean is from the value stated by the null hypothesis, the likelihood that we reject HO ______

increases

The criterion, or level of significance, in behavioral research is typically set at what probability value?

.05

State whether each of the following values for estimated Cohen's d has a small, medium, or large effect size. 1) 0.40 2) 1.20 3) 0.05 4) 0.10

1. Medium 2. Large 3. Small 4. Small

State whether the following situations describe a between-subjects design or a within-subjects design. --A sport psychologist compares mental functioning in a sample of athletes in four different sports.

Between subjects

On average, what do we expect the sample mean to be equal to?

Population mean

To check that a manipulation of social comparison made in the study was effective, Yip computed a one-way between-subjects ANOVA and reported the following result for one such check: F(2,120) = 6.42. Based on the information given, answer the following questions. a. How many groups were compared in this test? b. How many participants were observed in this study? c. Was the outcome of this test significant a a .05 level of significance?

a. 3 groups b. 123 participants c. Yes because we rejected the null hypothesis

State whether a post hoc test is necessary for each of the following results. a. F (1, 18) = 6.29, p<.05 b. F (4, 55) = 3.98, p< .05 c. F (2,33) = 2.03, p>.05

a. No... k=2 b. Yes...k>2 and the result is significant c. No...the result is not significant

Make a decision given the following values for the F statistic in a test with 3 and 20 degrees of freedom. a. Fobt = 3.05 b. Fobt = 4.00 c. Fobt = 5.35

a. Retain HO b. Reject HO c. Reject HO

The test statistic for a related-samples t test is +2.100. Using a .05 level of significance, would you retain or reject the null hypothesis under each of the following conditions? a. df = 10, two-tailed test b. df = 30, one-tailed test (upper tail) c. df = 20, two-tailed test d. df = 40, one-tailed test (lower tail)

a. Retain the HO b. Reject the HO c. Reject the HO d. Retain the HO

Explain the meaning of the following terms for an ANOVA: a. one-way b. between-subjects c. within-subjects

a. one factor is tested b. different subjects are in each level c. same subjects are in each level

A researcher measures the time it takes 13 men and 15 women to complete multiple tasks in a study. She compares the mean difference between men and women using the two independent sample t test. -Find tcrit -Make a decision if tobt = 1) 2.558 2) 1.602 3) 2.042 4) -2.500

tcrit = ± 2.056 (12+14=26) 1) 2.558- reject HO 2) 1.602- retain HO 3) 2.042- retain HO 4) -2.500- reject HO

Researchers record the number of errors on some behavioral task for 15 participants. They report a sample mean equal to 6 ± 1 (M ± SD). What is the critical value for a two tailed test with α = 0.01? Also, what is the decision if the following tobt equal: 1) 2.558 2) 1.602 3) 2.999 4) -3.404

tcrit = ±2.997 1) 2.558- retain HO 2) 1.602- retain HO 3) 2.999- reject HO 4) -3.404- reject HO

If the difference between two means is 4, what will the estimated Cohen's d value with a pooled sample standard deviation of... 1) 4 2) 8 3) 16 4) 40

1) 1 2) .50 3) .25 4) .10

The scores for a population are normally distributed with a mean equal to 25 and a standard deviation equal to 6. A researcher selects a sample of 36 students and measures a sample mean equal to 23. For this example... 1) What is the value of Cohen's d? 2) Is this effect size small, medium, or large?

1. 0.33 2. Medium

What are the three assumptions of the one-sample t test?

1. Normal 2. Random sampling 3. Independence

What are the four assumptions for the two-independent sample t test?

1. Normality 2. Random sampling 3. Independence 4. Equal variances

State the four assumptions for the one-way between-subjects ANOVA.

1. Normality 2. Random sampling 3. Independence 4. Homogeneity of variance

What are the two decisions that a researcher makes in hypothesis testing?

1. Reject HO 2. Retain HO

State the two criteria for theoretical sampling.

1. Sample with replacement 2. Order matters

The values listed below are the obtained values for a t statistic. 1) What is your decision for each if df = 30 and α = .05 for a two tailed test? 2) What is your decision for each if df = 30, and we change to α = .01 for an upper tail critical test? a. 2.050 b. 1.680 c. 2.834 d. 3.030

1a. reject HO 1b. retain HO 1c. reject HO 1d. reject HO --------------- 2a. retain HO 2b. retain HO 2c. reject HO 2d. retain HO

A researcher computes an ANOVA with 4 and 12 degrees of freedom. What is the critical value for this test at a .05 level of significance?

3.26

Son and Lee used a "within-subjects repeated measures design" to evaluate the effect of the amount of rice carbohydrates consumed during mealtime on blood pressure in older people with hypotension. Explain what the researchers mean by a within-subjects repeated-measures design.

A within-subjects repeated-measures design means that the same participants are observed before and again after some treatment.

How are the rejection regions, the probability of a type I error, the level of significance, and the alpha level related?

All four terms describe the same thing. The level of significance is represented by alpha, which defines the rejection region or region associated with the probability of committing a type I error

How does increasing sample size affect the estimate of the population variance?

As sample size increases, the sample variance more closely approximates the population variance

_______ measures the size of an effect in a population, whereas ______ measures whether an effect exists in a population

Effect size; hypothesis testing

What measure of effect size is most often reported with the t test?

Estimated Cohen's d

A researcher records the amount of computer use (in hours per day) in a sample of students and then matches the students based on their amount of computer use. Is this an example of matching through experimental manipulation or matching through natural occurrence?

Experimental manipulation

Of the two ways to select samples described in Chapter 9, which type of sampling is commonly used in experiments?

Experimental method: select one sample from the same population and randomly assign participants in the sample to groups

If SSbg = 40 in a one-way between-subjects ANOVA with five groups, what is the numerator of the F statistic?

MSbg = 40/4 = 10

What is the value of the degrees of freedom for each example listed below? a. A study comparing 10 matched pairs of scores b. A study involving 18 participants observed two times

a. df = 9 b. df = 17

Faith examined the impact of a mentoring program for elementary school-aged children on attitudes that mentors and children have about mentoring. Faith report that children's and mentors' ratings of the openness of the mentor significantly decreased from before to after the mentoring program, t(101) = 12.51. a. What was the sample size for this test? b. Was a repeated measures or a matched pairs designed used in this study?

a. n = 102 b. repeated measures design

A social psychologist records the number of outbursts among students at two schools. Assuming the same number of students were observed at each school, what is the sample size at each school, the decision, and the effect size for this study, based on the following statement. The number of outburst among students at the small school (M=3) was significantly less than the number recorded at the large school (M=8), t(38) = 4.19, p<.05 (d=0.25).

sample size = 20 reject HO medium effect size

The ____ is a normal-like distribution with greater variability in the tails than a normal distribution because the sample variance is substituted for the population variance to estimate the standard error in the distribution.

t distribution

What formula is used to find the probability of obtaining a sample mean from a given population?

z obt formula