ADVANCE STATISTICS COMPREHENSIVE EXASMINATIONS 2024

Question 1

What is the formula for calculating the coefficient of variation?
A. (Standard deviation / Mean) × 100%
B. (Mean / Standard deviation) × 100%
C. (Range / Mean) × 100%
D. (Mean / Range) × 100%

Answer 1

A

Question 2

Which of the following is not a measure of dispersion?
A. Variance
B. Standard deviation
C. Range
D. Mode

Answer 2

D

Question 3

What is the formula for calculating the sample size needed to estimate a population mean with
a specified margin of error?
A. n = (zσ / E)²
B. n = (tσ / E)²
C. n = (z / E)²
D. n = (t / E)²

Answer 3

A

Question 4

What is the difference between a one-tailed and a two-tailed test in hypothesis testing?
A. A one-tailed test is used when the null hypothesis is directional, while a two-tailed test is used when the null hypothesis is non-directional.
B. A one-tailed test is used when the null hypothesis is non-directional, while a two-tailed test is used when the null hypothesis is directional.
C. A one-tailed test is used when the sample size is small, while a two-tailed test is used when the sample size is large.
D. A one-tailed test is used when the population variance is known, while a two-tailed test is used when the population variance is unknown.

Answer 4

A

Question 5

Which of the following is not a type of probability sampling?
A. Simple random sampling
B. Convenience sampling
C. Systematic sampling
D. Stratified sampling

Answer 5

B

Question 6

. What is the formula for calculating the coefficient of determination (r²) in linear regression?
A. r² = (correlation coefficient)²
B. r² = (covariance / (standard deviation of x * standard deviation of y))²
C. r² = (covariance / (standard deviation of x * standard deviation of y))
D. r² = (correlation coefficient) / (standard deviation of x * standard deviation of y)

Answer 6

A

Question 7

What is the formula for calculating the expected value of a discrete random variable?
A. E(X) = ∑(x * P(x))
B. E(X) = ∑(x / P(x))
C. E(X) = ∑(P(x) / x)
D. E(X) = ∑(1 / P(x))

Answer 7

A

Question 8

. Which of the following is not a measure of central tendency?
A. Mean
B. Median
C. Mode
D. Standard deviation

Answer 8

D

Question 9

. What is the range of the following set of data: 5, 7, 9, 11, 13?
A. 6
B. 8
C. 10
D. 12

Answer 9

B

Question 10

. What is the formula for calculating the sample variance?
A. ∑(x - μ) / n
B. ∑(x - μ)² / n
C. ∑(x - μ) / (n - 1)
D. ∑(x - μ)² / (n - 1)

Answer 10

D

Question 11

What is the standard deviation of the following set of data: 2, 4, 6, 8, 10?
A. 2.0
B. 2.5
C. 3.0
D. 3.5

Answer 11

C

Question 12

What is the formula for calculating the z-score of a data point?
A. (x - μ) / σ
B. (x - σ) / μ
C. (μ - x) / σ
D. (σ - x) / μ

Answer 12

A

Question 13

What is the formula for calculating the confidence interval for a population mean?
A. x̄ ± zσ / √n
B. x̄ ± tσ / √n
C. x̄ ± zσ / n
D. x̄ ± tσ / n

Answer 13

A

Question 14

. What is the difference between descriptive and inferential statistics?
A. Descriptive statistics is used to make generalizations about a population while inferential statistics is used to summarize data.
B. Descriptive statistics is used to summarize and describe data while inferential statistics is used to make generalizations about a population based on a sample of data.
C. Descriptive statistics and inferential statistics are interchangeable terms.
D. Descriptive statistics and inferential statistics are both used to analyze data, but they serve different purposes.

Answer 14

B

Question 15

What is a population in statistics?
A. The entire group of individuals or objects that a researcher is interested in studying.
B. A characteristic of a sample, such as the sample mean or standard deviation.
C. A subset of a population that is selected for a study.
D. The range of values that a variable can take.

Answer 15

A

Question 16

What is a sample in statistics?
A. The entire group of individuals or objects that a researcher is interested in studying.
B. A characteristic of a sample, such as the sample mean or standard deviation.
C. A subset of a population that is selected for a study.
D. The range of values that a variable can take.

Answer 16

C

Question 17

What is a parameter in statistics?
A. The range of values that a variable can take.
B. The probability of observing a certain value or range of values for a variable.
C. A characteristic of a sample, such as the sample mean or standard deviation.
D. A characteristic of a population, such as the population mean or standard deviation.

Answer 17

D

Question 18

What is a statistic in statistics?
A. A characteristic of a sample, such as the sample mean or standard deviation.
B. A characteristic of a population, such as the population mean or standard deviation.
C. The probability of observing a certain value or range of values for a variable.
D. The range of values that a variable can take.

Answer 18

A

Question 19

What is the difference between a parameter and a statistic?
A. A parameter is a characteristic of a sample, while a statistic is a characteristic of a population.
B. A parameter is a characteristic of a population, while a statistic is a characteristic of a sample.
C. A parameter and a statistic are both used to analyze data, but they serve different purposes.
D. A parameter and a statistic are interchangeable terms.

Answer 19

B

Question 20

What is the mean of a data set?
A. middle value in a data set.
B. The most common value in a data set.
C. The difference between the highest and lowest values in a data set.
D. The sum of all the values in a data set divided by the number of values.

Answer 20

D

Question 21

What is the median of a data set?
A. The middle value in a data set.
B. The most common value in a data set.
C. The difference between the highest and lowest values in a data set.
D. The sum of all the values in a data set divided by the number of values.

Answer 21

A

Question 22

What is the mode of a data set?
A. The middle value in a data set.
B. The most common value in a data set.
C. The difference between the highest and lowest values in a data set.
D. The sum of all the values in a data set divided by the number of values.

Answer 22

B

Question 23

What is the range of a data set?
A. The middle value in a data set.
B. The most common value in a data set.
C. The difference between the highest and lowest values.
D. The sum of all the values in a data set divided by the number of values.

Answer 23

C

Question 24

What is the variance of a data set?
A. The number of standard deviations from the mean.
B. The average distance of each data point from the mean.
C. The difference between the highest and lowest values in a data set.
D. The sum of the squared deviations from the mean divided by the number of values minus one.

Answer 24

D

Question 25

What is the standard deviation of a data set?
A. The number of standard deviations from the mean.
B. The average distance of each data point from the mean.
C. The difference between the highest and lowest values in a data set.
D. The sum of the squared deviations from the mean divided by the number of values minus one.

Answer 25

B

Question 26

What is a z-score?
A. The number of standard deviations from the mean.
B. The average distance of each data point from the mean.
C. The difference between the highest and lowest values in a data set.
D. The sum of the squared deviations from the mean divided by the number of values minus one.

Answer 26

A

Question 27

What is a confidence interval?
A. The range of values within which we can be certain the sample statistic falls.
B. The range of values within which we can be certain the true population parameter falls.
C. The range of values within which we can be certain the true population parameter and sample statistic differ.
D. The range of values within which we can be certain the true population parameter and sample statistic are equal.

Answer 27

A

Question 28

What is a hypothesis test?
A. A statistical test used to determine whether a sample is representative of the population.
B. A statistical test used to determine whether there is a significant relationship between two variables.
C. A statistical test used to determine whether there is a significant difference between two or more groups.
D. A statistical test used to determine whether a sample mean is significantly different from a population mean.

Answer 28

C

Question 29

What is the null hypothesis in a hypothesis test?
A. The hypothesis that a sample is representative of the population.
B. The hypothesis that there is a significant relationship between two variables.
C. The hypothesis that there is a significant difference between two or more groups.
D. The hypothesis that there is no significant difference between a sample mean and a population mean.

Answer 29

D

Question 30

What is the alternative hypothesis in a hypothesis test?
A. The hypothesis that a sample is not representative of the population.
B. The hypothesis that there is a significant relationship between two variables.
C. The hypothesis that there is a significant difference between two or more groups.
D. The hypothesis that there is a significant difference between a sample mean and a population mean.

Answer 30

D

Question 31

What is a type I error in hypothesis testing?
A. Rejecting the null hypothesis when it is true.
B. Rejecting the null hypothesis when it is false.
C. Failing to reject the null hypothesis when it is true.
D. Failing to reject the null hypothesis when it is false.

Answer 31

A

Question 32

What is a type II error in hypothesis testing?
A. Rejecting the null hypothesis when it is true.
B. Failing to reject the null hypothesis when it is false.
C. Rejecting the alternative hypothesis when it is true.
D. Failing to reject the alternative hypothesis when it is true.

Answer 32

B

Question 33

What is the p-value in hypothesis testing?
A. The probability of making a type I error.
B. The probability of making a type II error.
C. The probability of observing a test statistic as extreme as the one calculated from the sample, assuming the null hypothesis is true.
D. The probability of observing a test statistic as extreme as the one calculated from the sample, assuming the alternative hypothesis is true.

Answer 33

C

Question 34

What is the formula for calculating the degrees of freedom in a chi-square test?
A. df = n - 1
B. df = k - 1
C. df = (n - 1)(k - 1)
D. df = n + k - 2

Answer 34

B

Question 35

What is the standard deviation?
A. The sum of the squared deviations from the mean, divided by the sample size.
B. The difference between the highest and lowest values in a dataset.
C. The average of the deviations from the mean.
D. The square root of the variance.

Answer 35

D

Question 36

Which of the following symbols denotes population mean?
X B. σ C. μ D. s

Answer 36

C

Question 37

A population consists of the five measurements 2, 6, 8, 0, and 1. How many different samples of size n = 2 can be drawn from the population?
A. 10 B. 20 C. 30 D. 45

Answer 37

A

Question 38

The following is the result of statistics test.
33 60 47 37 42 31 27 26 70 48
39 62 44 53 36 30 38 36 77 30
30 69 35 39 37 34 28 40 71 43

Organize a frequency distribution. What is your class interval?
A. 8 B. 9 C. 10 D. 11

Answer 38

B

Question 39

The following is the result of statistics test.
33 60 47 37 42 31 27 26 70 48
39 62 44 53 36 30 38 36 77 30
30 69 35 39 37 34 28 40 71 43

What is the mean?
A. 37.8 B. 38. 8 C. 39.8 D. 43

Answer 39

D

Question 40

The following is the result of statistics test.
33 60 47 37 42 31 27 26 70 48
39 62 44 53 36 30 38 36 77 30
30 69 35 39 37 34 28 40 71 43

What is the median?
A. 39.5 B. 40 C. 41 D. 42

Answer 40

A

Question 41

The following is the result of statistics test.
33 60 47 37 42 31 27 26 70 48
39 62 44 53 36 30 38 36 77 30
30 69 35 39 37 34 28 40 71 43

What is the mode?
A. 35 B. 36 C. 37 D. 40

Answer 41

B/C

Question 42

The following is the result of statistics test.
33 60 47 37 42 31 27 26 70 48
39 62 44 53 36 30 38 36 77 30
30 69 35 39 37 34 28 40 71 43

What is the standard deviation?
A. 14 B. 13 C. 12 D. 11

Answer 42

A

Question 43

The following is the result of statistics test.
33 60 47 37 42 31 27 26 70 48
39 62 44 53 36 30 38 36 77 30
30 69 35 39 37 34 28 40 71 43

If the highest possible score is 70, what is the class proficiency?
A. 61% B. 63% C. 64% D. 65%

Answer 43

A

Question 44

Refer to the following conditions. Answer options are:
A. 100% B. 96% C. 68% D.50%

If normally distributed test scores have a mean equal 40 and a standard deviation of 5, what percentage of their scores will be between:

44. 25 to 55

Answer 44

A

Question 45

Refer to the following conditions. Answer options are:
A. 100% B. 96% C. 68% D.50%

If normally distributed test scores have a mean equal 40 and a standard deviation of 5, what percentage of their scores will be between:

45. 35 and 45

Answer 45

C

Question 46

Refer to the following conditions. Answer options are:
A. 100% B. 96% C. 68% D.50%

If normally distributed test scores have a mean equal 40 and a standard deviation of 5, what percentage of their scores will be between:

30 and 50.

Answer 46

B

Question 47

Use this information to determine whether each of the following statements is:
A. true B. false C. lacking given information

47. May Ann scored 30 in English, 30 in Math, and 30 in science. Relative to other students, she did about equally in three subject areas.

Answer 47

B

Question 48

Use this information to determine whether each of the following statements is:
A. true B. false C. lacking given information

Marjorie scored 46 in English and 28 in math, relative to other students, she did better in English than in math.

Answer 48

B

Question 49

Use this information to determine whether each of the following statements is:
A. true B. false C. lacking given information

Junelyn scored 32 in both math and science. Relative to other students, she did better in Math than in Science.

Answer 49

B

Question 50

Here is how several individuals performed on an intelligence test. What is each person’s deviation IQ score if the mean of these scores is 100 and the sd is 16. Answer options:
A. 68 B. 84 C. 108 D. 132

50. Theodore scored 2 sd above the mean.,

Answer 50

D

Question 51

Here is how several individuals performed on an intelligence test. What is each person’s deviation IQ score if the mean of these scores is 100 and the sd is 16. Answer options:
A. 68 B. 84 C. 108 D. 132

51. George scored 1 s.d. below the mean.

Answer 51

B

Question 52

Here is how several individuals performed on an intelligence test. What is each person’s deviation IQ score if the mean of these scores is 100 and the sd is 16. Answer options:
A. 68 B. 84 C. 108 D. 132

52. Tina scored 0.5 sd above the mean.

Answer 52

C

Question 53

A blood pressure test was given to 350 women ages 20-36. It showed that their mean systolic pressure was 115. Hg, with a standard deviation of 11. mm Hg.

53. Determine the z score of a woman who had a systolic blood pressure reading of 148 mm Hg.
    A. 3 B. 2.8 C. 2.0 D. -2.0
54. The z-score for one woman was -1.15. What is her systolic blood pressure reading?
    A. 102 B. 113 C. 123 D. 134.

(TWO ANSWERS REQUIRED)

Answer 53

53. A
54. D

Question 54

For number 55- 57, refer to the following answer options:
A. 25% B. 50% C. 75% D.100%

A recent survey by the Philippine Statistics office determined that the median for monthly housing rent was P2 000. The first quartile for monthly rental was P 1 000. Find the percent of monthly housing rent that were:

55. more than P3 000
56. less than P 1000
57. between P 1000 and P3 000.

(THREE ANSWERS REQUIRED)

Answer 54

55. C
56. A
57. D

Question 55

For number 58 -60 , refer to the following information:

Answer Options:
A.7.2% B. 5.8% C. 7% D. 41% E. 46.8% F. 92.8%

Humans are on average , taller today than 200 years ago. Today, the mean height of 14 year-old boys is 65 inches. Use the following relative frequency distribution of heights of a group 14 yr. old boys from the 19th century to answer the following questions:

Height in inches - Percent of boys
#under 50 - 0.2%
#50-54 - 7%
#55-59 - 46%
#60-64 - 41%
#65-69 - 5.8%

58. What percent of the group of 19th century boys was at least 60 in. tall?
59. What is the probability that one of the 19th century selected at random was at least 55 in, tall but less than 65 in. tall?
60. How many percent of the population are will not meet the PNP height requirement of 55 in. in height?

(THREE ANSWERS REQUIRED)

Answer 55

58. E
59. D
60. A