Statistics final- Chapter 12

When are two samples considered to be related?

When we randomly select and assign participants to samples, making sure to pair each person in one sample with a particular person in the other sample

There ate two ways in which samples can be related. In a ___ design, each participant in one condition is paired with a participant in the other condition. Ina ___ design, each participant is tested under both conditions of the independent variable.

matched samples; repeated measure

At a card players' club, the poker players had a contest with the blackjack players to see who could win the most money. The appropriate design for testing the significance of the difference between the means is

independent samples t-test

The first 10 students who arrived for the Friday lecture filled out a questionnaire on their attitudes towards the instructor. the first 10 who were late for the lecture were spotted, and afterward filled out the same questionnaire. The appropriate design for testing the significance of the difference between the means is

independent samples t-test

The freshmen competed with the sophomores to see who could raise the most money by recycling. The appropriate design for testing the significance of the difference between the means is

independent samples t-test.

In an experiment, the proportion of variance accounted for" foes by another name. It is called the

effect size.

Following significant t-test, Clarinda wants to calculate her Cohen's d value. She has D-bar =2 and s(D)^2 =8. Calculate the correct Cohen's d value.

d=0.707

The sampling distribution of differences between means is the distribution of all possible

differences between two means with specified sample sizes, drawn from the raw score populations described by H(0).

A researcher asked 26 extroverts and 36 introverts how happy they were. The results are shown in the graph below. The t(obt) =2.96. Calculate the strength of the relationship using the squared Point-Biserial Correlation Coefficient.

+0.13

The nutrition class conducted a taste test in which 10 students rated the taste of regular oleo margarine and also rated the taste of fat-free oleo margarine. In a t-test for related samples, D-bar =2.0, s(D-bar) =1.0, and t(crit) =2.262. Construct a 95% confidence interval.

-0.26 ≤ µ(D) ≤ 4.26

If the variance for Sample 1 is 5 and the variance for Sample 2 is 3, where n(1)=10 and n(2)=12, what is s(x-bar(1) - x-bar(2))?

0.85

If ΣD^2 =220, ΣD =20, and N =10, what is S(D)?

1.41

A related sample t-test has resulted in a D-bar =15.1 and S(D-bar) =2.3. If the appropriate two-tailed t(crit) = 2.086, construct a 95% confidence interval.

10.30 ≤ µ(D) ≤ 19.90

For a study with a related samples design and 30 participants in which each participant is measured twice (repeated measures), what is the critical value? Assume a two-tailed test with α =0.05.

2.045

How is the t-test for related samples performed?

By conducting a one-sample t-test on the sample of difference scores

What is the next step in an experiment if the results of an independent samples t-test are statistically significant?

Compute a confidence interval for the difference between the µs.

One way to increase power is to minimize the variability of the raw scores. How is this accomplished?

Design and conduct the experiment so that all the subjects in a sample are treated in a consistent manner.

What does the standard error of the difference tell us?

How spread out the values of (x-bar(1) - x-bar(2)) are when the sampling distribution is created based on samples of the size we selected and our pooled variances.

How does increasing the size of the samples increase the power of an experiment?

Larger numbers of subjects result in larger degrees of freedom, which results in a smaller value of t(crit).

One way to increase power is to maximize the difference produced by the two conditions in the experiment. How is this accomplished?

Select two very different levels of the independent variable that are likely to produce a relatively large difference between the means.

What can we conclude if we reject the null hypothesis in an independent samples t-test?

The difference between our sample means is unlikely to be representing zero difference in the population means.

What does t(obt) indicate in an independent samples t-test?

The location of the sample mean inference relative to the mean of the sampling distribution of mean differences in standard error of the difference units.

What are we stating if we reject the null hypothesis?

The sample mean difference represents a difference between two population µs that is not zero.

What does the homogeneity of variance assumption state?

The variance in one population is equal to the variance in the other population.

What is pooled variance?

The weighted average of the sample variance.

How is the null hypothesis of the independent samples t-test verbalized?

There is no relationship between the independent variable and the dependent variable.

What should you conclude if two randomly selected sample means produce a confidence interval that is -1.51 ≤ µ(1) - µ(2) ≤ 2.62?

You are 95% confident that the interval between -1.51 and 2.62 contains the difference between µs for the two conditions.

In a related samples design, H0 states that

our sample mean represents a population of difference scores for which µ(D) = 0.

When conducting a two-sample t-test, the specific values of µ(1) and µ(2) are not as important as

the difference between µ(1) and µ(2).

What does the null hypothesis state in a two-tailed independent samples experiment?

H(0) : µ(1) - µ(2) = 0

What does the alternative hypothesis state in a two-tailed independent samples experiment?

H(a) : µ(1) - µ(2) does not = 0

You have stated your alternative hypothesis as H(a) : µ - µ(2) does not = 0. If x-bar(1) = 23, x-bar(2) = 25, n(1) = 15, n(2) = 15, and s(x-bar(1) - x-bar(2)) = 0.90, what is t(obt)?

-2.22

What are the degrees of freedom for an independent samples t-test that uses two samples with n=12 in each sample?

22

What are the degrees of freedom for an independent samples t-test that uses one sample with n=13 and one sample with n=15?

26

If ΣD =20, N=10, and S(D)^2 =4, what is t(obt) when H0 : µ(D) =0 and Ha : µ(D) does not = 0?

3.16

Suppose you tested two age groups on the number of details they could recall from a paragraph. The mean for the older group is 16, and the mean for the younger group is 14. further suppose that you fail to reject the null hypothesis for this independent samples t-test. Which of the following best accounts for the difference between these sample means?

The sample means probably came from the same population, and the difference is due to sampling error.

In the independent samples t-test, we always test whether the difference between x-bar(1) and x-bar(2) is significantly different from the

difference between µ(1) and µ(2) describe by H(0).

For x-bar(1) = 50, x-bar(2) =53, and s(x-bar(1) - x-bar(2)) =4.7, use a t(crit) =2.131 and compute a 95% confidence interval for µ(1) - µ(2).

-13.02 ≤ µ(1) - µ(2) ≤ 7.02

How many subjects participated in an independent samples t-test if a researcher reports t(20) = 3.68?

22

If a researcher predicts that the experimental treatment will produce an increase in an independent samples t-test (x-bar(1) - x-bar(2) < 0), how will the null hypothesis be stated?

H0 : µ(1) - µ(2) ≥ 0

If a researcher predicts that the experimental treatment will produce a decrease in an independent samples t-test (x-bar(1) - x-bar(2) > 0), how will the null hypothesis be stated?

H0 : µ(10 - µ(2) ≤ 0

Daniel conducted an independent samples t-test and found t(20) =0.57, p>.05. He then calculated his effect size and obtained a value of d=0.02. What should Daniel say in the report on his results?

He should indicate his t-test is not significant. He should, therefor, not report his effect size.

Which of the following is not one of the assumptions of the t-test for independent samples?

The standard deviation of at least one of the populations is known.

What is the standard error of the difference?

The standard deviation of the sampling distribution of the mean differences.

Suppose that you measure the IQ of 14 subjects with short index fingers and the IQ of 14 subjects with long index fingers. You compute an independent samples t-test, and the t(obt) is 0.29, which is not statistically significant. Which of the following is the most appropriate conclusion?

We do not have convincing evidence that our measured relationship between length of index finger and IQ is due to anything other than sampling error.

Suppose the average reading speed of 15 randomly selected elementary school students is 25, and the average reading speed of 15 randomly selected junior high school students is 31. You compute an independent samples t-test, and your t(obt) is 3.12, which is statistically significant which of the following is the most appropriate conclusion?

We have evidence that older students tend to read faster.

Using a line graph when interpreting the results of a two-sample experiment allows us to

envision the scatterplot that the data would form.

When we construct a 95% confidence interval, we are 95% sure that the

population mean difference falls within the interval.

When one has the option, a related samples design should be chosen over an independent samples design because

related samples result in less variability, and therefore the design is more powerful.

On the basis of a pretest on knowledge of foreign languages, each subject int he 9:00 class was matched with a subject in the 10:30 class. The 9:00 class used a participant approach to the study of Latin, and the 10:30 class used the Hiffendorf method. At the end of the term, the same Latin test was given to both classes. The appropriate design for testing the significance of the difference between the means is

related samples t-test

Eighteen obese volunteers weighed themselves before and after a two-day fast. The appropriate design for testing the significance of the difference between the means is

related samples t-test.

Ten volunteers recorded their blood pressure in a room with an aquarium and then in a room without one. the appropriate design for testing the significance of the difference between the means is

related samples t-test.

Suppose you perform a two-tailed independent samples t-test, using α = 0.05, with 15 participants in one group and 16 participants in the other group. Your t(obt) is 4.56, which is significant. Which of the following is the correct way to report this finding?

t(29)=4.56; p < 0.05

In a study to determine the effectiveness of pain management therapy in persons with chronic pain, twenty individuals experiencing chronic pain were randomly selected. Ten of these individuals were randomly assigned to receive pain management therapy and the other ten to receive no therapy. Descriptive statistics for each group are provided below. Conduct an appropriate t-test and determine the correct outcome.

t(crit) = 2.102, t(18)=2.45, p<0.05

The assumptions of the t-test for related samples are the same as those for the t-test for independent samples except for requiring

that each score in one sample be paired with a particular score in the other sample.

To determine the extent to which the conditions of the independent variable determine dependent scores, we should compute

the effect size.

N represents ____, whereas n represents ____.

the total number of scores in the study; the number of scores in each sample.

Two samples are said to be independent when

we randomly select and assign a participant to a sample without regard to other participants selected for either sample.

When H(0) is true, the mean of the sampling distribution of differences between means is equal to

zero