Question 1

With α = .05 and df = 8,the critical values for a two-tailed t test are t = ±2.306.Assuming all other factors are held constant,if the df value were increased to df = 20,what would happen to the critical values for t?​
A)​They would increase (move farther from zero).
B)​They would decrease (move closer to zero).
C)​They would stay the same.
D)​There is not enough information to answer.

Accepted Answer

As the degrees of freedom (df) increase, the critical t-values for a given alpha level (e.g., .05) decrease and move closer to zero. This is because the t-distribution approaches the normal distribution as df increases, resulting in a narrower distribution.

Question 2

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.

Accepted Answer

A larger sample size increases the power of the test, which means it increases the likelihood of rejecting the null hypothesis. However, the measures of effect size such as r² and Cohen's d are not affected by sample size as they are standardized measures that are independent of the sample size. Thus, the correct answer is B that the larger sample size increases the likelihood but has little influence on measures of effect size.

Question 3

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

Accepted Answer

A very small treatment effect can still be statistically significant if the sample size is large enough, as even a small difference may be unlikely to be observed by chance. Additionally, if the sample variance is small, this can further increase the likelihood of finding a significant result.

Question 4

What value is estimated with a confidence interval using the t statistic?​
A)​The value for an unknown sample mean
B)​The value for an unknown population mean
C)​The difference between two population means
D)​The difference between two sample means

Accepted Answer

The t statistic is used to estimate the value for an unknown population mean with a specified level of confidence.

Question 5

How does sample variance influence the likelihood of rejecting the null hypothesis and measures of effect size such as r² and Cohen's d? A)Larger variance increases both the likelihood and measures of effect size. B)Larger variance increases the likelihood but decreases measures of effect size. C)Larger variance decreases the likelihood but increases measures of effect size. D)Larger variance decreases both the likelihood and measures of effect size.

Accepted Answer

Larger variance decreases the precision of the data and results in a wider distribution of scores, making it more difficult to find statistically significant results. This decreases the likelihood of rejecting the null hypothesis (Type II error) and also decreases measures of effect size such as r² and Cohen's d, as the difference between groups may be overshadowed by the variability within each group. Therefore, option D is the correct answer.

Question 6

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 equation correctly describes the 90% confidence interval for μ? A)μ = 40 ± 2.353(4) B)μ = 40 ± 1.638(4) C)μ = 40 ± 2.353(2) D)μ = 40 ± 1.638(2)

Accepted Answer

To find the 90% confidence interval for the population mean (μ), we need to use the t-distribution since the population standard deviation is unknown. The formula for the confidence interval is:

CI = X ± t(α/2,df) * (s/√n)

Where X is the sample mean, t(α/2,df) is the t-value from the t-distribution table with degrees of freedom (df) = n - 1 and α = 1 - confidence level, s is the sample standard deviation and n is the sample size.

Substituting the given values, we get:

CI = 40 ± t(0.05,3) * (4/√4)
CI = 40 ± 2.353 * 2
CI = 40 ± 4.706

So, the correct equation is μ = 40 ± 2.353(2), which is choice C.

Question 7

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 α = .05,what is the correct statistical decision for this sample? 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.

Accepted Answer

The answer of A sample has a mean of M...

Question 8

With α = .05,what is the critical t value for a one-tailed test with n = 15?​
A)​t = 1.761
B)​t = 1.753
C)​t = 2.145
D)​t = 2.131

Accepted Answer

The critical t value for a one-tailed test with α = .05 and n = 15 is 1.761.

Question 9

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,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)d=0.001

Accepted Answer

Cohen's d is calculated by dividing the difference between the sample mean and population mean by the standard deviation. The formula is:

d = (M - μ) / s

In this case, M = 48 and μ = 46, so the numerator is 2. The denominator is the sample standard deviation, which can be found by taking the square root of the sample variance:

s = √16 = 4

Thus, d = 2 / 4 = 0.5.

Therefore, the correct answer is C.

Question 10

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 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.

Accepted Answer

The answer of A sample of n = 25 scores...

Question 11

A hypothesis test produces a t statistic of t = 2.20.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 = 11
B)​At least n = 12
C)​At least n = 13
D)​At least n = 14

Accepted Answer

Using a t-table or calculator, we can find that the critical t-value for a two-tailed test with α = .05 and degrees of freedom (df) = n-1 is approximately ±2.131. Since the calculated t-value (t = 2.20) is greater than the critical t-value, we reject the null hypothesis. In order for the researcher to reject the null hypothesis with a t-value of 2.20, the sample size must be large enough to provide enough precision in the estimate. Using a t-distribution table or calculator, we find that with df = n-1, a sample size of n = 13 would be needed to achieve a t-value of 2.20 with α = .05. Therefore, the best answer is C, at least n = 13.

Question 12

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

Accepted Answer

The t statistic is inversely related to the sample variance; thus, the sample with the smaller variance will produce the larger t statistic because the denominator of the t formula (which includes the variance) will be smaller, making the value of t larger.

Question 13

A sample of n = 16 scores produces a t statistic of t = 2.00.If the sample is used to measure effect size with r²,what value will be obtained for r²? A)r² = 2/20 B)r² = 4/20 C)r² = 2/19 D)r² = 4/19

Accepted Answer

The formula for calculating effect size using r (Cohen's r) from a t-test is r = sqrt(t^2 / (t^2 + df)), where df (degrees of freedom) is n - 1 for a one-sample t-test. Here, n = 16, so df = 15. Plugging in the values, r = sqrt(2^2 / (2^2 + 15)) = sqrt(4 / 19), which corresponds to choice D.

Question 14

Which of the following describes the function of a confidence interval?​
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.

Accepted Answer

A confidence interval uses a sample mean to estimate the corresponding population mean, along with a level of confidence to provide a range of likely values for the population parameter. Option B is incorrect as the purpose of a confidence interval is not to predict a sample mean. Option C is partially correct as a level of confidence is needed, but it is not used to estimate a sample mean. Option D is incorrect as the sample mean is not used to determine a level of confidence, but rather the opposite is true - a level of confidence is used to determine the width of the interval around the sample mean.

Question 15

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

Accepted Answer

For a two-tailed t-test with α = .01 and n = 16 subjects, the degrees of freedom (df) would be n - 1 = 15. Looking up the critical t value in a t-distribution table for df = 15 and α = .01 (two-tailed), the critical t value is approximately ±2.947.

Question 16

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 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.

Accepted Answer

The answer of A hypothesis test with a sample of...

Question 17

The results of a hypothesis test are reported as follows: t(15)= 2.70,p < .05.Based on this report,how many individuals were in the sample?​
A)​14
B)​15
C)​16
D)​17

Accepted Answer

The "t(15)" indicates the degrees of freedom, which is equal to the sample size minus 1 (n-1). So, 15 = n-1, which means n=16. Therefore, the correct answer is C.

Question 18

If other factors are held constant,which set of sample characteristics is most likely to reject a null hypothesis stating that m = 80?​
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

Accepted Answer

The likelihood of rejecting a null hypothesis increases with both a larger sample size (n) and a greater difference between the sample mean (M) and the population mean under the null hypothesis (m). Option D has the largest sample size and the greatest difference from the null hypothesis value, making it the most likely to reject the null hypothesis.

Question 19

If a sample of n = 16 scores is being used to make an 80% confidence interval estimate of the population mean,μ,what value(s)of t should be used?​
A)​t = 0
B)​t = ±2.131
C)​t = ±1.753
D)​t = ±1.341

Accepted Answer

The answer of If a sample of n = 16...

Question 20

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.

Accepted Answer

When the population variance or standard deviation is unknown, you must estimate it using the sample data. This introduces additional uncertainty into the calculation, and the uncertainty is reflected in the t distribution rather than the standard normal distribution. Therefore, you must use a t statistic instead of a z-score for a hypothesis test when the population variance or standard deviation is not known.

Quiz 9: Introduction to the T Statistic

With α = .05 and df = 8,the critical values for a two-tailed t test are t = ±2.306.Assuming all other factors are held constant,if the df value were increased to df = 20,what would happen to the critical values for t?

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?

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

What value is estimated with a confidence interval using the t statistic?

How does sample variance influence the likelihood of rejecting the null hypothesis and measures of effect size such as r² and Cohen's d?

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 equation correctly describes the 90% confidence interval for μ?

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 α = .05,what is the correct statistical decision for this sample?

With α = .05,what is the critical t value for a one-tailed test with n = 15?

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,the size of the treatment effect,as measured by Cohen's d,is ____.

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 hypothesis test produces a t statistic of t = 2.20.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?

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 sample of n = 16 scores produces a t statistic of t = 2.00.If the sample is used to measure effect size with r²,what value will be obtained for r²?

Which of the following describes the function of a confidence interval?

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

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?

The results of a hypothesis test are reported as follows: t(15) = 2.70,p < .05.Based on this report,how many individuals were in the sample?

If other factors are held constant,which set of sample characteristics is most likely to reject a null hypothesis stating that m = 80?

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

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.

Quiz 9: Introduction to the T Statistic

With α = .05 and df = 8,the critical values for a two-tailed t test are t = ±2.306.Assuming all other factors are held constant,if the df value were increased to df = 20,what would happen to the critical values for t?​

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?​

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

What value is estimated with a confidence interval using the t statistic?​

How does sample variance influence the likelihood of rejecting the null hypothesis and measures of effect size such as r2 and Cohen's d?​

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 equation correctly describes the 90% confidence interval for μ?​

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 α = .05,what is the correct statistical decision for this sample?​

With α = .05,what is the critical t value for a one-tailed test with n = 15?​

​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,the size of the treatment effect,as measured by Cohen's d,is ____.

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 hypothesis test produces a t statistic of t = 2.20.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?​

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 sample of n = 16 scores produces a t statistic of t = 2.00.If the sample is used to measure effect size with r2,what value will be obtained for r2?​

Which of the following describes the function of a confidence interval?​

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

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?​

The results of a hypothesis test are reported as follows: t(15) = 2.70,p < .05.Based on this report,how many individuals were in the sample?​

If other factors are held constant,which set of sample characteristics is most likely to reject a null hypothesis stating that m = 80?​

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

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.

With α = .05 and df = 8,the critical values for a two-tailed t test are t = ±2.306.Assuming all other factors are held constant,if the df value were increased to df = 20,what would happen to the critical values for t?

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?

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

What value is estimated with a confidence interval using the t statistic?

How does sample variance influence the likelihood of rejecting the null hypothesis and measures of effect size such as r² and Cohen's d?

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 equation correctly describes the 90% confidence interval for μ?

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 α = .05,what is the correct statistical decision for this sample?

With α = .05,what is the critical t value for a one-tailed test with n = 15?

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,the size of the treatment effect,as measured by Cohen's d,is ____.

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 hypothesis test produces a t statistic of t = 2.20.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?

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 sample of n = 16 scores produces a t statistic of t = 2.00.If the sample is used to measure effect size with r²,what value will be obtained for r²?

Which of the following describes the function of a confidence interval?

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

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?

The results of a hypothesis test are reported as follows: t(15) = 2.70,p < .05.Based on this report,how many individuals were in the sample?

If other factors are held constant,which set of sample characteristics is most likely to reject a null hypothesis stating that m = 80?

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