Psych stats 250 exM 2

Which of the following accurately describes a hypothesis test?

A) a descriptive technique that allows researchers to describe a population

B) a statistical technique that uses the data from a sample to evaluate a hypothesis about a population

C) a descriptive technique that allows researchers to describe a sample

D) a statistical technique that uses information about a population to evaluate a hypothesis about a sample

B

Which statement below accurately describes the relationship between the alpha level, the size of the critical region, and the risk of a Type I error?

A) As the alpha level increases, the size of the critical region decreases, and the risk of a Type II error increases.

B) As the alpha level increases, the size of the critical region increases, and the risk of a Type II error increases.

C) As the alpha level increases, the size of the critical region decreases, and the risk of a Type I error increases.

D) As the alpha level increases, the size of the critical region increases, and the risk of a Type I error increases.

D

A hypothesis test involves a comparison of which two elements?

A) research results from a population and a hypothesis about a sample

B) research results from a sample and a hypothesis about a population

C) research results from a sample and a hypothesis about the sample

D) research results from a population and a hypothesis about the population

B

A researcher is interested in whether a new teaching method influences the public speaking skills of students in an introductory to communications class. The researcher knows that public speaking skills in the class are normally distributed with µ = 10 and σ = 2. Which is the null hypothesis for this research study?

A) µteaching method = 2

B) µteaching method = 10

C) µteaching method ≠ 2

D) µteaching method ≠ 10

B

Why are t statistics more variable than z-scores?

A) The extra variability is caused by variations in experimental control.

B) The extra variability is caused by variations in the sample variance.

C) The extra variability is caused by variations in the sample mean.

D) The extra variability is caused by variations in the population mean.

B

If α = 0.05 for a two-tailed hypothesis test, how are the boundaries for the critical region determined?

A) Boundaries are drawn so there is 5% (0.05) in the center of the distribution.

B) Boundaries are drawn so there is 5% (0.05) in each tail of the distribution.

C) Boundaries are drawn so there is 10% (0.10) in each tail of the distribution.

D) Boundaries are drawn so there is 2.5% (0.025) in each tail of the distribution.

D

Which statement below is consistent with making a Type I error?

A) concluding that a treatment has an effect when it really does

B) concluding that a treatment has no effect when it really does

C) concluding that a treatment has no effect when it really has no effect

D) concluding that a treatment has an effect when it really has no effect

D

If a hypothesis test produces a z-score in the critical region, which decision should be made?

A) reject the alternative hypothesis

B) fail to reject the null hypothesis

C) reject the null hypothesis

C

Which statement below is not consistent with the distribution of sample means?

A) The distribution of sample means depicts the means of all the random samples of a particular sample size.

B) The distribution of sample means tends to pile up around the population standard deviation.

C) The distribution of sample means tends to pile up around the population mean.

D) The distribution of sample means tends to be approximately normal.

B

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

A) The samples are the same size and have the same variance.

B) The samples have the same mean and the same variance.

C) The samples are the same size and have the same mean.

D) The samples are the same size, have the same mean, and have the same variance.

D

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

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

B) None of these options are differences between t and z.

C) The t statistic computes the standard error by dividing the standard deviation by n – 1 instead of dividing by n.

D) The t statistic uses the sample mean in place of the population mean.

A

One sample has n = 10 scores and a variance of s2 = 20, and a second sample has n = 15 scores and a variance of s2 = 30. What can be concluded about the pooled variance for these two samples?

A) It will be closer to 30 than to 20

B) It will be closer to 20 than to 30

C) This cannot be determined by the information provided

D) It will be exactly halfway between 20 and 30

Which of the following is not a measure of effect size?

A) r^2

B) Cohen's d

C) Hartley’s F-max

D) Confidence interval

A researcher conducts a test to examine the homogeneity of variance assumption of an independent-samples t test. From Levene’s test, the obtained p-value is .34. Given this number, which of the following best summarizes the outcome from Levene’s test.

A) The homogeneity assumption was violated

B) There is not enough information for us to conclude whether the assumption was satisfied or violated

C) The homogeneity assumption was satisfied

An independent-measures research study uses n = 15 participants in one group and n = 12 participants in a second group to compare two treatment conditions. What is the df value for the t statistic computed for the corresponding hypothesis test?

A) 26

B) 25

C) 24

D) 27

Which of the following is not an advantage of using a repeated-measures design?

A) Repeated-measures designs require fewer participants

B) Repeated-measures designs tend to have more power

C) Repeated-measures designs remove bias related to individual differences

D) Repeated-measures designs eliminate confounding variables

Which of the following is the correct null hypothesis for an independent-measures t test?

A) M1 - M2 not equal to 0

B) µ1 - µ2= 0

C) µ1 - µ2 not equal to 0

D) M1 - M2 = 0

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

A) compare the mathematics skills for 9th-grade boys relative to 9th-grade girls

B) examine the development of vocabulary as a group of children mature from age 2 to age 3

C) compare the blood-pressure readings before medication and after medication for a group of patients with high blood pressure

D) examine the long-term effectiveness of a stop-smoking treatment by interviewing individuals 2 months and 6 months after the treatment ends

If a confidence interval contains zero, I have found a statistically significant finding and reject the null hypothesis.

True

False

For which of the following situations would a repeated-measures research design be appropriate?

A) comparing pain tolerance with and without acupuncture needles

B) comparing self-esteem for students who participate in school athletics versus those who do not

C) comparing verbal solving skills for science majors versus art majors at a college

D) comparing mathematical skills for girls versus boys at age 10

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

A) closer to 6 than to 10

B) closer to 10 than to 6

C) This cannot be determined by the information provided

D) exactly halfway between 6 and 10

Which of the following is not an assumption of the independent-samples t-test?

A) The two populations must be normal

B) The observations in each sample must be independent

C) The two populations must have equal variances

D) The residuals must be normally distributed

In a one-sample t-test, what are the formulas for variance, standard error, test statistic, and degrees of Freedom

V: s²=SS/n-1

SE: sm = s/√𝑛

T stat: t = (M- μ)/sm

df: n-1

In a two-sample t-test independent samples (pooled variance), what are the formulas for variance, standard error, test statistic, and degrees of Freedom

V: s²p = SS1 + SS2 / df1 + df2

SE: s(M1-M2) = (All squared root) (s²p/n1 + s²p/n2)

T stat: t = ((M1-M2) - (mu1 - mu2)) / s(M1-M2)

df: n1 + n2 - 2

In Two sample t-test dependent (related) samples (D represents the difference score), what are the formulas for variance, standard error, test statistic, and degrees of Freedom

V: s² = SS/df

SE: smd = √𝑠^2/𝑛 or 𝑠𝑀𝐷 = 𝑠/√𝑛

t stat: t = (Md - mu,d)/smd

df: npairs - 1

In a one-sample t-test, what are the formulas for the estimated Cohen’s d, r² and Confidence Intervals

Estimated Cohen’s d: estimated d = (M - mu)/s

r²: r² = t²/t²+df

CI: mu = M ± tcrit * sm

In a two-sample t-test independent samples pooled variance, what are the formulas for the estimated Cohen’s d, r², and Confidence Intervals

Estimated Cohen’s d: estimated d = (M1-M2)/√𝑠²𝑝

r²: r² = t²/t²+df

CI: mu1 - mu2 = M1-M2 ± tcrit * s(M1-M2)

In a two-sample t-test with dependent (related) samples (D represents the difference score), what are the formulas for the estimated Cohen’s d, r², and Confidence Intervals

Estimated Cohen’s d: estimated d = Md/s

r²: r² = t²/t²+df

CI: mu, d = Md ± tcrit * smd

what is the formula for HOMOGENEITY OF VARIANCE

fmax = s²larger/s²smaller

Put the following steps in the correct order. Write numbers 1-5 next to each step.

Calculate the test statistic

State the null and alternative hypotheses

Make a decision about the null hypothesis

Determine the critical value/region

State the conclusion in words

3

1

4

2

5

A university researcher wants to know whether a new study-skills workshop changes the average number of hours students spend studying each week. Historically, students at the university study an average of 12 hours per week, with a population standard deviation of 4 hours. A random sample of 36 students who attended the workshop reports an average of 13.5 hours per week.

The researcher uses a= .05

1) What is the population mean?

2) What is the sample mean?

3) What is the population SD?

4) What is the sample size?

5) What is the significance level?

6) Is this a one-tailed or two-tailed test?

7) Why?

8) Write the null and alternative hypothesis

1) mu = 12

2) M = 13.5

3) sigma = 4

4) n = 36

5) a = .05

6) two-tailed

7) Because it is measuring a change

8) Null: mu = 12, Alt: mu not = 12

A researcher wants to determine whether a mindfulness intervention reduces average anxiety scores. The population average anxiety score is 50.

What is the null and alternative hypothesis?

Is this a one-tailed or two-tailed test?

Null: mu = 50, Alt: mu > 50

One tailed

A researcher wants to know whether a new training program changes average resting heart rate. The population average resting heart rate is 72 bpm.

What is the null and alternative hypothesis?

Is this a one-tailed or two-tailed test?

Null: mu = 72, Alt: mu not = 72

Two-tailed

A health researcher believes that students who participate in a sleep education program will sleep more than 7 hours per night on average.

What is the null and alternative hypothesis?

Is this a one-tailed or two-tailed test?

Null: mu = 7, Alt: mu > 7

One-tailed

Two-tailed test, (a =. 05)

Critical z-score(s):

z=±1.96

One-tailed test, (a =. 05), upper-tail

Critical z-score

z =+1.65

One-tailed test, (a =. 05), lower-tail

Critical z-score:

z = -1.65

Why is the critical z-score different for a one-tailed test versus a two-tailed test?

2-tailed divides a-level and one-tailed doesn’t have to split it

A psychologist knows that the population average score on a test-anxiety measure is 40, with a population standard deviation of 8.

After participating in a relaxation intervention, a sample of 25 students has an average score of 36. The researcher uses a two-tailed test with (a = .05).

1) What is the null and alternative hypothesis?

2) What are the criteria for decision-making?

3) Calculate the SE

4) Calculate the test statistic

5) Does the value fall out of the critical value region

6) Make a decision

7) Write a conclusion

8) Interpret the result

9) If an error occurred in this, which would it be?

1) Null: mu = 40, Alt: mu not = 40

2) a = .05, Z-critical values: +-1.96

3) 1.6

4) -2.5

5) calculated z= -2.5, critical z: z= +-1.96

6) reject the null hypothesis

7) Participating in a relaxation intervention had a significant effect on the scores for test anxiety, z = -2.5, p< .05.

8) The relaxation intervention did help reduce test anxiety. Since the z-score falls beyond the critical region; it rejects the null.

9) Type 1 error

The average resting heart rate for adults is 70 bpm, with a population standard deviation of 10 bpm. An exercise scientist believes that a new training program will reduce resting heart rate.

A sample of 36 participants completes the program. Their average resting heart rate is 68 bpm. The researcher uses (a = .05).

1) What is the null and alternative hypothesis?

2) What are the criteria for decision-making?

3) Calculate the SE

4) Calculate the test statistic

5) Does the value fall out of the critical value region

6) Make a decision

7) Write a conclusion

8) Interpret the result

9) If an error occurred in this, which would it be?

1) Null: mu = 70, Alt: mu < 70

2) a = .05, Z-critical values: -1.65

3) 1.67

4) -1.2

5) calculated z= -1.2, critical z: z= -1.65

6) Fail to reject the null hypothesis

7) The program did not have a significant effect on reducing the resting heart rate, z = -1.2, p > .05.

8) The new training program did not reduce heart rate significantly. The critical value we got from the z-score did not fall within the critical region, so we fail to reject the null.

9) Type 2 error

Researchers know that college students sleep an average of 7 hours per night, with a population standard deviation of 1.2 hours. A health researcher wants to know whether students who participate in a new sleep-health program sleep more than 7 hours per night. A sample of 49 students participate in the program. Their average sleep is 7.4 hours per night. Use: a =. 05

1) What is the null and alternative hypothesis?

2) Identify what type of test

3) What are the criteria for decision-making?

4) Calculate the SE

5) Calculate the test statistic

6) Does the value fall out of the critical value region

7) Make a decision

8) Write a concluding sentence

9) Interpret the results

10) If an error occurred in this, which would it be?

1) Null: mu = 7, Alt: mu > 7

2) One-tailed (upper)

3) a = .05, z-critical value: +1.65

4) 0.1714

5) +2.33

6) Calculated z: +2.33, Critical z: z = +1.65

7) Reject the null hypothesis

8) The new sleep program had a significant effect, increasing the 7 hours of sleep, z = +2.33, p < .05.

9) The study did manage to find a way to increase how many hours of sleep college students get. The critical value from the z-score falls in the critical region, making it reject the null hypothesis.

10) Type 1 error

In your own words, what is the purpose of hypothesis testing?

Makes a hypothesis about a population and then takes a sample from the population to test if the hypothesis is true.

What does the null hypothesis generally represent?

When the treatment has no effect on the population

What does it mean to reject the null hypothesis?

The treatment did have an effect on the population

A statistically significant result means that ...

The treatment did have an effect on the population. Their score falls in the critical region.

One sample has n = 10 scores and a variance of s2 = 20, and a second sample has n = 15 scores and a variance of s2 = 30. What can be concluded about the pooled variance for these two samples?

A) It will be closer to 30 than to 20

B) It will be closer to 20 than to 30

C) This cannot be determined by the information provided

D) It will be exactly halfway between 20 and 30

A)

Which of the following is not a measure of effect size?

A) r2

B) Cohen's d

C) Hartley’s F-max

D) Confidence interval

C)

A researcher conducts a test to examine the homogeneity of variance assumption of an independent-samples t test. From Levene’s test, the obtained p-value is .34. Given this number, which of the following best summarizes the outcome from Levene’s test.

A) The homogeneity assumption was violated

B) There is not enough information for us to conclude whether the assumption was satisfied or violated

C) The homogeneity assumption was satisfied

C)

An independent-measures research study uses n = 15 participants in one group and n = 12 participants in a second group to compare two treatment conditions. What is the df value for the t statistic computed for the corresponding hypothesis test?

A) 26

B) 25

C) 24

D) 27

B)

Which of the following is not an advantage of using a repeated-measures design?

A) Repeated-measures designs require fewer participants

B) Repeated-measures designs tend to have more power

C) Repeated-measures designs remove bias related to individual differences

D) Repeated-measures designs eliminate confounding variables

D)

Which of the following is the correct null hypothesis for an independent-measures t test?

A) M1 - M2 not = 0

B) µ1 - µ2= 0

C) µ1 - µ2 not = 0

D) M1 - M2 = 0

B)

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

A) compare the mathematics skills for 9th-grade boys relative to 9th-grade girls

B) examine the development of vocabulary as a group of children mature from age 2 to age 3

C) compare the blood-pressure readings before medication and after medication for a group of patients with high blood pressure

D) examine the long-term effectiveness of a stop-smoking treatment by interviewing individuals 2 months and 6 months after the treatment ends

A)

If a confidence interval contains zero, I have found a statistically significant finding and reject the null hypothesis.

True

False

False

For which of the following situations would a repeated-measures research design be appropriate?

A) comparing pain tolerance with and without acupuncture needles

B) comparing self-esteem for students who participate in school athletics versus those who do not

C) comparing verbal solving skills for science majors versus art majors at a college

D) comparing mathematical skills for girls versus boys at age 10

A)

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

A) closer to 6 than to 10

B) closer to 10 than to 6

C) This cannot be determined by the information provided

D) exactly halfway between 6 and 10

D)

Which of the following is not an assumption of the independent-samples t-test?

A) The two populations must be normal

B) The observations in each sample must be independent

C) The two populations must have equal variances

D) The residuals must be normally distributed

D)