Stats

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

f

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

t

The alpha level determines the risk of a Type I error

t

On average, what value is expected for the t statistic when the null hypothesis is true? a. 0 c. 1.96 b. 1 d. t > 1.96

a

A sample of n = 4 scores has SS = 48. What is the estimated standard error for the sample mean? a. 1 c. 4 b. 2 d. 16

b

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. A larger sample increases both the likelihood and measures of effect size. b. A larger sample increases the likelihood but has little influence on measures of effect size. c. A larger sample decreases the likelihood but has little influence on measures of effect size. d. A larger sample decreases both the likelihood and measures of effect size.

b

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.

t

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

t

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

t

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

t

If a treatment has a very small effect, then what is a likely outcome for a hypothesis test evaluating the treatment? a. A Type I error b. A Type II error c. Correctly reject the null hypothesis d. Correctly fail to reject the null hypothesis

b

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 c. M = 90 and small sample variance b. M = 85 and large sample variance d. M = 90 and large sample variance

c

With = .01 the two-tailed critical region for a t test using a sample of n = 16 subjects would have boundaries of ____. a. t = ±2.602 c. t = ±2.947 b. t = ±2.583 d. t = ±2.921

c

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.

f

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

t

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 ____. a. d = 0.125 b. d = 0.25 c. d = 0.50 d. Cohen's d cannot be computed without knowing the sample size

c

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

f

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.

t

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

t

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

t

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

t

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 c. n = 100 with s2 = 100 b. n = 25 with s2 = 400 d. n = 100 with s2 = 400

c

Under what circumstances can a very small treatment effect be statistically significant? a. If the sample size is big and the sample variance is small b. If the sample size and the sample variance are both big c. If the sample size is small and the sample variance is big d. If the sample size and the sample variance are both small

a

When is there a risk of a Type I error? a. Whenever H0 is rejected b. Whenever H1 is rejected c. Whenever the decision is "fail to reject H0" d. The risk of a Type I error is independent of the decision from a hypothesis test.

a

Which of the following describes what a confidence interval does? a. It uses a sample mean to estimate the corresponding population mean. b. It uses a population mean to predict a sample mean. c. It uses a level of confidence to estimate a sample mean. d. It uses the sample mean to determine a level of confidence

a

Which set of characteristics will produce the smallest value for the estimated standard error? a. A large sample size and a small sample variance b. A large sample size and a large sample variance c. A small sample size and a small sample variance d. A small sample size and a large sample variance

a

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? a. Reject the null hypothesis and conclude that the treatment has no effect. b. Reject the null hypothesis and conclude that the treatment has an effect. c. Fail to reject the null hypothesis and conclude that the treatment has no effect. d. Fail to reject the null hypothesis and conclude that the treatment has an effect

b

Which of the following is an accurate definition of a Type I error? a. Rejecting a false null hypothesis b. Rejecting a true null hypothesis c. Failing to reject a false null hypothesis d. Failing to reject a true null hypothesis

b

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? a. u = 40 ± 2.353(4) c. u = 40 ± 2.353(2) b. u = 40 ± 1.638(4) d. u = 40 ± 1.638(2)

c

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? a. The two t statistics will be identical. b. The sample with the larger variance will produce the larger t statistic. c. The sample with the smaller variance will produce the larger t statistic. d. There is no way to predict the relationship between the two t statistics

c

When is there a risk of a Type II error? a. Whenever H0 is rejected b. Whenever H1 is rejected c. Whenever the decision is "fail to reject H0" d. The risk of a Type II error is independent of the decision from a hypothesis test

c

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? a. > 80 c. < 80 b. > 80 d. < 80---underlined

d

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

f

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.

t

4. What is 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 increases and the risk of a Type I error increases. b. As the alpha level increases, the size of the critical region increases and the risk of a Type I error decreases. 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 decreases and the risk of a Type I error decreases.

a

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? a. 0.30 b. 0.70 c. p > 0.70 d. This cannot be determined without more information

a

Which of the following accurately describes the effect of increasing the sample size? a. Increases the standard error and has no effect on the risk of a Type I error b. Decreases the standard error and has no effect on the risk of a Type I error c. Increases the risk of a Type I error and has no effect on the standard error d. Decreases the risk of a Type I error and has no effect on the standard error

b

If is held constant at .05, what is the relationship between sample size, the critical region, and the risk of a Type I error? a. As sample size increases, the critical region expands and the risk of a Type I error increases. b. As sample size increases, the critical region shrinks and the risk of a Type I error increases. c. As sample size increases, the critical region expands and the risk of a Type I error decreases. d. There is no relationship between sample size, the critical region, and the risk of a Type I error

d

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? a. t = 0 c. t = ±1.753 b. t = ±2.131 d. t = ±1.341

d

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 d. All of the other options are results of increasing alpha.

d

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

t

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

t

If other factors are held constant, what is the effect of increasing the sample size? a. It will increase the estimated standard error and increase the likelihood of rejecting H0. b. It will increase the estimated standard error and decrease the likelihood of rejecting H0. c. It will decrease the estimated standard error and increase the likelihood of rejecting H0. d. It will decrease the estimated standard error and decrease the likelihood of rejecting H0.

c

Which of the following accurately describes the effect of increasing the alpha level? a. Increases the standard error and has no effect on the risk of a Type I error b. Decreases the standard error and has no effect on the risk of a Type I error c. Increases the risk of a Type I error and has no effect on the standard error d. Decreases the risk of a Type I error and has no effect on the standard error

c

Which of the following is an accurate definition for the power of a statistical test? a. The probability of rejecting a true null hypothesis b. The probability of supporting true null hypothesis c. The probability of rejecting a false null hypothesis d. The probability of supporting a false null hypothesis

c

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.

f

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.

f

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

f

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.

f

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.

f

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.

f

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

f

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.

f

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

f

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

f

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

t

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

t

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.

t

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

t

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.

t

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

t

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.

t

2. Which of the following accurately describes the critical region? a. Outcomes with a very low probability if the null hypothesis is true b. Outcomes with a high probability if the null hypothesis is true c. Outcomes with a very low probability whether or not the null hypothesis is true d. Outcomes with a high probability whether or not the null hypothesis is true

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. 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 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. A sample mean near 80 with = .05 b. A sample mean near 80 with = .01 c. A sample mean much different than 80 with = .05 d. A sample mean much different than 80 with = .01

c

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? 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.

d

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 d. all of the above

d

What is the consequence of 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 has no effect c. Concluding that a treatment has no effect when it really does d. Concluding that a treatment has an effect when it really has no effect

d

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? a. 39 b. 40 c. 41 d. It cannot be determined from the information given

a

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 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 researcher administers a treatment to a sample of participants selected from a population with µ = 80. If the researcher obtains a sample mean of M = 88, which combination of factors is most likely to result in rejecting the null hypothesis? a. = 5 and n = 25 c. = 10 and n = 25 b. = 5 and n = 50 d. = 10 and n = 50

b

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? a. 0.33 c. 2.00 b. 0.50 d. 3.00

b

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? a. 4 c. 2 b. 2 d. 1

b

A sample of n = 4 scores has SS = 60. What is the variance for this sample? a. 30 c. 16 b. 20 d. 15

b

If other factors are held constant, what is the effect of increasing the sample variance? a. It will increase the estimated standard error and increase the likelihood of rejecting H0. b. It will increase the estimated standard error and decrease the likelihood of rejecting H0. c. It will decrease the estimated standard error and increase the likelihood of rejecting H0. d. It will decrease the estimated standard error and decrease the likelihood of rejecting H0.

b

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? a. The larger sample is more likely to reject the hypothesis and will produce a larger value for Cohen's d. b. The larger sample is more likely to reject the hypothesis but the two samples will have the same value for Cohen's d. c. The larger sample is less likely to reject the hypothesis and will produce a larger value for Cohen's d. d. The larger sample is less likely to reject the hypothesis but the two samples will have the same value for Cohen's d.

b

What is the sample variance and the estimated standard error for a sample of n = 9 scores with SS = 72? a. s2 = 9 and sM = 3 c. s2 = 3 and sM = 3 b. s2 = 9 and sM = 1 d. s2 = 3 and sM = 1

b

When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution? a. It is almost perfectly normal. b. It is flatter and more spread out than the normal distribution. c. It is taller and narrower than the normal distribution. d. There is no consistent relationship between the t distribution and the normal distribution

b

Why are t statistics more variable than z-scores? a. The extra variability is caused by variations in the sample mean. b. The extra variability is caused by variations in the sample variance. c. The extra variability is caused by variations in the df value. d. None of the other options explains the extra variability for t statistics.

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

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? a. M = 6 b. M = 82 c. M = 86 d. This cannot be answered without knowing the sample size.

c

Which combination of factors will increase the chances of rejecting the null hypothesis? a. A large standard error and a large alpha level b. A large standard error and a small alpha level c. A small standard error and a large alpha level d. A small standard error and a small alpha level

c

Which of the following accurately describes a hypothesis test? a. A descriptive technique that allows researchers to describe a sample b. A descriptive technique that allows researchers to describe a population c. An inferential technique that uses the data from a sample to draw inferences about a population d. An inferential technique that uses information about a population to make predictions about a sample

c

Which of the following is an accurate definition of a Type II error? a. Rejecting a false null hypothesis b. Rejecting a true null hypothesis c. Failing to reject a false null hypothesis d. Failing to reject a true null hypothesis

c