More Chapter 8: Hypothesis Testing

Under what circumstances can a very small treatment effect be statistically significant?

if the sample size is big and the sample variance is small

If a sample of n = 16 scores is being used to make an 80% confidence interval estimate of the population mean, what value(s) of t should be used?

t = ±1.341

With = .01 the two-tailed critical region for a t test using a sample of n = 16 subjects would have boundaries of ____.

t = ±2.947

A researcher is evaluating a treatment that is expected to increase scores. If a one-tailed test with = .05 is used, then the critical region consists of z-scores greater than 1.65.

true

A sample of n = 4 scores with SS = 48 has a variance of 16 and an estimated standard error of 2

true

A significant treatment effect does not necessarily indicate a large treatment effect

true

Although hypothesis tests are affected by sample size, it has little or no influence on measures of effect size, such as r2 or Cohen's d.

true

As sample size increases, the critical region boundaries for a two-tailed test with = .05 will move closer to zero.

true

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

true

If a hypothesis test using a sample of n = 16 scores produces a t statistic of t = 2.15, then the correct decision is to reject the null hypothesis for a two-tailed test with = .05.

true

If a research report includes the term significant result, it means that the null hypothesis was rejected.

true

If other factors are held constant, as the sample size increases, the estimated standard error decreases

true

If other factors are held constant, the larger the size of the treatment effect, the greater the power of the hypothesis test.

true

If random samples, each with n = 20 scores, are selected from a population, and the z-score and t statistic are computed for each sample, the t statistics will be more variable than the z-scores.

true

In general, the null hypothesis states that the treatment has no effect on the population mean.

true

Most researchers would like the hypothesis test to reject the null hypothesis

true

The alpha level determines the risk of a Type I error

true

The critical region for a hypothesis test consists of sample outcomes that are very unlikely to occur if the null hypothesis is true.

true

The null hypothesis is stated in terms of the population, even though the data come from a sample

true

The power of a hypothesis test is the probability that the sample mean will be in the critical region if the treatment has an effect.

true

The sample mean will always be exactly in the center of a confidence interval that is estimating the value of the population mean.

true

The value obtained for Cohen's d is independent of the sample size

true

When the population variance or standard deviation is not known, you must use a t statistic instead of a z-score for a hypothesis test.

true

A sample of n = 4 scores is selected from a population with an unknown mean. The sample has a mean of M = 40 and a variance of s2 = 16. Which of the following is the correct 90% confidence interval for u?

u = 40 ± 2.353(2)

On average, what value is expected for the t statistic when the null hypothesis is true?

0

A sample of n = 25 scores has a mean of M = 40 and a variance of s2 = 100. What is the estimated standard error for the sample mean?

2

Describe a hypothesis test.

An inferential technique that uses the data from a sample to draw inferences about a population

Describe the effect of increasing the alpha level.

Increases the risk of a Type I error and has no effect on the standard error

When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution?

It is flatter and more spread out than the normal distribution.

When is there a risk of a Type I error?

Whenever H0 is rejected

When is there a risk of a Type II error?

Whenever the decision is "fail to reject H0"

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

s2 = 9 and sM = 1

A Type I error occurs when a treatment has no effect but the decision is to reject the null hypothesis.

true

A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population which is known to have a mean of = 80. The results will be examined using a one-tailed hypothesis test. Which of the following is the correct statement of the null hypothesis?

≤ 80

If a hypothesis test is found to have power = 0.70, then what is the probability that the test will result in a Type II error?

0.30

A sample of n = 16 individuals is selected from a population with = 60 and = 6 and a treatment is administered to the sample. After treatment, the sample mean is M = 63. What is the value of Cohen's d for this sample?

0.50

A sample of n = 4 scores has SS = 48. What is the estimated standard error for the sample mean?

2

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

20

A researcher conducts a hypothesis test using a sample of n = 40 from an unknown population. What is the df value for the t statistic?

39

If a treatment has a very small effect, then what is a likely outcome for a hypothesis test evaluating the treatment?

A Type II error

Which set of characteristics will produce the smallest value for the estimated standard error?

A large sample size and a small sample variance

If other factors are held constant, how does sample size influence the likelihood of rejecting the null hypothesis and measures of effect size such as r2 and Cohen's d?

A larger sample increases the likelihood but has little influence on measures of effect size.

A researcher administers a treatment to a sample of participants selected from a population with µ = 80. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis?

A sample mean much different than 80 with = .05

What combination of factors will increase the chances of rejecting the null hypothesis?

A small standard error and a large alpha level

4. What is the relationship between the alpha level, the size of the critical region, and the risk of a Type I error?

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

What is the consequence of a Type I error?

Concluding that a treatment has an effect when it really does not.

Describe the effect of increasing the sample size.

Decreases the standard error and has no effect on the risk of a Type I error

Definition of a Type II error.

Failing to reject a false null hypothesis

A sample has a mean of M = 39.5 and a standard deviation of s = 4.3, and produces a t statistic of t = 2.14. For a two-tailed hypothesis test with = .05, what is the correct statistical decision for this sample?

It is impossible to make a decision about H0 without more information.

Which of the following describes what a confidence interval does?

It uses a sample mean to estimate the corresponding population mean.

If other factors are held constant, what is the effect of increasing the sample size?

It will decrease the estimated standard error and increase the likelihood of rejecting H0.

If other factors are held constant, what is the effect of increasing the sample variance?

It will increase the estimated standard error and decrease the likelihood of rejecting H0.

A treatment is administered to a sample of n = 9 individuals selected from a population with a mean of = 80 and a standard deviation of = 12. After treatment, the effect size is measured by computing Cohen's d, and a value of d = 0.50 is obtained. Based on this information, what is the mean for the treated sample?

M = 86

Describe the critical region.

Outcomes with a very low probability if the null hypothesis is true

A two-tailed hypothesis test is being used to evaluate a treatment effect with = .05. If the sample data produce a z-score of z = 2.24, then what is the correct decision?

Reject the null hypothesis and conclude that the treatment has an effect.

Definition of a Type I error.

Rejecting a true null hypothesis

Why are t statistics more variable than z-scores?

The extra variability is caused by variations in the sample variance

Two samples from the same population both have M = 84 and s2 = 20; however, one sample has n = 10 and the other has n = 20 scores. Both samples are used to evaluate a hypothesis that = 80 and to compute Cohen's d. How will the outcomes for the two samples compare?

The larger sample is more likely to reject the hypothesis but the two samples will have the same value for Cohen's d.

Define for the power of a statistical test.

The probability of rejecting a false null hypothesis

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.

A researcher expects a treatment to produce an increase in the population mean. The treatment is evaluated using a one tailed hypothesis test, and the test produces z = +1.85. Based on this result, what is the correct statistical decision? a. The researcher should reject the null hypothesis with = .05 but not with = .01. b. The researcher should reject the null hypothesis with either = .05 or = .01. c. The researcher should fail to reject H0 with either = .05 or = .01. d. This cannot be answered without additional information.

a

A researcher conducts a hypothesis test to evaluate the effect of a treatment. The hypothesis test produces a z-score of z = 2.37. Assuming that the researcher is using a two-tailed test, what decision should be made?

a. The researcher should reject the null hypothesis with = .05 but not with = .01.

By selecting a larger alpha level, a researcher is ________.

a. attempting to make it easier to reject H0 b. better able to detect a treatment effect c. increasing the risk of a Type I error

Increasing the alpha level (for example from = .01 to = .05) ____.

a. increases the probability of a Type I error b. increases the size of the critical region c. increases the probability that the sample will fall into the critical region

A hypothesis test with a sample of n = 25 participants produces a t statistic of t = +2.53. Assuming a one-tailed test with the critical region in the right-hand tail, what is the correct decision? a. The researcher can reject the null hypothesis with = .05 but not with = .01. b. The researcher can reject the null hypothesis with either = .05 or = .01. c. The researcher must fail to reject the null hypothesis with either = .05 or = .01. d. It is impossible to make a decision about H0 without more information.

b

A sample of n = 25 scores produces a t statistic of t = 2.062. If the researcher is using a two-tailed test, then which of the following is the correct statistical decision? a. The researcher can reject the null hypothesis with = .05 but not with = .01. b. The researcher can reject the null hypothesis with either = .05 or = .01. c. The researcher must fail to reject the null hypothesis with either = .05 or = .01. d. It is impossible to make a decision about H0 without more information.

c

If other factors are held constant, which set of sample characteristics is most likely to produce a significant t statistic? a. n = 25 with s2 = 100 b. n = 25 with s2 = 400 c. n = 100 with s2 = 100 d. n = 100 with s2 = 400

c

If other factors are held constant, which set of sample characteristics is most likely to reject a null hypothesis stating that = 80? a. M = 85 and small sample variance b. M = 85 and large sample variance c. M = 90 and small sample variance d. M = 90 and large sample variance

c

A sample is selected from a population with = 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, the size of the treatment effect, as measured by Cohen's d, is ____.

d = 0.50

A Type I error occurs when a treatment actually does have an effect on the scores but the effect was not large enough to reject the null hypothesis.

false

A research report states "t(8) = 2.00, p > .05." For this test, r2 = 2/10.

false

A researcher administers a treatment to a sample of n = 16 selected from a population with = 40 and = 8. If the sample mean after treatment is M = 42, then Cohen's d = 1.00.

false

As the sample size is increased, the distribution of t statistics becomes flatter and more spread out

false

For a one tailed test evaluating a treatment that is supposed to decrease scores, a researcher obtains t(8) = 1.90. For = .05, the correct decision is to reject the null hypothesis.

false

For a two-tailed test with = .05 and a sample of n = 16, the boundaries for the critical region are t = ±2.120.

false

If a hypothesis test leads to rejecting the null hypothesis, it means that the data did not provide enough evidence to conclude that the treatment has an effect.

false

If the null hypothesis states that = 70 and a researcher obtains a sample with M = 73 and s2 = 9, then Cohen's d = 0.33.

false

If the sample data are in the critical region with = .05, then the same sample data would still be in the critical region if were changed to .01.

false

If two samples each have the same mean, the same number of scores, and are selected from the same population, then they will also have identical t statistics.

false

In a hypothesis test, a large value for the sample variance increases the likelihood that you will find a significant treatment effect.

false

In a research report, the notation p < .05 indicates that the probability of a Type I error is less than .05

false

In general, the larger the value of the sample variance, the greater the likelihood of rejecting the null hypothesis.

false

You can reduce the risk of a Type I error by using a larger sample

false