exam 3

A researcher expects that a newly developed shoe used by a sample of n = 6 individuals will reduce running speeds compared to a sample of n = 11 individuals using a control condition shoe. What is the critical t-value for the one-tailed hypothesis test with α = 0.05?

-1.753

It is expected that a treatment will reduce scores on a variable. If α = 0.05, what is the critical t value for a one-tailed hypothesis test with n = 15?

-1.761

The results of a hypothesis test are reported as follows in a scientific report: t(15) = 2.70, p < 0.05. Based on this report, how many individuals were in the sample?

16

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

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

If a researcher is using a t statistic to test a null hypothesis about a population, what information is needed from the population to calculate the tstatistic?

The researcher does not need to know any information about the population.

A researcher completes a hypothesis test using a = .05. Based on the evidence from the sample, the researcher decides to reject the null hypothesis. Which statement below is true?

The researcher might have made a Type I error, but the probability is less than 5%.

Which of the following accurately describes a hypothesis test?

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

A researcher is interested in having as much ability as possible to identify a treatment effect if one really exists. Which of the following strategies should they employ?

change the sample size from n = 25 to n = 100

A sample is selected from a population with µ = 46, and a treatment is administered to the sample. After treatment, the sample mean is M = 48 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen's d?

d=.50

Which of the following is an accurate definition of a Type I error?

rejecting a true null hypothesis

A random sample with n = 20 scores has df = 19.

true

Two samples each have n = 4 scores. If the first sample has a variance of s2 = 10 and the second sample has a variance of s2 = 6, what is the estimated standard error for the sample mean difference?

2

A researcher is using a two-tailed hypothesis test with α = 0.05 to evaluate the effect of a treatment. If the boundaries for the critical region are t = ± 2.080, then how many individuals are in the sample?

22

One sample has a sample size of n = 8 and SS = 168. A second sample has a sample size of n = 6 and SS = 126. What is the pooled variance for these two samples?

24.5

A sample with a mean of M = 40 and a variance of s2 = 12 has an estimated standard error of 2 points. How many scores are in the sample?

3

An independent-measures research study uses a total of 40 participants to compare two treatment conditions. What is the df value for the t statistic computed for the corresponding hypothesis test?

38

If n = 57 for a two-tailed hypothesis test in which a t-test should be utilized, which df value should be referenced when using the abridged tdistribution table in the textbook in order to set the critical t values for the hypothesis test?

40

A directional hypothesis test has a critical region that consists of the extreme ends of both the left and right side of the t distribution.

False

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?

It will be closer to 30 than to 20.

A sample of n = 25 scores produces a t statistic of t = +2.052. If the researcher is conducting a two-tailed hypothesis test, which of the following is the correct statistical decision?

The researcher should fail to reject the null hypothesis with either α = 0.05 or α = 0.01.

Two samples from the same population both have n = 10 scores with M = 45. If the t statistic is computed for each sample, then what is the relationship between the two t values?

The sample with the smaller variance will produce the larger t statistic.

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

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

A researcher selects a sample and administers a treatment for anxiety to the individuals in the sample. If the sample is used for a hypothesis test, what does the alternative hypothesis (H1) say about the treatment? Group of answer choices

The treatment has an effect on anxiety

A researcher conducts a research study to examine whether there is a difference between two treatments regarding anxiety. Which of the following is consistent conceptually with the null hypothesis? Group of answer choices

There is no difference between the two treatments among the general population regarding anxiety.

What is the effect of decreasing the alpha level (for example, from α = 0.05 to α = 0.01)?

This action increases the likelihood of failing to reject H0 and increases the risk of a Type II error.

A sample has a mean of M = 39.50, a standard deviation of s = 4.30, and produces a t statistic of t = +2.14. For a two-tailed hypothesis test, which of the following is the correct statistical decision for this sample? Group of answer choices

This is impossible to determine based on the provided information.

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

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

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

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

What statement below is consistent with making a Type II error?

concluding that a treatment has no effect when it really does

By selecting a smaller alpha level, it _____

decreases the likelihood that H0 is rejected

An independent-measures research study uses a total of 40 participants to compare two treatment conditions. What is the df value for the t statistic computed for the corresponding hypothesis test? Group of answer choices

df = 38

Which of the following is an accurate definition of a Type II error?

failing to reject a false null hypothesis

A Type I error occurs when a treatment has an effect but the decision is to fail to reject the null hypothesis.

false

A directional hypothesis test has a critical region that consists of the extreme ends of both the left and right side of the t distribution

false

A research study compares the mean weight for a sample of n = 36 participants before they begin a dieting routine and then again six weeks later. This is an example of an independent-measures design.

false

A researcher decides to lower the alpha level that determines the critical region(s) prior to conducting a hypothesis test. This will increase the power of the hypothesis test.

false

Compared to a z-score, a hypothesis test with a t statistic requires less information from the sample

false

Compared to a z-score, a hypothesis test with a t statistic requires less information from the sample.

false

If a researcher does not uncover sufficient evidence for a treatment effect in a hypothesis test, then they would include the statement of "p < 0.05" when writing their research report.

false

If a researcher rejects the null hypothesis when conducting a hypothesis test, it means that the sample data failed to provide sufficient evidence to conclude that the treatment had an effect.

false

If two sample sizes are not equal, the pooled variance value will be closer to the individual sample variance that has a larger variance value.

false

In a hypothesis test, if the sample data is determined to be in the critical region with α = 0.05, then all of the same sample data would still be in the critical region if α were changed to 0.01.

false

It is possible for the probability of a Type I error (p-value) obtained from a t-test to be 0.

false

Larger sample sizes increase the likelihood that an independent-measures t test will find a statistically significant difference, as well as the computed value for Cohen's d.

false

The alpha level determines the risk of a Type II error.

false

The estimated standard error is a measure of central tendency.

false

If other factors are held constant, which set of sample characteristics is most likely to produce a statistically significant t statistic?

n = 100 with s2 = 100

A researcher conducts a hypothesis test using a sample from an unknown population. If df = 30 for the t statistic and M = 46 and s2 = 10, how many individuals were in the sample?

n = 31

An independent-measures study comparing two treatment conditions produces a t statistic with df = 16. If the two samples are the same size, how many participants were in each of the samples?

n=9

If a hypothesis test is found to have power = 0.80, which is the probability that the test will result in a Type II error? Group of answer choices

p = 0.20

A hypothesis test involves a comparison of which two elements?

research results from a sample and a hypothesis about a population

A sample of n = 4 scores has SS = 60. Which is the variance for this sample

s 2 = 20

A sample of n = 4 scores has SS = 60. Which is the variance for this sample?

s 2 = 20

What is the sample variance and estimated standard error for a sample of n = 9 scores with SS = 72?

s 2 = 9 and sM = 1

A sample of n = 25 scores has a mean of M = 40 and a standard deviation of s = 10. What is the estimated standard error for the sample mean?

sM = 2

A sample of n = 4 scores has a variance of s2 = 64. What is the estimated standard error for the sample mean?

sM = 4

Which of the following accurately describes the critical region?

sample means that are very unlikely to be obtained if the null hypothesis is true

One sample has a variance of s2 = 12 and a second sample has a variance of s2 = 8. Because we don't know the sample sizes, which of the following most accurately describes the pooled variance for the two samples?

somewhere between 8 and 12

A researcher is examining whether daily yoga reduces stress. The researcher assigns n = 7 individuals to engage in daily yoga for three months and finds an average stress score of M = 16 with SS = 123. A second group of n = 6 individuals assigned to a control group for the three months had a stress score of M = 21 with SS = 141. Which of the following is most consistent with the results of conducting a one-tailed independent-measures t test with α = .05?

t = -1.83 and reject the null hypothesis

A researcher is examining whether daily yoga reduces stress. The researcher assigns n = 7 individuals to engage in daily yoga for three months and finds an average stress score of M = 16 with SS = 123. A second group of n = 6 individuals assigned to a control group for the three months had a stress score of M = 21 with SS = 141. Which of the following is most consistent with the results of conducting a one-tailed independent-measures ttest with α = .05?

t = -1.83 and reject the null hypothesis

Which of the following is consistent with what r2 represents as a measure of effect size?

the portion of variability in a sample attributable to a treatment effect relative to the total variability in the sample

A Type II error occurs when a researcher concludes that a treatment has no effect when it actually does have an effect.

true

A larger difference between two sample means increases the likelihood that an independent-measures t test will find a statistically significant difference, as well as the computed value for Cohen's d.

true

Conceptually, the independent-measures t test equation assesses the ratio of the actual difference between two sample means relative to how much difference should exist, on average, between two sample means when the null hypothesis is true.

true

If other factors are held constant, the larger the sample size is, the greater the likelihood of rejecting the null hypothesis.

true

Two samples are selected from a population, and a treatment is administered to the samples. If both samples have the same mean and the same variance, a researcher is more likely to reject the null hypothesis and find a significant treatment effect with a sample of n = 100 than with a sample of n = 4.

true

A researcher predicts that scores in treatment A will be higher than scores in treatment B. Which of the following is the correct null hypothesis for a one-tailed test evaluating this prediction?

µA ≤ µB

An instructor is interested in whether frequent feedback in their course to a small sample of students influences student performance. The instructor knows that final class scores are normally distributed with µ = 85 and σ = 6. Which is the alternative hypothesis for this research study?

µfrequent feedback ≠ 85