FMITANL Statistics

Which of the following statements is true? It is possible for a distribution to have two means. It is possible for a distribution to have two medians. It is possible for a distribution to have two modes. It is possible for a distribution to have two medians or two modes.

it is possible for a distribution to have two modes

In a population with s = 8, a score of X = 44 corresponds to a z-score of z = -0.50. What is the population mean? m = 36 m = 40 m = 48 m = 52

m=48

A sample from a population with m = 40 and s = 8 has a mean of M = 36. If the sample mean corresponds to a z = -1.00, then how many scores are in the sample? n = 64 n = 16 n = 8 n = 4

n=4

The students in a psychology class seemed to think that the midterm exam was very easy. If they are correct, what is the most likely shape for the distribution of exam scores? Symmetrical Positively skewed Negatively skewed Normal

negatively skewed

What is the shape of the distribution for the following set of data? Scores: 1, 2, 3, 3, 4, 4, 4 5, 5, 5, 5, 6 Symmetrical Positively skewed Negatively skewed Normal

negatively skewed

If a distribution of scores is shown in a bar graph, you know that the scores were measured on a(n) _________ scale of measurement. nominal or ordinal ordinal or interval interval or ratio discrete or continuous

nominal or ordinal

The participants in a research study are classified as high, medium, or low in self-esteem. What measurement scale is being used to classify self-esteem? Nominal Ordinal Interval Ratio

ordinal

Using letter grades (A, B, C, D, and E) to classify student performance on an exam is an example of measurement on a(n) _______ scale of measurement. nominal ordinal interval ratio

ordinal

A normal distribution has m = 80 and s = 10. What is the probability of randomly selecting a score greater than 90 from this distribution? p = 0.8413 p = 0.1587 p = 0.3085 p = 0.6915

p=0.1587

A researcher administers a treatment to a sample of participants selected from a population with m = 80. If the researcher obtains a sample mean of M = 88, which combination of factors is most likely to result in rejecting the null hypothesis? s = 5 and a = .01 s = 5 and a = .05 s = 10 and a = .01 s = 10 and a = .05

s = 5 and a = .05

Which of the following symbols identifies the population standard deviation? s italicized s2 s s 2

s italicized

A population has m = 50. What value of ó would make X = 55 an extreme value out in the tail of the distribution? s = 1 s = 5 s = 10 Cannot determine with the information given

s=1

On an exam with a mean of m = 70, you have a score of X = 75. Which of the following values for the standard deviation would give you the highest position within the class? s = 1 s = 5 s = 10 Cannot determine from the information given

s=1

On an exam with m = 52, you have a score of X = 44. Which value for the standard deviation would give you the highest position in the class distribution? s = 2 s = 4 s = 8 Cannot determine from the information given

s=8

If sample variance is computed by dividing SS by n, then the average value of the sample variances from all the possible random samples will be _______ the population variance. smaller than larger than exactly equal to unrelated to

smaller than

What are the values for SS and variance for the following sample of n = 4 scores? Sample: 1, 1, 0, 4 SS = 9 and variance = 3 SS = 9 and variance = 2.25 SS = 18 and variance = 6 SS = 18 and variance = 9

ss=9 and variance=3

A characteristic, usually a numerical value, which describes a sample is called a _______. parameter statistic variable constant

statistic

Under what circumstances is a score that is 15 points above the mean an extreme score relatively far from the mean? When the population mean is much larger than 15 When the population standard deviation is much larger than 15 When the population mean is much smaller than 15 When the population standard deviation is much smaller than 15

when the population standard deviation is much smaller than 15

A distribution with m = 35 and s = 8 is being standardized so that the new mean and standard deviation will be m = 50 and s = 10. In the new, standardized distribution, your score is X = 45. What was your score in the original distribution? X = 30 X = 31 X = 39 X = 45

x=31

Scores on the SAT form a normal distribution with a mean of m = 500 with s = 100. If the state college only accepts students who score in the top 60% on the SAT, what is the minimum score needed to be accepted? X = 475 X = 525 X = 440 X = 560

x=475

A distribution with m = 55 and s = 6 is being standardized so that the new mean and standard deviation will be m = 50 and s = 10. When the distribution is standardized, what value will be obtained for a score of X = 58 from the original distribution? X = 53 X = 55 X = 58 X = 61

x=55

What z-score values form the boundaries for the middle 60% of a normal distribution? z = +0.25 and z = -0.25 z = +0.39 and z = -0.39 z = +0.52 and z = -0.52 z = +0.84 and z = -0.84

z = +0.84 and z = -0.84

What z-score value separates the highest 70% of the scores in a normal distribution from the lowest 30%? z = 0.52 z = 0.84 z = -0.52 z = -0.84

z=-0.52

Which of the following z-score values represents the location farthest from the mean? z = +0.50 z = +1.00 z = -1.00 z = -2.00

z=-2.00

If a sample of n = 4 scores is obtained from a population with m = 70 and s = 12, what is the z-score corresponding to a sample mean of M = 73? z = 0.25 z = 0.50 z = 1.00 z = 2.00

z=0.50

A random sample of n = 4 scores is obtained from a population with a mean of m = 80 and a standard deviation of s = 10. If the sample mean is M = 90, what is the z-score for the sample mean? z = 20.00 z = 5.00 z = 2.00 z = 1.00

z=2.00

My electric bills for June, July, and August last summer were $75, $75, and $150, respectively. What was the mean amount for the three bills? $75 $100 $125 $150

$100

For a population with m = 70 and s = 8, what is the z-score corresponding to X = 82? +0.25 +0.75 +1.25 +1.50

+1.50

For a population with m = 80 and s = 6, what is the z-score corresponding to X = 68? -0.50 -2.00 +2.00 -12.00

-2.00

What is the probability of randomly selecting a z-score less than z = -1.25 from a normal distribution? 0.8944 0.1056 0.3944 0.2112

0.1056

A normal distribution has a mean of m = 70 with s = 10. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 82? 0.7698 0.3849 0.1151 0.8849

0.1151

A normal distribution has a mean of m = 100 with s = 20. If one score is randomly selected from this distribution, what is the probability that the score will be less than X = 84? 0.7881 0.5762 0.2881 0.2119

0.2119

A vertical line is drawn through a normal distribution at z = 0.80. What proportion of the distribution is on the right-hand side of the line? 0.7881 0.2119 0.2881 0.5762

0.2119

A normal distribution has a mean of m = 40 with s = 10. If a vertical line is drawn through the distribution at X = 35, what proportion of the scores are on the left side of the line? 0.3085 0.6915 0.0668 0.9332

0.3085

A random sample of n = 9 scores is obtained from a normal population with m = 40 and s = 18. What is the probability that the sample mean will be greater than M = 43? 0.4325 0.3085 0.1587 0.0228

0.3085

A normal distribution has a mean of m = 100 with s = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 100 and X = 130? 0.9332 0.0668 0.4332 0.8664

0.4332

What proportion of a normal distribution is located between z = 0 and z = +1.50? 0.9332 0.0668 0.4332 0.8664

0.4332

A sample of n = 9 individuals is selected from a population with m = 60 and s = 6, and a treatment is administered to the sample. After treatment, the sample mean is M = 63. What is the value of Cohen's d for this sample? 0.33 0.50 1.00 2.00

0.50

A sample of n = 4 scores is selected from a normal population with a mean of m = 50 and a standard deviation of s = 20. What is the probability of obtaining a sample mean greater than M = 48? p = 0.6554 p = 0.3446 p = 0.5793 p = 0.4207

0.5793

A random sample of n = 9 scores is selected from a normal distribution with m = 80 and s = 12. What is the probability that the sample mean will be between 76 and 84? 0.9974 0.6426 0.3830 0.2586

0.6426

A random sample of n = 16 scores is obtained from a normal population with m = 40 and s = 8. What is the probability that the sample mean will be within 2 points of the population mean? 0.3830 0.6826 0.8664 0.9544

0.6826

What is the probability of randomly selecting a z-score greater than z = -0.75 from a normal distribution? 0.7734 0.2266 0.2734 0.4532

0.7734

What proportion of a normal distribution is located between z = -1.25 and z = +1.25? 0.8944 0.2112 0.3944 0.7888

0.7888

A normal distribution has a mean of m = 70 with s = 12. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 58? 0.8413 0.1577 0.3413 0.6826

0.8413

A vertical line is drawn through a normal distribution at z = 1.20. What proportion of the distribution is on the left-hand side of the line? 0.8849 0.1151 0.3849 0.7698

0.8849

A normal distribution has a mean of m = 70 with s = 12. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 55? 0.3944 0.1056 0.8944 0.7888

0.8944

If an entire population with m = 60 and s = 8 is transformed into z-scores, then the distribution of z-scores will have a mean of ___ and a standard deviation of ___. 0; 1 60; 1 0; 8 60; 8 (unchanged)

0; 1

What is the variance for the following population of scores? Scores: 5, 2, 5, 4 6 2 1.5 1.22

1.5

For a particular population, a sample of n = 4 scores has an expected value of 10. For the same population, a sample of n = 25 scores would have an expected value of _____. 4 8 10 20

10

What is the value of S(X - 1)2 for the scores 1, 2, 1, 4? 10 16 36 49

10

For the following distribution, what percentage of the individuals have scores of X = 1?Xf5248352312 2% 5% 10% 20%

10%

A population distribution has s = 6. What position in this distribution is identified by a z-score of z = +2.00? 2 points above the mean 2 points below the mean 12 points above the mean 12 points below the mean

12 points above the mean

A set of N = 8 scores has a mean of m = 11. If 16 points are added to one of the scores, what is the new value for the population mean? 10 11 12 13

13

How many individual scores are in the following distribution? n = 4 n = 6 n = 13 cannot be determined

13

What is the value of SS (sum of squared deviations) for the following population? Population: 2, 3, 0, 5 13 38 13/4 = 3.25 38/4 = 9.50

13

What is the value of S(X + 1) for the scores 2, 4, 7? 10 11 13 16

16

What is the median for the set of scores shown in the frequency distribution table?Xf5141322314 1 1.5 2 2.5

2

What is the value of SS (sum of squared deviations) for the following sample? Sample: 1, 3, 2, 2 0.50 2 4 18

2

What is the value of SX2 for the scores 1, 0, 2, 4? 14 21 28 49

21

What is the mean for the population of scores shown in the frequency distribution table?Xf5241332212 15/5 = 3 15/10 = 1.50 29/5 = 5.80 29/10 = 2.90

29/10=2.90

In a population with a standard deviation of s = 5, a score of X = 44 corresponds to a z-score of z = 2.00. What is the population mean? 49 54 39 34

34

A sample is selected from a population with m = 50 and s = 12. If the sample mean of M = 56 produces a z-score of z = +1.00, then how many scores are in the sample? 2 4 9 16

4

A sample of n = 4 scores is selected from a population with m = 40 with s = 8, and the sample mean is M = 43. What is the standard error for the sample mean? 8 4 3 2

4

What is the value of S(X - 2) for the scores 2, 3, 5? 4 6 8 10

4

A sample of n = 6 scores has a standard deviation of s = 3. What is the value of SS, the sum of the squared deviations for this sample? 54 45 18 15

45

A population of n = 8 scores has SX = 40. What is the population mean? 320 20 5 0.2

5

A sample of n = 36 scores is selected from a population with s = 12. If the sample mean of M = 56 produces a z-score of z = +3.00, then what is the population mean? 50 52 54 56

50

If random samples, each with n = 9 scores, are selected from a normal population with m = 80 and s = 18, how much difference, on average, should there be between a sample mean and the population mean? 2 points 3 points 6 points 18 points

6 points

Samples of size n = 9 are selected from a population with m = 80 with s = 18. What is the expected value for the distribution of sample means? 6 18 80/3 80

80

for a population with m = 100 and s = 20, what is the X value corresponding to z = -0.75? 85 95 105 115

85

A researcher administers a treatment to a sample of participants selected from a population with m = 80. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis? A sample mean near 80 with a = .05 A sample mean near 80 with a = .01 A sample mean much different than 80 with a = .05 A sample mean much different than 80 with a = .01

A sample mean much different than 80 with a = .05

What is the relationship between the alpha level, the size of the critical region, and the risk of a Type I error? As the alpha level increases, the size of the critical region increases, and the risk of a Type I error increases. As the alpha level increases, the size of the critical region increases, and the risk of a Type I error decreases. As the alpha level increases, the size of the critical region decreases, and the risk of a Type I error increases. As the alpha level increases, the size of the critical region decreases, and the risk of a Type I error decreases

As the alpha level increases, the size of the critical region increases, and the risk of a Type I error increases.

With a = .05, how are the boundaries for the critical region determined? Boundaries are drawn so there is 2.5% (.025) in each tail of the distribution. Boundaries are drawn so there is 5% (.05) in each tail of the distribution. Boundaries are drawn so there is 10% (.10) in each tail of the distribution. Boundaries are drawn so there is 5% (.05) in the center of the distribution.

Boundaries are drawn so there is 2.5% (.025) in each tail of the distribution.

Even if a treatment has an effect, it is still possible to obtain a sample mean that is very similar to the original population mean. What outcome is likely if this happens? Reject H0 and make a Type I error Correctly reject H0 Fail to reject H0 and make a Type II error Correctly fail to reject H0

Fail to reject H0 and make a Type II error

Which of the following correctly describes the effect of increasing the alpha level (for example, from .01 to .05)? Increase the likelihood of rejecting H0 and increase the risk of a Type I error Decrease the likelihood of rejecting H0 and increase the risk of a Type I error Increase the likelihood of rejecting H0 and decrease the risk of a Type I error Decrease the likelihood of rejecting H0 and decrease the risk of a Type I error

Increase the likelihood of rejecting H0 and increase the risk of a Type I error

In a population of N = 6, five of the individuals all have scores that are exactly 1 point above the mean. From this information, what can you determine about the score for the 6th individual? It is also above the mean by 1 point. It is below the mean by 1 point. It is below the mean by 5 points. There is not enough information to describe the 6th score.

It is below the mean by 5 points.

For a normal population with m = 40 and s = 10, which of the following samples has the highest probability of being obtained? M £ 4= 38 for a sample of n = 4 M £ 4= 36 for a sample of n = 4 M £ 4= 38 for a sample of n = 100 M £ 4= 36 for a sample of n = 100

M £ 4= 38 for a sample of n = 4

For a sample of n = 100 scores, X = 45 corresponds to z = 0.50 and X = 52 corresponds to z = +1.00. What are the values for the sample mean and standard deviation? M = 31 and s = 7 M = 31 and s = 14 M = 38 and s = 7 M = 38 and s = 14

M=38 and S=14

A treatment is administered to a sample of n = 9 individuals selected from a population with a mean of m = 80 and a standard deviation of s = 12. After treatment, the effect size is measured by computing Cohen's d, and a value of d = 0.50 is obtained. Based on this information, what is the mean for the treated sample? M = 6 M = 82 M = 86 Cannot answer without knowing the sample size

M=86

What is the most likely shape for a distribution with a mean of 40 and a mode of 45? Symmetrical Positively skewed Negatively skewed Either positively or negatively skewed

Negatively Skewed

What frequency distribution graph is appropriate for scores measured on a nominal scale? Only a histogram Only a polygon Either a histogram or a polygon Only a bar graph

Only a bar graph

A two-tailed hypothesis test is being used to evaluate a treatment effect with a = .05. If the sample data produce a z-score of z = -2.24, what is the correct decision? Reject the null hypothesis and conclude that the treatment has no effect Reject the null hypothesis and conclude that the treatment has an effect Fail to reject the null hypothesis and conclude that the treatment has no effect Fail to reject the null hypothesis and conclude that the treatment has an effect

Reject the null hypothesis and conclude that the treatment has an effect

What is measured by the denominator of the z-score test statistic? The average distance between M and m that would be expected if H0 was true The actual distance between M and m The position of the sample mean relative to the critical region Whether or not there is a significant difference between M and m

The average distance between M and m that would be expected if H0 was true

Last week Sarah had exams in math and in Spanish. On the math exam, the mean was m = 40 with s = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was m = 60 with s = 8, and Sarah had a score of X = 68. For which class should Sara expect the better grade? Math Spanish The grades should be the same because the two exam scores are in the same location. There is not enough information to determine which is the better grade.

The grades should be the same because the two exam scores are in the same location

Which of the following is an accurate definition for the power of a statistical test? The probability of rejecting a true null hypothesis The probability of supporting true null hypothesis The probability of rejecting a false null hypothesis The probability of supporting a false null hypothesis

The probability of rejecting a false null hypothesis

When is there a risk of a Type II error? Whenever H0 is rejected Whenever H1 is rejected Whenever the decision is "fail to reject H0" The risk of a Type II error is independent of the decision from a hypothesis test.

Whenever the decision is "fail to reject H0"

You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to fail to reject the null hypothesis. If the treatment actually does have an effect, which of the following is true? You have made a Type I error. You have made a Type II error. You might have made a Type I error, but the probability is only 5% at most. You have made the correct decision.

You have made a Type II error.

You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis. Which of the following is true? You have made a Type I error. You have made a Type II error. You might have made a Type I error, but the probability is less than 5%. You have made the correct decision.

You might have made a Type I error, but the probability is less than 5%.

For a research study comparing attitude scores for males and females, participant gender is an example of what kind of variable? An independent variable A dependent variable A quasi-independent variable A quasi-dependent variable

a quasi-independent variable

For the following frequency distribution of exam scores, what is the lowest score on the exam?Xf90-94385-89480-84575-79270-741 X = 70 X = 74 X = 90 Cannot be determined

cannot be determined