Deck 12: Sampling Distributions, Sampling Distribution of the Mean: the Normal Deviate Z Test

Question 1

A normally distributed set of population scores has a mean of 65 and a standard deviation of 10.2. The mean, of the sampling distribution of the mean, for samples of size 48 equals _________.

A) 1.35
B) 60
C) 65
D) none of these

Answer 1

65

Question 2

As sample size increases, _________.

A) decreases
B) increases
C) stays the same
D) approaches s

Answer 2

decreases

Question 3

If the variability of the raw score population increases and N is held constant, _________.

A) decreases
B) increases
C) stays the same
D) need more information

Answer 3

increases

Question 4

The sampling distribution of the mean gives _________.

A) all the values the sample mean can take
B) the probability of getting each mean value if sampling is random from the H 0 population
C) all the values the sample standard deviation can take
D) the probability of getting each standard deviation value if sampling is random from the H 0 population
E) all the values the sample mean can take and the probability of getting each mean value if sampling is random from the H 0 population

Question 5

The sampling distribution of the mean _________.

A) is always normally distributed
B) is normally distributed if the population raw scores are normally distributed
C) is considered normally distributed if N > 300
D) is normally distributed if the population raw scores are normally distributed and is considered normally distributed if N > 300

Question 6

Data analysis involving statistical inference basically involves _________.

A) determining the standard deviation of the scores
B) calculating the appropriate statistic
C) evaluating the statistic based on its sampling distribution
D) calculating the appropriate statistic and evaluating the statistic based on its sampling distribution

Question 7

The normal deviate test is used with _________.

A) a replicated measures design
B) an independent groups design
C) a single sample design
D) a multi-group design

Question 8

The mean attention span for adults in a certain village is 15 minutes with a standard deviation of 6.4. The mean of all possible samples of size 30, taken from that population equals _________.

A) 15
B) 0.50
C) 30
D) 2.34

Question 9

The Null Hypothesis Population is an actual or theoretical set of population scores that would result if _________.

A) the experiment were done on the entire population and the independent variable had no effect
B) the experiment were done on the sample and the independent variable had no effect
C) the experiment were done on the entire population and the independent variable had a real effect
D) the subjects in the population believed the null hypothesis was true

Question 10

Which of the following apply to the sampling distribution of the mean?

A) = µ
B) =
C) the variability of the distribution depends on N
D) the shape of the distribution is always normal
E) = , = and the variability of the distribution depends on N

Question 11

For the population and sample size given in question 8, the standard error of the mean equals _________.

A) 4.8
B) 1.47
C) 0.21
D) 65

Question 12

Sampling distributions can be obtained empirically by _________.

A) determining all possible samples of size N that can be formed from the Null Hypothesis Population
B) calculating the statistic for each of the samples
C) calculating the probability of getting each value of the statistic, if chance alone is operating
D) selecting several samples from all possible samples and calculating the statistic for those samples
E) a, b and c

Question 13

The mean attention span for adults in a certain village is 15 minutes with a standard deviation of 6.4. What is the probability of randomly selecting a sample of 30 scores from this population that has a mean attention span equal to or greater than 17 minutes?

A) 0.3783
B) 0.0436
C) 0.0446
D) 0.4564

Question 14

The sampling distribution of a statistic _________.

A) gives all the values a statistic can take
B) gives the probability of getting each value of a statistic under the assumption it had resulted due to chance alone
C) is a probability distribution
D) all of these

Question 15

We can reject H 0 if _________.

A) z obt = z crit
B) z obt ≥ z crit
C) z obt ≤ z crit
D) | z obt | ≥ | z crit |

Question 16

The mean attention span for adults in a certain village is 15 minutes with a standard deviation of 6.4. If the means of all possible samples of size 30 is taken from this population, will equal _________.

A) 3.0
B) 6.4
C) 0.21
D) 1.17

Question 17

Which of the following are true?

A) is the mean of the sampling distribution of the mean
B) is the standard deviation of the raw scores
C) both of these
D) none of these

Question 18

For the z test, the critical region for rejection of H 0 _________.

A) is determined only by a
B) is determined by a and N
C) allows us to accept the null hypothesis
D) depends on N

Question 19

A sampling distribution gives all the values a statistic can take, along with _________.

A) the probability of getting each value if sampling is random from the Null Hypothesis Population
B) the probability of getting each value under the assumption that it had resulted due to chance alone
C) the number of samples in the distribution
D) the probability of getting each value if sampling is random from the Null Hypothesis Population and the probability of getting each value under the assumption that it had resulted due to chance alone

Question 20

To use the z test, _________.

A) µ and s must be specified
B) the sampling distribution of should be normal
C) the population of raw scores must be normally distributed
D) and s must be specified and the sampling distribution of should be normal

Question 21

An English teacher has been teaching a sixth grade composition class for many years. He has the feeling that over the past several years, the writing ability of students has changed. A national test of proficiency in composition was administered 5 years ago. The resulting distribution of scores was normally shaped, had a mean of 85 and a standard deviation of 10.9. In order to test his feeling, he gives his present class of 43 students the same proficiency test. The resulting mean is 80 and the standard deviation is 8.7. Using the z test with a = 0.05 2 tail , what is your conclusion?

A) reject H 0 ; the present class appears deficient in composition writing
B) retain H 0 ; the present class is not deficient in composition writing
C) accept H 0 ; the present class is not deficient in composition writing
D) reject H 0 ; the present class is not deficient in composition writing

Question 22

If one draws all possible samples for various values of N from the same population of raw scores, as N increases _________.

A) the mean of the sampling distribution of the mean increases
B) the mean of the sampling distribution of the mean stays the same
C) the mean of the sampling distribution of the mean decreases
D) none of these

Question 23

If we take all possible samples from a normally distributed population, which of the following sample sizes will yield the smallest variation in the means of the samples?

A) 1
B) 85
C) 120
D) 5
E) 15

Question 24

Referring to question 29,how high must N be to be able to detect a µ real = 53 with a power of 0.8000?

A) 158
B) 222
C) 173
D) 248

Question 25

Referring to question 29, the probability of making a Type II error is _________.

A) 0.7764
B) 0.2400
C) 0.2236
D) 0.6459

Question 26

If one draws all possible samples for various values of N from the same population of raw scores, as N increases _________.

A) the standard error of the mean increases
B) the standard error of the mean stays the same
C) the standard error of the mean decreases
D) the standard error of the mean cannot be calculated

Question 27

An English teacher has been teaching a sixth grade composition class for many years. He has the feeling that over the past several years, the writing ability of students has changed. A national test of proficiency in composition was administered 5 years ago. The resulting distribution of scores was normally shaped, had a mean of 85 and a standard deviation of 10.9. In order to test his feeling, he gives his present class of 43 students the same proficiency test. The resulting mean is 80 and the standard deviation is 8.7. The obtained value of the appropriate statistic for testing H 0 is _________.

A) z obt = - 0.46
B) z obt = +3.01
C) z obt = - 3.01
D) z obt = - 0.45

Question 28

The critical value of the statistic _________.

A) is independent of alpha
B) is equal to alpha
C) is always the same in the z distribution
D) depends on alpha

Question 29

The critical value for the z distribution using a = 0.05 2 tail is _________.

A) ±1.96
B) ±2.58
C) ±1.64
D) ±2.33

Question 30

The area under the critical region for rejection must _________.

A) equal alpha
B) be less than alpha
C) be greater than alpha
D) equal one-half of alpha

Question 31

A set of sample scores from an experiment has an N = 28 and a mean = 52. H 1 is directional, predicting an effect of the independent variable which decreases the magnitude of the dependent variable. H 0 asserts the sample is a random sample from a population of scores where µ = 55 and s = 12. a = 0.05_{1 tail}. Using the z test to analyze the data, what is the correct conclusion regarding H 0 ?

A) reject H 0 ; the independent variable has a real effect
B) retain H 0 ; we cannot conclude that the independent variable has a real effect
C) accept H 0 ; the independent variable has no effect
D) reject H 0 ; the independent variable has no effect

Question 32

An English teacher has been teaching a sixth grade composition class for many years. He has the feeling that over the past several years, the writing ability of students has changed. A national test of proficiency in composition was administered 5 years ago. The resulting distribution of scores was normally shaped, had a mean of 85 and a standard deviation of 10.9. In order to test his feeling, he gives his present class of 43 students the same proficiency test. The resulting mean is 80 and the standard deviation is 8.7. Using the z test with a = 0.05 2 tail , the appropriate critical value is _________.

A) z crit = - 1.645
B) z crit = ±1.96
C) z crit = - 1.96
D) z crit = ± 1.645

Question 33

A set of sample scores from an experiment has an N = 28 and a mean = 52. H 1 is directional, predicting an effect of the independent variable which decreases the magnitude of the dependent variable. H 0 asserts the sample is a random sample from a population of scores where µ = 55 and s = 12. a = 0.05_{1 tail}. Using the z test to analyze the data, the power of the experiment to detect a real effect such that µ real = 53 is _________.

A) 0.3541
B) 0.7764
C) 0.7600
D) 0.2236

Question 34

A set of sample scores from an experiment has an N = 28 and a mean = 52. H 1 is directional, predicting an effect of the independent variable which decreases the magnitude of the dependent variable. H 0 asserts the sample is a random sample from a population of scores where µ = 55 and s = 12. a = 0.05_{1 tail}. Using the z test to analyze the data, z obt = _________.

A) - 1.322
B) - 0.250
C) - 7.000
D) - 0.132

Question 35

Power increases with _________.

A) increasing N
B) increasing magnitude of the effect of the independent variable
C) increasing a level
D) the magnitude of the difference between µ real and µ null
E) all of these

Question 36

A set of sample scores from an experiment has an N = 28 and a mean = 52. H 1 is directional, predicting an effect of the independent variable which decreases the magnitude of the dependent variable. H 0 asserts the sample is a random sample from a population of scores where µ = 55 and s = 12. a = 0.05_{1 tail}. Using the z test to analyze the data, z crit = _________.

A) +1.96
B) - 1.96
C) - 1.645
D) +1.645

Question 37

Referring to question 29, if N is increased to 90, power = _________ to detect a real effect such that µ real = 53.

A) 0.8524
B) 0.9103
C) 0.4761
D) 0.5142

Question 38

A raw score distribution that is negatively skewed will produce a sampling distribution of the mean for N = 4 which is _________.

A) also negatively skewed
B) normally distributed
C) positively skewed
D) cannot be determined

Question 39

In cases where N > 1, the relationship between the raw score population standard deviation and the standard error is _________.

A) the standard error is greater than the standard deviation
B) the standard error is less than the standard deviation
C) the standard error equals the standard deviation
D) the standard error is the standard deviation

Question 40

A raw score distribution which has a moderate negative skew will result in a sampling distribution of the mean for N = 42 that is _________.

A) also negatively distributed
B) normally distributed
C) positively skewed
D) cannot be determined

Question 41

The sampling distribution of the mean varies with the size of the sample.

Question 42

If one draws two samples of size N from a distribution of raw scores (with replacement), then the means of the two samples will _________.

A) be equal
B) perhaps be equal but not necessarily
C) be equal to the standard error
D) be equal to 1.0

Question 43

The sampling distribution of z varies with the size of the sample.

Question 44

To use the z test the data _________.

A) must be normally distributed
B) must be sampled from a normal distribution
C) should be sampled from a normal distribution if sample size is 10
D) can be any shape if N = 10
E) should be normal distributed if sample size is 10

Question 45

If the population standard deviation is 19.0 and the sample size is 19, then the standard error equals _________.

A) 19.00
B) 1.00
C) 4.36
D) cannot be determined; need to know population mean

Question 46

The sampling distribution of the mean is always normally distributed.

Question 47

What we are testing with the z test in this chapter is _________.

A) the sample mean
B) the population mean
C) the sample error
D) the standard error

Question 48

The symbol for the standard error of the mean is .

Question 49

A health psychologist knows the smoking population at the hospital where she works smokes an average of 18 cigarettes per day with a standard deviation of 7. She plans to conduct a program to reduce smoking. If she has 25 persons in her program, what is the power to detect a real effect of the program such that cigarette consumption is reduced, on the average, by 5 cigarettes? Assume population normality and use a = 0.05 1 tail .

A) Insufficient information
B) 0.9732
C) 0.9463
D) 0.8925

Question 50

Could the following sample reasonably have been drawn from a normal population with a mean of 20 and standard deviation of 1.5 using a = 0.01 2 tail ? X : 21, 21, 21, 20, 22, 20, 22?

A) yes
B) no
C) cannot be tested with z test
D) The correct answer cannot be determined from the information provided.

Question 51

The symbol for the mean of the sampling distribution of the mean is .

Question 52

The sampling distribution of z must be normally distributed to use the z test.

Question 53

The critical value for the z distribution using a = 0.01 2 tail is _________.

A) ±1.96
B) ±2.58
C) ±1.64
D) ±2.33

Question 54

The normal deviate test uses the mean of the sample as a basic statistic.

Question 55

What would one conclude about the null hypothesis that a sample of N = 46 with a mean of = 104 could reasonably have been drawn from a population with the parameters of = 100 and s = 8? Use a = 0.05 2 tail .

A) accept H₀
B) reject H₁
C) reject H₀
D) retain H₀

Question 56

If z obt had a value of 4.50 in the direction opposite from that predicted by the directional H ₁ and z crit was 2.58, one would _________.

A) accept H₀
B) reject the alternative hypothesis
C) retain H₀
D) reject H₀

Question 57

Generally speaking, if the sampling distribution of a statistic is indeterminate (impossible to determine), the statistic cannot be used for inference.

Question 58

Assuming that the population mean is 47.2 and the population deviation is 6.4, what is the z obt value for a sample mean of 52.1 if N = 8?

A) 1.96
B) 2.17
C) 1.73
D) 0.77

Question 59

Which of the following statements is(are) false?

A) The sampling distribution of a statistic gives (1) all the values that the statistic can take and (2) the probability of getting each value if sampling is random from the null hypothesis population.
B) The sampling distribution of a statistic gives (1) all the values that the statistic can take and (2) the probability of getting each value under the assumption that it resulted from chance alone.
C) The critical region for rejection of the null hypothesis is 1 - (the area under the curve that contains all the values of the statistic that allow rejection of the null hypothesis).
D) They are all true.

Question 60

The sampling distribution of z is always normally distributed.

Question 61

Power + Beta = 1.

Question 62

= , regardless of the shape of the sampling distribution of the mean.

Question 63

The critical value of a statistic is the value of the statistic that bounds the critical region for rejection of H 0 .

Question 64

Increasing N increases the real effect of the independent variable.

Question 65

A sampling distribution is based on the assumption that the independent variable has an effect on the dependent variable.

Question 66

In general, Alpha + Beta = 1.

Question 67

The z test does not depend on the shape of the sampling distribution of .

Question 68

If H 0 is false, a high level of power increases the probability we will reject it.

Question 69

To use the z test, µ and s must be specified.

Question 70

Power is the sensitivity of the experiment to detect a real effect of the independent variable, if there is one.

Question 71

Power and Beta are directly related.

Question 72

Alpha and Beta are inversely related.

Question 73

Only one sampling distribution can apply to any given problem or experiment.

Question 74

The power of the z test increases with sample variability.

Question 75

The sampling distribution of the mean is made up of mean scores.

Question 76

High power is desirable in an experiment.

Question 77

Using the sample standard deviation as an estimate for the population standard deviation is an example of interval estimation.

Question 78

The critical region for rejection of H 0 is the area under the curve that contains all the values of the statistic that fail to allow rejection of H 0 .

Question 79

As N increases, the variability of the sampling distribution of the mean increases.

Question 80

The binomial distribution is an example of a sampling distribution.