PSY 2310: Module 10

Use the "One-Sample t Test" output to determine the population mean (i.e., the test value) in this study.

3000

Compute the degrees of freedom for this study.

35

Use the "One-Sample Statistics" output to determine what the mean of the sample was in this study.

3680

Locate the t critical value for a sample of N = 50, with alpha set at α = .05 in the right tail.

1.6766

What is the critical t value for this one-tailed test with an alpha level of α = .05?

1.6896

Use the "One-Sample Statistics" output to determine how many people were in this study (i.e., the size of the sample).

15

Use the "One-Sample t Test" output to determine the obtained t value in this study.

2.536

Compute the single-sample t value for this study.

2.67

Compute the standard error of the mean.

2.87 SD/√n

Use the "One-Sample t Test" output to determine if the null hypothesis of this study should be rejected.

The null hypothesis should be rejected because the p value (Sig.) is less than .05.

A researcher wants to assess people's knowledge of a topic by using a 10-question True/False test. Which value could be of theoretical interest to this researcher, and therefore, function as a null hypothesis test?

The researcher could use wither "10" or "5" in this situation because both values represent a level of performance that might be of theoretical interest to the researcher.

Identify the type of hypothesis testing error you may have made and why.

Type II Error - may have failed to reject a false H0.

A random sample of 40 parents completed a questionnaire about gun safety laws in the United States. Responses ranged from 1 to 5, with 5 indicating more agreement that gun safety laws should be more strict. The general public had a mean of 3.2 and a standard deviation of about 1.22. You were testing whether the mean for the sample of parents (M = 3.8) is different from the population mean. What decision should you make about the null hypothesis for this study?

reject the null hypothesis

Researchers can only make a Type I error if they __________.

reject the null hypothesis

The following results from a single-sample t test are reported in a journal article, t(59) = 2.24, p = .03, d = .78. Should the researcher reject or fail to reject the null hypothesis assuming an alpha = .05?

reject

Should you reject or fail to reject the null hypothesis?

reject the null hypothesis

When you enter data into SPSS, each person's data (i.e., score) goes in its own __________.

row

A random sample of 40 parents completed a questionnaire about gun safety laws in the United States. Responses ranged from 1 to 5, with 5 indicating more agreement that gun safety laws should be more strict. The general public had a mean of 3.2 and a standard deviation of about 1.22. You were testing whether the mean for the sample of parents (M = 3.8) is different from the population mean. Find the t critical value for an alpha level, α = .05.

2.0227

A random sample of 40 parents completed a questionnaire about gun safety laws in the United States. Responses ranged from 1 to 5, with 5 indicating more agreement that gun safety laws should be more strict. The general public had a mean of 3.2 and a standard deviation of about 1.22. You were testing whether the mean for the sample of parents (M = 3.8) is different from the population mean. Compute the t test statistic for this study.

3.11

A random sample of 40 parents completed a questionnaire about gun safety laws in the United States. Responses ranged from 1 to 5, with 5 indicating more agreement that gun safety laws should be more strict. The general public had a mean of 3.2 and a standard deviation of about 1.22. You were testing whether the mean for the sample of parents (M = 3.8) is different from the population mean. What are the degrees of freedom (df) for this study?

39 from n-1 40 - 1 = 39

Compute the degrees of freedom (df) for a single-sample t test is the sample size is N = 50.

49

The following results from a single-sample t test are reported in a journal article, t(59) = 2.24, p = .03, d = .78. How many people participated in the study?

60

The mean estimated monthly salary from the 15 psychology majors was M = 3,680, and the actual monthly salary was μ = 3,000. So, the mean difference is 680. The typical amount of sampling error was computed as 268.186. For this example, the observed difference between the sample mean and the population mean was __________; the difference expected due to sampling error was __________.

680; 268.186

What is the one-tailed null hypothesis for this study?

< 37

After hearing of these results regarding the differences between the attitudes of scientists and the public, a researcher wonders if this difference is a function of the level of education overall or if it is specific to science education. Thus, this researcher obtains a sample of 50 people who have a Ph.D. in the humanities and plans to compare their mean level of agreement to the mean level of agreement of scientists (41). He is not sure what to expect, so he chooses to complete a two-tailed test. What is the two-tailed null hypothesis for this study?

= 41

Last fall, a sample of N = 20 freshmen was selected to participate in a new 4-hour training program designed to improve study skills. To evaluate the effectiveness of the new program, the sample was compared with the rest of the freshmen class. All freshmen must take the English Language Skills course, and the mean score on the final exam for the entire freshmen class was μ = 81.75. The students in the new program had a mean score of M = 83.54 with a standard deviation of SD = 12.82. Test if the study skills training program produced a significant difference in scores using a two-tailed test with an α = .01. What is the symbolic null hypothesis (H0)?

= 81.75

Identify which of the following statements represents an accurate interpretation of the results of this study, including effect size, in APA format.

Freshmen who participated in the English Language Skills course, and also participated in the new four-hour training program designed to improve study skills (M = 83.54), did not have final exam scores significantly different from the population of freshmen who only participated in the English Language Skills course (µ = 81.75), t(19) = 0.62, p > .01. The effect size indicates an expected increase in final exam scores of 0.14 standard deviation when participating in the English Language Skills course and the four-hour study skills program versus the English Language Skills course only.

The degrees of freedom (df) for a single sample t test are computed as __________.

N-1

Should this researcher be concerned with violating any assumptions associated with this test?

No, all assumptions are met. The researcher can conduct this hypothesis test.

What is the verbal research hypothesis (H1)?

The mean estimated final exam score of the population of freshmen who participated in the new 4-hour training program and the English Language Skills course is different than the actual mean freshmen final exam score of 81.75 points.

What is the verbal null hypothesis (H0)?

The mean estimated final exam score of the population of freshmen who participated in the new 4-hour training program and the English Language Skills course is not different than the actual mean freshmen final exam score of 81.75 points.

The critical value for a one-tailed t test with α = .05 __________.

changes based on the size of the sample (i.e., N) being used

The critical value for a t test will get __________ as sample size increases.

closer to zero

One of the differences between a z for a sample mean test and a single sample t test is that __________.

the single sample t test uses the sample standard deviation to compute an estimate of the typical amount of sampling error

When using the z for a sample mean you can compute the standard error of the mean, but when using a t for a sample mean, you must estimate the standard error of the mean.

true

The only computational difference between the z for a sample mean formula and the single sample t formula is the way __________.

typical sampling error is computed

Which of the following symbols should be used to represent a two-tailed research hypothesis?

≠

A random sample of 40 parents completed a questionnaire about gun safety laws in the United States. Responses ranged from 1 to 5, with 5 indicating more agreement that gun safety laws should be more strict. The general public had a mean of 3.2 and a standard deviation of about 1.22. You were testing whether the mean for the sample of parents (M = 3.8) is different from the population mean. What is the research hypothesis for this study?

≠ 3.2

What is the two-tailed alternative/research hypothesis for this study?

≠ 41

What is the symbolic research hypothesis (H1)?

≠ 81.75

What is the critical value for this study, α = .01, two-tailed?

+ 2.8609

The critical value for a one-tailed z test with α = .05 is always __________.

+1.65 or -1.65

Which of the following alpha values creates a greater probability of a Type II error?

0.01

Use the "One-Sample t Test" output to determine the p value in this study.

0.024

Which of the following alpha values creates a greater probability of a Type I error?

0.05

Which of the following alpha values results in more statistical power?

0.05

Calculate the effect size (Cohen's d).

0.14 M - μ/ SD

Compute the effect size (d).

0.44

A random sample of 40 parents completed a questionnaire about gun safety laws in the United States. Responses ranged from 1 to 5, with 5 indicating more agreement that gun safety laws should be more strict. The general public had a mean of 3.2 and a standard deviation of about 1.22. You were testing whether the mean for the sample of parents (M = 3.8) is different from the population mean. Compute the effect size (d) for this study.

0.49

Compute the t-value for this study.

0.624 M - μ/ SD/√n

If the research hypothesis indicates that scores will decrease, the critical values will be __________.

negative

Which of the following will increase as the sample size increases (assuming everything else is held constant)? Select two.

not Statistical power Critical t value

For which of the following hypothesis testing steps is there a difference between one-tailed and two-tailed tests? (You should choose three of the following five steps.)

not Step 3: defining the critical region not Step 5: computing the effect size no idea

How is the single-sample t test different from the z test for a sample mean?

not The single-sample t test requires knowledge of a population mean and the z test for a sample mean does not.

When using a one-tailed significance test, if the research hypothesis predicts an increase (or positive change), the critical region will be on the __________ side of the distribution.

positive

If the obtained t value is further from zero than the critical value, you should __________.

reject the null hypothesis

A representative sample of Americans were asked to indicate their agreement with a series of eight statements about childhood vaccines, such as the following: Childhood vaccines should be required. Strongly Disagree 1 2 3 4 5 Strongly Agree The responses to the eight questions were summed to form a single measure of support of childhood vaccines, which ranged from a possible total score of 8 to 40. The scores formed an interval scale that was normally distributed. The mean response on this scale for the general public was μ = 37. A researcher wonders if scientists are more likely to agree with this statement than the public. To test this possibility, she obtains a sample of 36 scientists and asks them the same questions. Their average level of agreement with this statement was 41, with a standard deviation of s = 9. The researcher is testing if the average value for the sample of scientists is significantly higher than 37. What is the one-tailed research hypothesis for this study?

> 37

When should you conduct a one-tailed test?

A one-tailed test should be conducted when the research hypothesis predicts scores will increase or if it predicts scores will decrease.

Last fall, a sample of N = 20 freshmen was selected to participate in a new 4-hour training program designed to improve study skills. To evaluate the effectiveness of the new program, the sample was compared with the rest of the freshmen class. All freshmen must take the English Language Skills course, and the mean score on the final exam for the entire freshmen class was μ = 81.75. The students in the new program had a mean score of M = 83.54 with a standard deviation of SD = 12.82. Test if the study skills training program produced a significant difference in scores using a two-tailed test with an α = .01. Which is the appropriate analysis for this data?

A t-test because σ is unknown.

Using the SPSS output from the analysis, should the researcher reject or fail to reject the null hypothesis?

Fail to Reject H0

Identify the correct decision and APA format results for this analysis.

Fail to Reject H0, t(19) = 0.62, p > .01

Why is your decision to conduct a one-tailed rather than a two-tailed test potentially important?

One- and two-tailed tests have different critical regions and, therefore, may have lead to different conclusions about the null hypothesis.

PRACTICE QUESTION

PRACTICE QUESTION

The results of a single-sample t test are reported as t(44) = -3.35, p < .001, d = 0.50. If the alpha level is set at .05 in the left tail, what is the correct decison to make regarding the null hypothesis?

Reject the null hypothesis

What do the results of the significance test tell you?

That the difference observed between scientists' attitudes toward childhood vaccines and the public's attitudes is unlikely to be due to sampling error.

What does the effect size tell you? Select all that apply.

The difference between the scientists' attitudes toward childhood vacines and the public's attitudes in standard deviation units.

A random sample of 40 parents completed a questionnaire about gun safety laws in the United States. Responses ranged from 1 to 5, with 5 indicating more agreement that gun safety laws should be more strict. The general public had a mean of 3.2 and a standard deviation of about 1.22. You were testing whether the mean for the sample of parents (M = 3.8) is different from the population mean. Which of the following best represents the results for this study written in APA format?

The sample of 40 parents reported significantly higher average agreement scores (M = 3.8) regarding gun laws needing to be stricter versus the general public (μ = 3.2), t(39) = 3.11, p < .05, d = 0.49. The average agreement scores on the gun control questionnaire were 0.49 of a standard deviation higher than those of the general population.

What does the estimated standard error of the mean measure?

The typical distance between all possible sample means of a given size and the population mean.

When performing a t test, increasing the sample size will __________ the amount of sampling error expected. This means the denominator of the t test will be __________.

decrease; smaller

The results of a single-sample t test are reported as t(44) = -3.35, p < .001, d = 0.50. If the alpha level is set at .05 in the left tail, what is the correct decision to make regarding the null hypothesis?

medium

As the sample size increases, the critical region for a t test __________.

stays the same size (equal to 5% of the distribution), but its location changes

A z test and a t test will have different critical regions because __________.

t critical values differ based on the sample size.

You use a single sample t when __________.

the IV defines one sample and the DV is measured on an interval/ratio scale and you do not know the population standard deviation

The basic structure for both z-tests and t-tests is such that the numerator is __________ and the denominator is __________.

the observed difference between means; the difference expected by chance (sampling error)

The single-sample t test should be used when comparing a sample mean to a population mean and when __________.

the population standard deviation is not known

When computing an effect size for a single sample t test, the denominator is __________.

the sample standard deviation

A random sample of 40 parents completed a questionnaire about gun safety laws in the United States. Responses ranged from 1 to 5, with 5 indicating more agreement that gun safety laws should be more strict. The general public had a mean of 3.2 and a standard deviation of about 1.22. You were testing whether the mean for the sample of parents (M = 3.8) is different from the population mean. What is the null hypothesis for this study?

=3.2

Based on your answer to Question 16, the researcher might have made a __________ error.

Type I

The number in the parentheses in the character string "t(14)=2.22, p<.05, d=.57" is the __________.

degrees of freedom

The degrees of freedom are used to __________.

determine the critical value

Generally, you should report __________, but it is acceptable to report __________ when you are computing your statistical tests by hand.

exact p values; p > .05 or p < .05

Researchers can only make a Type II error if they __________.

fail to reject the null hypothesis

One-tailed significance tests __________.

have one critical region that is either on the positive or negative side of a distribution

When performing a single-sample t test, which of the following assumptions if the most difficult to assess?

homogeneity of variance

How can you decrease the denominator of the t-test?

increase N

As sample size increases, what happens to the estimated standard error of the mean?

it decreases

The following results from a single-sample t test are reported in a journal article, t(59) = 2.24, p = .03, d = .78. How would you describe the size of the effect?

large