Question 1

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

Accepted Answer

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

Question 2

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.

Accepted Answer

A) True 
 B)False

Question 3

Which of the following samples will have the smallest value for the estimated standard error?

Accepted Answer

A)  n = 25 with s2 = 100
B)  n = 25 with s2 = 400
C)  n = 100 with s2 = 100
D)  n = 100 with s2 = 400

Question 4

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

Accepted Answer

A) True 
 B)False

Question 5

In order to estimate a population mean with a confidence interval, you first must estimate a range of values for t.

Accepted Answer

A) True 
 B)False

Question 6

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

Accepted Answer

A)  s2 = 9 and sM = 3
B)  s2 = 9 and sM = 1
C)  s2 = 3 and sM = 3
D)  s2 = 3 and sM = 1

Question 7

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

Accepted Answer

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.

Question 8

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

Accepted Answer

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

Question 9

A sample with a mean of M = 40 and a variance of s2 = 20 has an estimated standard error of 2 points.How many scores are in the sample?

Accepted Answer

A)  4
B)  5
C)  10
D)  25

Question 10

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

Accepted Answer

A)  0
B)  1
C)  1.96
D)  t > 1.96

Question 11

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

Accepted Answer

A) True 
 B)False

Question 12

If two samples, each with n = 20 scores, are selected from the same population and both have the same mean (M = 53) and the same variance (s2 = 12), then they will also have the same t statistic.

Accepted Answer

A) True 
 B)False

Question 13

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 μ?

Accepted Answer

A)  μ = 40 ± 2.353(4) 
B)  μ = 40 ± 1.638(4) 
C)  μ = 40 ± 2.353(2) 
D)  μ = 40 ± 1.638(2)

Question 14

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?

Accepted Answer

A)  They would increase (move farther from zero) .
B)  They would decrease (move closer to zero) .
C)  They would stay the same.
D)  not enough information to answer

Question 15

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

Accepted Answer

A)  1
B)  2
C)  4
D)  16

Question 16

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

Accepted Answer

A)  n = 25 with s2 = 100
B)  n = 25 with s2 = 400
C)  n = 100 with s2 = 100
D)  n = 100 with s2 = 400

Question 17

Why are t statistics more variable than z-scores.

Accepted Answer

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)  Non of the other options explains the extra variability for t statistics.

Question 18

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 t statistic?

Accepted Answer

A)  You must know the population mean.
B)  You must know the population variance or standard deviation.
C)  You must know the population mean and the variance or standard deviation.
D)  The t statistic does not require any information about the population.

Question 19

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

Accepted Answer

A)  t = ±2.602
B)  t = ±2.583
C)  t = ±2.947
D)  t = ±2.921

Question 20

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

Accepted Answer

A) True 
 B)False

Exam 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?

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

A sample with a mean of M = 40 and a variance of s2 = 20 has an estimated standard error of 2 points.How many scores are in the sample?

Correct AnswerverifiedShow Answer

In order to estimate a population mean with a confidence interval, you first must estimate a range of values for t.

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Which of the following samples will have the smallest value for the estimated standard error?

Correct AnswerverifiedShow Answer

Why are t statistics more variable than z-scores.

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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.

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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 t statistic?

Correct AnswerverifiedShow Answer

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 μ?

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

If two samples, each with n = 20 scores, are selected from the same population and both have the same mean (M = 53) and the same variance (s2 = 12), then they will also have the same t statistic.

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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A sample with a mean of M = 40 and a variance of s² = 20 has an estimated standard error of 2 points.How many scores are in the sample?

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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 μ?

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If two samples, each with n = 20 scores, are selected from the same population and both have the same mean (M = 53) and the same variance (s² = 12), then they will also have the same t statistic.

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

Correct Answer
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