Research Methods Chapter 9

If two samples are selected from the same population and both have the same size (n = 25) and the same mean (M = 53), then they will also have the same t statistic.

F

For a hypothesis test using a t statistic, the boundaries for the critical region will change if the sample size is changed. (Assume that the alpha level is held constant).

T

Which set of sample characteristics is most likely to produce a significant t statistic? 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 large sample size and a small sample variance

What is the effect of a large value for the estimated standard error. a. a larger value for t and a greater likelihood of rejecting the null hypothesis b. a larger value for t and a lower likelihood of rejecting the null hypothesis c. a smaller value for t and a greater likelihood of rejecting the null hypothesis d. a smaller value for t and a lower likelihood of rejecting the null hypothesis

a larger value for t and a greater likelihood of rejecting the null hypothesis

The estimated standard error, sM, provides a measure of the average or standard distance between ______. a. a score and the population mean (X and μ) b. a sample mean and the population mean (M and μ) c. a score and the sample mean (X and M) d. None of the other options is correct.

a sample mean and the population mean (M and μ)

Which set of sample characteristics is most likely to produce a large 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 small sample size and a large sample variance

A hypothesis test produces a t statistic of t = 2.14. If the researcher is using a two-tailed test with α = .05, how large does the sample have to be in order to reject the null hypothesis? a. at least n = 13 b. at least n = 14 c. at least n = 15 d. at least n = 16

at least n = 16

A sample is selected from a population with μ = 60 and a treatment is administered to the sample. After treatment, the sample mean is M = 66 with a sample variance of s2 = 100. Based on this information, the size of the treatment effect, as measured by Cohen's d, is ____. a. d = 0.06 b. d = 0.60 c. d = 0.66 d. Cohen's d cannot be computed without knowing the sample size.

d = 0.60

With α = .05 and df = 8, the critical value for a one-tailed t test is t = 1.860. Assuming all other factors are held constant, if the df value were increased to df = 20, the critical value of t would ______. a. increase b. decrease c. stay the same d. not enough information to answer

decrease

Which of the following samples will produce the largest value for the estimated standard error? a. n = 25 with s2 = 100 b. n = 25 with s2 = 400 c. n = 16 with s2 = 100 d. n = 16 with s2 = 400

n = 16 with s2 = 400

A sample of n = 4 scores has a mean of M = 35 and SS = 48. What are the values for the sample standard deviation and the estimated standard error for the sample mean? a. s = 16 and sM = 4 b. s = 16 and sM = 2 c. s = 4 and sM = 1 d. s = 4 and sM = 2

s = 4 and sM = 2

What is the sample variance and the estimated standard error for a sample of n = 4 scores with SS = 300? a. s2 = 10 and sM = 5 b. s2 = 100 and sM = 20 c. s2 = 10 and sM = 20 d. s2 = 100 and sM = 5

s2 = 100 and sM = 5

A sample of n = 25 scores has a mean of M = 40 and a variance of s2 = 100. If this sample is being used to test a null hypothesis stating that μ = 43, then what is the t statistic for the sample? a. t = -3/20 = -0.15 b. t = -0.30 c. t = -3/4 = -0.75 d. t = -3/2 = -1.50

t = -3/2 = -1.50

With α = .05, what is the critical t value for a one-tailed test with n = 25? a. t = 1.711 b. t = 2.064 c. t = 2.708 d. t = 2.060

t = 2.064

As the value of df increases, the t distribution tends to become flatter and more spread out.

T

Assuming all other factors are held constant, t statistics tend to be more variable than z-scores.

T

For a two-tailed hypothesis test with α = .05 and a sample of n = 16 scores, the boundaries for the critical region would be t = ±2.131.

T

If other factors are held constant, increasing the number of scores in the sample will increase the likelihood of rejecting the null hypothesis.

T

In a t statistic, the estimated standard error provides a measure of how much difference is reasonable to expect between a sample mean and the population mean.

T

In general, a large value for a t statistic (far from zero) is an indication that the sample data are not consistent with the null hypothesis.

T

The boundaries for the critical region for a two-tailed test using a t statistic with α = .05 will never be less than ±1.96.

T

The size of the estimated standard error, sM, is partially determined by the size of the sample variance.

T

When n is small (less than 30), the t distribution ______. a. is almost identical in shape to the normal z distribution b. is flatter and more spread out than the normal z distribution c. is taller and narrower than the normal z distribution d. cannot be specified, making hypothesis tests impossible

is flatter and more spread out than the normal z distribution

A sample is selected from a population with µ = 80. If the sample has a mean of M = 85, which of the following will produce the largest value for t? a. n = 9 and s2 = 16 b. n = 9 and s2 = 4 c. n = 25 and s2 = 16 d. n = 25 and s2 = 4

n = 25 and s2 = 4

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

0

A sample of n = 10 scores has M = 58, s2 = 160, and an estimated standard error of 4 points. Which of these values will probably decrease if the sample size is increased to n = 100? a. the value of M b. the value of s2 c. the value of the standard error, sM d. None of the other choices is likely to be changed very much by increasing n.

the value of the standard error, sM

A sample of n = 9 scores has SS = 72. What is the estimated standard error for the sample mean? a. 9 b. 3 c. 1 d. cannot answer without knowing the sample mean

1

A researcher reports a significant treatment effect with t(24) = 3.04. How many scores were in the sample? a. 23 b. 24 c. 25 d. Cannot determine without additional information.

25

Which combination of factors has the greatest likelihood of rejecting the null hypothesis? a. A large sample size and a large sample variance. b. A large sample size and a small sample variance. c. A small sample size and a large sample variance. d. A small sample size and a small sample variance.

A large sample size and a small sample variance.

A sample of n = 4 individuals is obtained from a population with μ = 80. Which set of sample statistics would produce the most extreme value for t? a. M = 84 and s2 = 8 b. M = 84 and s2 = 32 c. M = 88 and s2 = 8 d. M = 88 and s2 = 32

M = 88 and s2 = 8

A sample of n = 25 scores is obtained from a population with μ = 80. Which of the following sets of sample statistics is most likely to reject the null hypothesis? a. M = 85 with s2 = 10 b. M = 90 with s2 = 10 c. M = 85 with s2 = 100 d. M = 90 with s2 = 100

M = 90 with s2 = 10

A sample of n = 9 scores has SS = 200. What is the variance for this sample? a. 25 b. 5/3 c. 25/9 d. 5

25

A sample of n = 16 individuals is selected from a population with μ = 80 and a treatment is administered to the sample. After treatment, the sample mean is M = 84 and the sample variance is s2 = 100. If Cohen=s d is used to measure effect size for this study, what value will be obtained for d? a. 4/2.5 = 1.60 b. 0.40 c. 0.04 d. cannot be determined without additional information

0.40

If a sample consists of n = 15 individuals, then what is the df value for the t statistic? a. 16 b. 15 c. 14 d. cannot be determined from the information given

14

A sample of n = 16 scores has a mean of M = 40 and a variance of s2 = 64. What is the estimated standard error for the sample mean? a. 16 b. 4 c. 2 d. 1

2

A sample of n = 4 scores has SS = 48. What is the estimated standard error for this sample? a. 12 b. 16 c. 4 d. 2

2

A sample of n = 9 scores has a mean of M = 46 and a variance of s2 = 36. What is the estimated standard error for this sample? a. 12 b. 6 c. 4 d. 2

2

The results of a hypothesis test are reported as follows: t(29) = 2.70, p < .05. Based on this report, how many individuals were in the sample? a. 28 b. 29 c. 30 d. cannot be determined from the information provided

30

A hypothesis test produces t = 2.00 for a sample of n = 16 scores. What is the value of r2? a. 2/18 b. 2/17 c. 4/20 d. 4/19

4/19

If other factors are held constant, which of the following is a consequence of increasing the sample size? a. An increased standard error and an increased likelihood of rejecting H0. b. An increased standard error and a decreased likelihood of rejecting H0. c. A decreased standard error and an increased likelihood of rejecting H0. d. A decreased standard error and a decreased likelihood of rejecting H0.

A decreased standard error and an increased likelihood of rejecting H0.

In a hypothesis test using a t statistic, what is the influence of using a larger sample? a. A larger sample tends to lower the likelihood of rejecting the null hypothesis. b. A larger tends to increase the likelihood of rejecting the null hypothesis. c. The size of the variance has no impact on the outcome of the hypothesis test. d. Cannot determine without more information.

A larger tends to increase the likelihood of rejecting the null hypothesis.

Which of the following is a major difference between a hypothesis test with the t statistic formula and the test with a z-score? a. You must calculate the sample variance (or standard deviation) for the t statistic but not for the z-score b. You must know the population variance (or standard deviation) for the z-score but not for the t statistic c. You use the unit normal table to find critical values for the z-score test but not for the t test. d. All of the other options are major differences.

All of the other options are major differences.

To calculate a t statistic, what information is needed from the sample? a. the value for n b. the value for M c. the value for s or s2 d. All of the other options are needed to compute t.

All of the other options are needed to compute t

As sample size increases _______. a. the value of df also increases b. the t distribution becomes more like a normal distribution c. the critical values of t move become smaller d. All of the other options are true as sample size increases

All of the other options are true as sample size increases

A researcher reports a significant treatment effect with t(15) = 2.56, p < .05. The study used a sample of n = 15 participants.

F

A sample of n = 15 scores will produce a t statistic with df = 16.

F

A sample of n = 25 scores with a sample variance of s2 = 100 would have an estimated standard error of 4 points.

F

As sample size increases, the estimated standard error also increases.

F

As the sample variance increases, the estimated standard error decreases.

F

For a two-tailed test with α = .05 and a sample of n = 25, the boundaries for the critical region are t = ±2.060.

F

If other factors are held constant, the value of Cohen's d increases as the sample variance increases.

F

In a hypothesis test using the t statistic, an increase in the size of the sample variance produces an increase in the likelihood that the null hypothesis will be rejected.

F

In a hypothesis test, the larger the value for the sample variance, the more likely it is that you will reject the null hypothesis.

F

In general, an increase in the sample variance makes is more likely that the t statistic will be large enough to reject the null hypothesis.

F

In general, the larger the value of the estimated standard error, the greater the likelihood of rejecting the null hypothesis.

F

Increasing the alpha level from α = .01 to α = .05 will produce an increase in the estimated standard error.

F

Measures of effect size, such as r2 or Cohen's d, are not greatly influenced by sample variance.

F

Two separate samples, each with n = 30 scores, from the same population will produce identical t statistics if the two sample means are equal.

F

If two samples are selected from the same population, under what circumstances will the two samples have exactly the same t statistic? a. If the sample size (n) is the same for both samples. b. If the samples are the same size and have the same mean. c. If the samples are the same size and have the same mean and have the same sample variance. d. None of the other options are correct.

If the samples are the same size and have the same mean and have the same sample variance.

A sample has a mean of M = 39.5 and a standard deviation of s = 4.3. In a two-tailed hypothesis test with α = .05, this sample produces a t statistic of t = 2.14. Based on this information, the correct statistical decision is ______. a. The researcher can reject the null hypothesis with α = .05 but not with α = .01. b. The researcher can reject the null hypothesis with either α = .05 or α = .01. c. The researcher must fail to reject the null hypothesis with either α = .05 or α = .01. d. It is impossible to make a decision about H0 without more information.

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

*****In a hypothesis test using a t statistic, what is the influence of a large sample variance? a. Larger variance tends to lower the likelihood of rejecting the null hypothesis. a. Larger variance tends to increase the likelihood of rejecting the null hypothesis. b. The size of the variance has no impact on the outcome of the hypothesis test. c. Cannot determine without more information.

Larger variance tends to increase the likelihood of rejecting the null hypothesis.

A sample of n = 25 individuals is selected from a population with μ = 80, and a treatment is administered to the sample. Which set of sample characteristics is most likely to lead to a decision that there is a significant treatment effect? 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

M = 90 and small sample variance

A sample is selected from a population with μ = 80, and a treatment is administered to the sample. If the sample variance is s2 = 20, which set of sample characteristics is most likely to lead to a decision that there is a significant treatment effect? a. M = 85 for a sample of n = 25 b. M = 85 for a sample of n = 100 c. M = 90 for a sample of n = 25 d. M = 90 for a sample of n = 100

M = 90 for a sample of n = 100

If a sample of n = 25 scores produces a t statistic of t = -2.36, which of the following decisions is justified? a. Reject H0 with α = .05 but fail to reject with α = .01. b. Reject H0 with α = .05 or with α = .01. c. Fail to reject H0 with α = .05 and fail to reject with α = .01. d. Fail to reject H0 with α = .05 but reject H0 with α = .01.

Reject H0 with α = .05 but fail to reject with α = .01.

A hypothesis test produces t = 2.062 for a sample of n = 25 scores. For a two-tailed test with α = .05, the correct decision is to reject the null hypothesis.

T

A sample is selected from a population with μ = 50 and a treatment is administered to the sample. Assuming that the sample mean is M = 55, you are more likely to reject the null hypothesis with a sample of n = 100 than with a sample of n = 4.

T

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

T

Except for the population mean, μ, all the numbers in the t statistic formula come from the sample data.

T

For a hypothesis test with a t statistic, the estimated standard error provides a measure of how much difference is reasonable to expect between the sample mean and the population mean.

T

For a one-tailed test with α = .05 and a sample of n = 25, the critical value for the t statistic is t = 1.711.

T

For any fixed value of α, the critical values for the t statistic will move closer to zero as df increases.

T

In general, an increase in the sample size makes is more likely that the t statistic will be large enough to reject the null hypothesis.

T

Measures of effect size, such as r2 or Cohen's d, are not greatly influenced by sample size.

T

The distribution of t statistics tends to be flatter and more spread out than a normal distribution.

T

The larger the value for df, the more a t distribution resembles a normal distribution.

T

The shape of the t distribution changes as the sample size changes.

T

The t distribution is symmetrical and has a mean of zero.

T

The t statistic is used for hypothesis tests in situations where the population standard deviation (or variance) is unknown.

T

When the population variance or standard deviation is not known, it is impossible to use a z-score for a hypothesis test.

T

As sample variance increases, what happens to the likelihood of rejecting the null hypothesis and what happens to measures of effect size such as r2 and Cohen's d? a. The likelihood increases and measures of effect size increase. b. The likelihood increases and measures of effect size decrease. c. The likelihood decreases and measures of effect size increase. d. The likelihood decreases and measures of effect size decrease.

The likelihood decreases and measures of effect size decrease.

As the sample size increases, what happens to the likelihood of rejecting the null hypothesis and what happens to measures of effect size such as r2 and Cohen's d? a. The likelihood increases and measures of effect size increase. b. The likelihood increases and measures of effect size are relatively unchanged. c. The likelihood decreases and measures of effect size increase. d. The likelihood decreases and measures of effect size are relatively unchanged.

The likelihood increases and measures of effect size are relatively unchanged.

The results of a hypothesis test are reported as follows: t(18) = 2.25, p < .05. Based on this report, what was the statistical decision and how big was the sample? a. The null hypothesis was rejected using a sample of n = 18. b. The null hypothesis was rejected using a sample of n = 19. c. The null hypothesis was not rejected using a sample of n = 18. d. The null hypothesis was not rejected using a sample of n = 18.

The null hypothesis was rejected using a sample of n = 19.

A hypothesis test with a sample of n = 25 participants produces a t statistic of t = 2.53. Assuming a two-tailed test, a. The researcher can reject the null hypothesis with α = .05 but not with α = .01. b. The researcher can reject the null hypothesis with either α = .05 or α = .01. c. The researcher must fail to reject the null hypothesis with either α = .05 or α = .01. d. It is impossible to make a decision about H0 without more information.

The researcher can reject the null hypothesis with α = .05 but not with α = .01.

A sample of n = 25 scores produces a t statistic of t = 2.05. If the researcher is using a two-tailed test with α = .05, the correct statistical decision is ______. a. The researcher can reject the null hypothesis with α = .05 but not with α = .01. b. The researcher can reject the null hypothesis with either α = .05 or α = .01. c. The researcher must fail to reject the null hypothesis with either α = .05 or α = .01. d. It is impossible to make a decision about H0 without more information.

The researcher must fail to reject the null hypothesis with either α = .05 or α = .01.

Several samples, each with n = 9 scores, are selected from a population. If the t statistic and the z-score are computed for each sample mean, which of the following is probably true? a. The average t statistic will be larger than the average z-score. b. The average t statistic will be smaller than the average z-score. c. The set of t statistics will be more variable that the set of z-scores. d. The set of t statistics will be less variable that the set of z-scores.

The set of t statistics will be more variable that the set of z-scores.

Which of the following is a fundamental difference between the t statistic and a z-score? a. The t statistic uses the sample mean in place of the population mean. b. The t statistic uses the sample variance in place of the population variance. c. The t statistic computes the standard error by dividing the standard deviation by n - 1 instead of dividing by n. d. All of the above are differences between t and z.

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

What is measured by the estimated standard error, sM? a. how spread out the scores are in the sample. b. how spread out the scores are in the population. c. how much difference is reasonable to expect between a sample mean and the population mean. d. how much difference is reasonable to expect between the t statistic and the corresponding z-score.

how spread out the scores are in the population

Under what circumstances can a very small treatment effect be statistically significant? a. if the sample size 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

if the sample size big and the sample variance is small

If a researcher reports a t statistic with df = 20, how many individuals were in the sample? a. n = 19 b. n = 20 c. n = 21 d. cannot be determined from the information given

n = 21

What t values form the boundaries of the critical region for a two-tailed test using a sample of n = 9 scores and an alpha level of .05? a. t = ±1.860 b. t = ±1.833 c. t = ±2.306 d. t = ±2.262

t = ±2.306

With α = .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 b. t = ±2.583 c. t = ±2.947 d. t = ±2.921

t = ±2.947

Two samples from the same population both have n = 10 scores with M = 45. If the t statistic is computed for each sample, then ______. 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.

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

What is the estimated standard error for a sample of n = 4 scores with a variance of s2 = 36? a. the square root of (36/4) b. the square root of (36/3) c. 36/4 d. 36/3

the square root of (36/4)

Which of the following terms is not required when using the t statistic? a. n b. σ c. df d. s or s2 or SS

σ