Deck 13: Students T Test for Single Samples

Question 1

As the degrees of freedom increase, the correspondence between the t and z distributions _________.

A) increases
B) decreases
C) remains the same
D) cannot be determined

Answer 1

increases

Question 2

The 95% confidence interval arrived at from a particular experiment is 72-79. This means that _________.

A) the probability is 0.95 that µ falls between 72-79
B) the probability is 0.95 that the interval 72-79 contains
C) the probability is 0.95 that the interval 72-79 contains µ
D) a and c

Answer 2

the probability is 0.95 that the interval 72-79 contains µ

Question 3

The degrees of freedom for the t test for single samples are _________.

A) N
B) N - 1
C) N - 2
D) depends on alpha

Answer 3

N - 1

Question 4

In a correlative study, _________.

A) a value of r ≠ 0 in the sample, means that there is a nonzero correlation in the population
B) a nondirectional alternative hypothesis states that r ≠ 0
C) the null hypothesis for a nondirectional alternative hypothesis states that r = 0
D) a nondirectional alternative hypothesis states that r = 0
E) a nondirectional alternative hypothesis states that r ≠0 and the null hypothesis for a nondirectional alternative hypothesis states that r = 0

Question 5

| t crit | for any alpha level is _________ | z crit | for N less than infinity.

A) greater than
B) the same as
C) less than
D) none of these

Question 6

In a t test, when the size of the sample is increased, the confidence interval _________.

A) increases
B) decreases
C) stays the same
D) changes shape

Question 7

We lose one degree of freedom in calculating _________.

A) s
B)
C) t obt (single sample)
D) s and t obt (single sample)

Question 8

is an estimate of _________.

A) µ
B) s
C)
D) s.

Question 9

Which of the characteristics below distinguishes the t statistic from the z statistic?

A) the proportion of area beyond a particular positive t value is equal to the proportion of area below the corresponding negative t
B) the z distribution has a mean of zero while the t distribution does not
C) In the t distribution the area under the curve beyond a value of ±1.96 is greater than that of the normal curve
D) all of these

Question 10

For a given N , the interval that bounds the population mean at the 99% confidence level is _________ that which bounds the population mean at the 95% confidence level.

A) equal to
B) greater than
C) less than
D) can t be determined without knowing

Question 11

The df associated with evaluating the significance of r obt are _________.

A) N
B) N - 1
C) N - 2
D) need more information

Question 12

The confidence interval for the population mean is _________.

A) a range of values which probably contains the population mean
B) a range of values which contains the population mean
C) the same from sample-to-sample
D) a range of values which probably contains the population mean and the same from sample-to-sample

Question 13

In an independent groups experiment, if we must estimate the population standard deviation to determine the significance of the sample results, the appropriate inference test is the _________.

A) sign test
B) z test
C) t test
D) none of these

Question 14

When using the t test, we reject H 0 _________.

A) if t obt ≤ t crit
B) if | t obt | ≥ | t crit |
C) if | t obt | ≤ | t crit |
D) if t obt ≥ t crit

Question 15

The mean of the t distribution equals _________.

A) the mean of the population of raw scores
B) 0
C) 1
D) s

Question 16

In a correlated groups experiment, if we must estimate the population standard deviation to determine the significance of the sample results, the appropriate statistical test is _________.

A) t test
B) sign test
C) z test
D) none of these

Question 17

As the df increases, the t distribution _________.

A) gets more symmetrical
B) approaches the normal distribution
C) stays the same
D) becomes more skewed

Question 18

Which of the following represents a sampling distribution?

A) the binomial distribution
B) the z distribution
C) the t distribution
D) all of these
E) the z and t distributions

Question 19

The t test differs from the z test in that _________.

A) with the t test we estimate s
B) with the t test we estimate µ
C) the z distribution is a family of curves
D) the t distribution is a family of curves
E) with the t test we estimate s and the t distribution is a family of curves

Question 20

With which statistical test do we determine the probability of getting the obtained results or those more extreme assuming the differences in results were due to chance alone?

A) sign test
B) z test
C) t test
D) all of these

Question 21

For a given value of alpha, the critical value of t is _______ than the critical value of z .

A) no different
B) less
C) greater
D) none of these

Question 22

As N gets infinitely large, the critical value of t equals the critical value of z .

Question 23

A researcher believes that women today weigh less than in previous years. To investigate this belief, she randomly samples 41 adult women and records their weights. The scores have a mean of 111 lbs. and a standard deviation of 12.4. A local census taken several years ago shows the mean weight of adult women was 115 lbs. The obtained value of the appropriate statistic for testing H 0 is _________.

A) t obt = - 2.07
B) t obt = +2.07
C) t obt = - 0.32
D) t obt = +0.32

Question 24

The sample mean is an example of _________.

A) interval estimation
B) point estimation
C) confidence point
D) confidence numbers

Question 25

For N = 20, the degrees of freedom for the test of the significance of the correlation coefficient ( r ) is _________.

A) 20
B) 21
C) 19
D) 18

Question 26

If r = 0.84 and N = 5, the value of t obt for the test of the significance of r is _________.

A) 1.96
B) 2.40
C) 2.68
D) 3.46

Question 27

The 95% confidence interval of the mean for = 13.0, s = 1.6, and N = 21 is _________.

A) 12.01 to 13.99
B) 12.27 to 13.73
C) 11.05 to 15.05
D) 12.95 to 14.95

Question 28

The mean of the t distribution equals _________.

A) 0
B) 1
C) N
D) N - 1

Question 29

A researcher believes that women today weigh less than in previous years. To investigate this belief, she randomly samples 41 adult women and records their weights. The scores have a mean of 111 lbs. and a standard deviation of 12.4. A local census taken several years ago shows the mean weight of adult women was 115 lbs. The df for determining t crit = _________.

A) 41
B) 40
C) 39
D) need more information

Question 30

How many t distributions are there?

A) 1
B) 2
C) 30
D) one for each value of df

Question 31

If the population parameters are known, the t test is _________ powerful than the z test.

A) more
B) less
C) equally
D) need more information

Question 32

A researcher believes that women today weigh less than in previous years. To investigate this belief, she randomly samples 41 adult women and records their weights. The scores have a mean of 111 lbs. and a standard deviation of 12.4. A local census taken several years ago shows the mean weight of adult women was 115 lbs. Using a = 0.01 1 tail , the critical value of the appropriate statistic for testing H ₀ is _________.

A) - 1.684
B) - 2.423
C) ±1.684
D) ±2.423

Question 33

A researcher believes that women today weigh less than in previous years. To investigate this belief, she randomly samples 41 adult women and records their weights. The scores have a mean of 111 lbs. and a standard deviation of 12.4. A local census taken several years ago shows the mean weight of adult women was 115 lbs. What do you conclude, using the appropriate inference test and a = 0.01 1 tail ?

A) accept H 1
B) accept H 0
C) reject H 0
D) retain H 0
E) accept H 1 and reject H 0

Question 34

As N gets _______, the critical value of t gets _________.

A) larger; larger
B) smaller; smaller
C) larger; smaller
D) smaller; larger

Question 35

For N = 20, the value of r crit for a = 0.05 2 tail is _________.

A) 0.4329
B) 0.3783
C) 0.4438
D) 0.5614

Question 36

As N increases becomes a _________ estimate of .

A) better
B) worse
C) meaningless
D) biased

Question 37

The proper use of the t test requires that _________.

A) the sampling distribution of is normal
B) N ≥ 30
C) the sampling distribution of is normal and N ≥30
D) the sampling distribution of is normal or N ≥30

Question 38

Use the data presented in the text, Chapter 7, question 12. In that question, r obt = - 0.69 and N = 10. Using a = 0.05 2 tail , is this a significant value for r obt ?

A) Yes, df = 9, r crit = ±0.6021
B) Yes, df = 8, r crit = ±0.6319
C) Yes, df = 8, r crit = - 0.6319
D) Yes, df = 8, r crit = +0.6319

Question 39

The _______ confidence interval for the population mean is always wider than the _______ confidence interval for the population mean.

A) 99%; 95%
B) 95%; 99%
C) both of these
D) none of these

Question 40

If = 30, s = 5.2, = 28.0, s = 6.1 and N = 13, the value of the most powerful statistic to test the significance of the sample mean is _________.

A) - 1.18
B) 1.96
C) 2.18
D) - 1.39

Question 41

Which of the following are not characteristics of the t distribution?

A) has a mean = 0.
B) has a standard deviation greater than 1.00 for df less than infinity.
C) varies with df.
D) has no negative values.
E) all of these are characteristics of the t distribution.

Question 42

The t distribution is a family of curves that vary with the degrees of freedom.

Question 43

"Degrees of freedom" for any statistic is defined as _________.

A) N
B) N - 1
C) the number of scores that are free to vary in calculating the statistic
D) N - 1and the number of scores that are free to vary in calculating the statistic

Question 44

The degrees of freedom equal N - 1 for the t test for single samples.

Question 45

The t test requires that the sampling distribution of t be normally distributed.

Question 46

There are two values for t crit when H 1 is directional.

Question 47

To test the significance of r obt , the df = N - 2.

Question 48

In general, the z test is more powerful than the t test because _________.

A) with the z test, the sample mean is closer to the population mean than with the t test
B) with the t test we lose a degree of freedom
C) the standard deviation of the sample raw scores is larger with the t test
D) with the z test, we know ó , whereas with the t test, we must estimate it.

Question 49

The 95% confidence interval is defined as _________.

A) an interval such that we are 95% confident that the population value lies within the interval
B) an interval such that the probability is 0.95 that the interval contains the population value
C) an interval such that we can reject H ₀ at á = 0.05
D) a and b

Question 50

The sampling distribution of t differs from the sampling distribution of z in that _________.

A) there is only one sampling distribution of z (the normal distribution) for all N , while there are many sampling distributions for t , depending on sample size.
B) the sampling distribution of z is more narrow, except when N equals infinity.
C) the means of the two distributions are different
D) all of these
E) a and b

Question 51

t crit must always be positive.

Question 52

If we have to estimate s , we should use the z test.

Question 53

If N t test, the population of raw scores should be normally distributed.

Question 54

Confidence interval is defined as _________.

A) a range of values that probably contains the population value
B) a range of values that probably contains the population mean
C) a range of values that probably contain the population standard deviation
D) all of these

Question 55

The 99% confidence interval is defined as _________.

A) an interval such that we are 99% confident that the population value lies within the interval
B) an interval such that the probability is 0.99 that the interval contains the population value
C) an interval such that we can reject H ₀ at á = 0.01
D) an interval such that we are 99% confident that the population value lies within the interval and an interval such that the probability is 0.99 that the interval contains the population value

Question 56

Confidence limits are defined as _________.

A) the highest and lowest score in the sample set of scores
B) the values that lie outside of the confidence interval
C) the values that bound the confidence interval
D) the values that lie within the confidence interval

Question 57

As the degrees of freedom increase, the t distribution becomes more like the z distribution.

Question 58

Generally speaking, the more confidence we have that the interval contains the population mean, the larger is the interval.

Question 59

The t test is more sensitive than the z test.

Question 60

The sampling distribution of t _________.

A) gives all possible different t values of size N and the probability of getting each value if sampling is random from the null-hypothesis population
B) is defined as a probability distribution of the t values that would occur if all possible different samples of size N were drawn from the null hypothesis population
C) varies uniquely with N
D) all of these
E) a and b

Question 61

determines the confidence interval for the population mean.

Question 62

For a two-tailed test, if | t obt | ≥ | t crit |, reject H ₀.

Question 63

If r obt is not equal to zero, r cannot equal zero.

Question 64

If | r obt | > | r crit |, we reject the assumption that r = 0.

Question 65

The t test is more powerful than the z test.

Question 66

The 99% confidence limit is always wider than the 95% confidence interval.

Question 67

In the t test s is used to estimate s .

Question 68

The t test for single samples is used when the population parameters µ and s are unknown.

Question 69

The t test requires that the sampling distribution of is normal.

Question 70

If r > 0.50, then there must be a nonzero correlation in the population.

Question 71

The t distribution is the same for all sample sizes.

Question 72

In general t crit is greater than z crit at the same a level.

Question 73

The mean of the t distribution equals 0 for all sample sizes.

Question 74

The 95% confidence interval means that 95% of the time = .

Question 75

The confidence interval is one example of point estimation.

Question 76

When df = ¥ the t distribution is identical to the z distribution.

Question 77

In general, if r = 0, then r = 0.

Question 78

The t test can only be applied to a nondirectional alternative hypothesis.

Question 79

In general, if r ≠ 0, then r must not equal 0.

Question 80

By definition the degrees of freedom for all statistical tests equals N - 1.