Deck 9: Introduction to the T Statistic

Question 1

A researcher conducts a hypothesis test using a sample of n = 20 from an unknown population.What is the df value for the t statistic?

A)19
B)20
C)21
D)Cannot be determined from the information given

Answer 1

A

Question 2

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.

Answer 2

B

Question 3

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

Answer 3

C

Question 4

A sample with a mean of M = 40 and a variance of s² = 20 has an estimated standard error of 1 point.How many scores are in the sample?

A)4
B)5
C)20
D)21

Question 5

A researcher is using a two-tailed hypothesis test with α = .05 to evaluate the effect of a treatment.If the boundaries for the critical region are t = ± 2.080,then how many individuals are in the sample?

A)n = 22
B)n = 21
C)n = 20
D)Impossible to determine without more information

Question 6

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

A)n = 4 with s² = 16
B)n = 4 with s² = 64
C)n = 16 with s² = 16
D)n = 16 with s² = 64

Question 7

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 samples are the same size and have the same variance
B)If the samples are the same size and have the same mean
C)If the samples have the same mean and the same variance
D)If the samples are the same size and have the same mean and the same variance

Question 8

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

A)30
B)20
C)16
D)15

Question 9

A sample of n = 16 scores has a mean of M = 65 and an estimated standard error of 2 points.What is the sample variance?

A)s² = 64
B)s² = 36
C)s² = 16
D)s² = 4

Question 10

A sample of n = 25 scores has a mean of M = 40 and a standard deviation of s = 10.What is the estimated standard error for the sample mean?

A)4
B)2
C)?0v2
D)1

Question 11

A researcher conducts a hypothesis test using a sample from an unknown population.If the t statistic has df = 30,how many individuals were in the sample?

A)n = 29
B)n = 30
C)n = 31
D)Cannot be determined from the information given

Question 12

Which of the following is not needed to compute a t statistic?

A)A hypothesized value for the population mean
B)The value of the population variance or standard deviation
C)The value of the sample mean
D)The value of the sample variance or standard deviation

Question 13

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)Not enough information to answer

Question 14

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

Question 15

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

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

Question 16

A sample of n = 9 scores has a variance of s² = 36.What is the estimated standard error for the sample mean?

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

Question 17

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

Question 18

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 these are differences between t and z.

Question 19

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.

Question 20

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?

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 21

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.

Question 22

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.

Question 23

A sample is selected from a population with μ = 70,and a treatment is administered to the sample.After treatment,the sample mean is M = 74,and Cohen's d is d = 1.00.What is the value of the sample variance?

A)s² = 2
B)s² = 4
C)s² = 16
D)It is impossible to determine the sample variance without more information.

Question 24

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

Question 25

A sample of n = 25 scores produces a t statistic of t = 2.062.If the researcher is using a two-tailed test,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.

Question 26

If other factors are held constant,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 sample variance increases both the likelihood and measures of effect size.
B)Larger sample variance increases the likelihood but has little influence on measures of effect size.
C)Larger sample variance decreases the likelihood but has little influence on measures of effect size.
D)Larger sample variance decreases both the likelihood and measures of effect size.

Question 27

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.

Question 28

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.

Question 29

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

Question 30

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,what is the value of Cohen's d?

A)d = 0.125
B)d = 0.25
C)d = 0.50
D)Cohen's d cannot be computed without knowing the sample size.

Question 31

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 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

Question 32

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

Question 33

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

Question 34

How does sample variance influence the estimated standard error and measures of effect size such as r² and Cohen's d?

A)Larger variance increases both the standard error and measures of effect size.
B)Larger variance increases the standard error but decreases measures of effect size.
C)Larger variance decreases the standard error but increases measures of effect size.
D)Larger variance decreases both the standard error and measures of effect size.

Question 35

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

Question 36

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

Question 37

A researcher selects a sample from a population with  = 30 and uses the sample to evaluate the effect of a treatment.After treatment,the sample has a mean of M = 32 and a variance of s² = 6.Which of the following would definitely increase the likelihood of rejecting the null hypothesis?

A)Increase the number of individuals in the sample
B)Increase the sample mean
C)Decrease the sample variance
D)All of the other options will increase the likelihood of rejecting the null hypothesis.

Question 38

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.

Question 39

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

Question 40

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.

Question 41

Which of the following is the correct way to report the results of a hypothesis test and a measure of effect size using a t statistic?

A)t(19)= 2.30,r² = 0.42,p < .05
B)t(19)= 2.30,p < .05,r² = 0.42,
C)r² = 0.42,t(19)= 2.30 ,p < .05
D)t = 2.30,df = 19,p < .05,r² = 0.42

Question 42

Which combination of factors would definitely increase the width of a confidence interval?

A)Increase the sample mean and increase the size of the sample
B)Decrease the sample mean and increase the size of the sample
C)Increase the sample mean and increase the percentage of confidence
D)Decrease the sample mean and decrease the percentage of confidence

Question 43

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

Question 44

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.

Question 45

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.

Question 46

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

Question 47

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?

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 48

If two samples from the same population are the same size and have the same mean,then they will have the same t statistic.

Question 49

A sample of n = 16 scores with a sample variance of s² = 64 has an estimated standard error of 4 points.

Question 50

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

Question 51

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

Question 52

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

Question 53

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

Question 54

Which of the following would have no effect on the width of a confidence interval?

A)Increase the sample mean
B)Increase the size of the sample
C)Increase the percentage of confidence
D)Increase the sample variance

Question 55

A random sample with n = 20 scores has df = 19.

Question 56

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)Cannot be determined from the information provided

Question 57

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

Question 58

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

Question 59

For a hypothesis test using a t statistic,the boundaries for the critical region will change if the sample size is changed.

Question 60

A researcher selects a sample from a population with a mean of $\mu$ = 40 and administers a treatment to the individuals in the sample.If the treatment is expected to decrease scores,which of the following is the correct statement of the null hypothesis for a one-tailed test?

A) $\mu$ > 40
B) $\mu$ < 40.
C) $\mu$ > 40.,
D) $\mu$ < 40,

Question 61

If other factors are held constant,as the sample variance increases,the estimated standard error also increases.

Question 62

Although you can compute a z-score for a single score (a sample of n = 1),it is impossible to compute a t statistic for a sample that has only one score.Explain why.

Question 63

A research report states "t(15)= 2.31,p < .05." For this study,the sample had n = 16 scores.

Question 64

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.

Question 65

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

Question 66

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

Question 67

For a one-tailed test with α = .05 and a sample of n = 9,the critical value for the t statistic is t = 1.860.

Question 68

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

Question 69

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

Question 70

If other factors are held constant,the bigger the sample is,the greater the likelihood of rejecting the null hypothesis.

Question 71

A sample of n = 16 scores has a mean of M = 58 with SS = 960.Use the sample to construct the 90% confidence interval for µ.

Question 72

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

Question 73

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

Question 74

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

Question 75

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

Question 76

Two samples are selected from a population,and a treatment is administered to the samples.If both samples have the same mean and the same variance,you are more likely to find a significant treatment effect with a sample of n = 100 than with a sample of n = 4.

Question 77

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

Question 78

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.

Question 79

The t distribution for df = 4 is flatter and more spread out than the t distribution for df = 20.

Question 80

If the 90% confidence interval for µ is from 40 to 50,then the sample mean is M = 45.