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MCQ TESTING OF HYPOTHESIS MCQ 13.1

MCQ 13.4

A statement about a population developed for the purpose of testing is called:

Any statement whose validity is tested on the basis of a sample is called:

(a) Hypothesis

(a) Null hypothesis

(b) Hypothesis testing

(b) Alternative hypothesis

(c) Level of significance

(c) Statistical hypothesis

(d) Test-statistic

(b) Simple hypothesis

The hypothesis is the supposition that we want to test.

In the statistical hypothesis we receive most of the parameters, so we can test a sample within those parameters.

MCQ 13.2 Any hypothesis which is tested for the purpose of rejection under the assumption that it is true is called:

MCQ 13.5

(a) Null hypothesis

(a) Research hypothesis

(b) Alternative hypothesis

(b) Composite hypothesis

(c) Statistical hypothesis

(c) Simple hypothesis

(d) Composite hypothesis

(d) Statistical hypothesis

The Null hypothesis serves as counter-weight in order to prove the alternative hypothesis.

A statistical hypothesis is an assumption about a population parameter

MCQ 13.3

MCQ 13.6

A statement about the value of a population parameter is called:

A statement that is accepted if the sample data provide sufficient evidence that the null hypothesis is false is called:

(a) Null hypothesis

A quantitative statement about a population is called:

(b) Alternative hypothesis

(a) Simple hypothesis

(c) Simple hypothesis

(b) Composite hypothesis

(d) Composite hypothesis

(c) Statistical hypothesis

In the null hypothesis we do not have all the parameters so we try to approximate it.

(d) Alternative hypothesis The alternative hypothesis is the one that we want prove

(d) None of the above

The alternative hypothesis is also called:

It’s simple hypothesis because in its included a parameter in the statement

(a) Null hypothesis

MCQ 13.11

(b) Statistical hypothesis

A hypothesis may be classified as:

MCQ 13.7

(c) Research hypothesis

(a) Simple

(d) Simple hypothesis

(b) Composite

The research hypothesis is the assumption upon the outcome of an experiment.

(c) Null

MCQ 13.8

The simple and the composite are types of hypothesis based on the information used in the statement.

A hypothesis that specifies all the values of parameter is called: (a) Simple hypothesis (b) Composite hypothesis (c) Statistical hypothesis (d) None of the above

(d) All of the above

MCQ 13.12 The probability of rejecting the null hypothesis when it is true is called: (a) Level of confidence (b) Level of significance

From the simple hypothesis we can prove samples.

(c) Power of the test

MCQ 13.9

(d) Difficult to tell

The hypothesis μ ≤ 10 is a:

The level of confidence is used to calculate the critical value.

(a) Simple hypothesis (b) Composite hypothesis (c) Alternative hypothesis (d) Difficult to tell.

MCQ 13.13 The dividing point between the region where the null hypothesis is rejected and the region where it is not rejected is said to be:

Because in order to describe the hypothesis we must have more information.

(a) Critical region

MCQ 13.10

(c) Acceptance region

If a hypothesis specifies the population distribution is called:

(d) Significant region

(b) Critical value

(a) Simple hypothesis

The critical value defines the regions of acceptance and rejection.

(b) Composite hypothesis

MCQ 13.14

(c) Alternative hypothesis

If the critical region is located equally in both sides of the sampling distribution of test-statistic, the test is called:

(d) All of the above

(a) One tailed

As we base our decisions in the alternative hypothesis, the value that we want to test is on the left side.

(b) Two tailed

MCQ 13.18

(c) Right tailed

Testing Ho: μ = 25 against H1: μ ≠ 20 leads to:

(d) Left tailed

(a) Two-tailed test

We use two tail when our null hypothesis states an (b) Left-tailed test equality. (c) Right-tailed test MCQ 13.15 (d) Neither (a), (b) and (c) The choice of one-tailed test and two-tailed test depends upon:

As we are testing an equality, we must search for the experimental value in both sides.

(a) Null hypothesis

MCQ 13.19

(b) Alternative hypothesis (c) None of these

A rule or formula that provides a basis for testing a null hypothesis is called:

(d) Composite hypotheses

(a) Test-statistic

In the alternative we base our decisions because it’s the one that we want to succeed.

(b) Population statistic

MCQ 13.16

(d) None of the above

Test of hypothesis Ho: μ = 50 against H1: μ > 50 leads to:

It’s also called hypothesis test, and it helps us to know if our approximation is correct.

(a) Left-tailed test

MCQ 13.20

(b) Right-tailed test

The range of test statistic-Z is:

(c) Two-tailed test

(a) 0 to 1

(d) Difficult to tell

(b) -1 to +1

Because we want to know if the value is going to be beyond the critical value on the right side.

(c) 0 to ∞

MCQ 13.17 Test of hypothesis Ho: μ = 20 against H1: μ < 20 leads to:

(c) Both of these

(d) -∞ to +∞ The tails never touch the x vertex. MCQ 13.21

(a) Right one-sided test

The range of test statistic-t is:

(b) Left one-sided test

(a) 0 to ∞

(c) Two-sided test

(b) 0 to 1

(c) -∞ to +∞

(c) Best decision

(d) -1 to +1

(d) All of the above

The t student follows the same principle of that of the Z.

Is when we do not accept as correct that in fact is correct.

MCQ 13.22

MCQ 13.26

If Ho is true and we reject it is called:

1 – α is also called:

(a) Type-I error (b) Type-II error (c) Standard error (d) Sampling error

(a) Confidence coefficient (b) Power of the test (c) Size of the test (d) Level of significance

Is the alfa error

The confidence coefficient is the complement of the level of significance.

MCQ 13.23

MCQ 13.27

The probability associated with committing type-I error is:

1 – α is the probability associated with:

(a) β

(a) Type-I error (b) Type-II error

(b) α

(c) Level of confidence

(c) 1 – β

(d) Level of significance

(d) 1 – α

The level of confidence is calculated as 1 minus alfa.

MCQ 13.24

MCQ 13.28

A failing student is passed by an examiner, it is an example of:

Area of the rejection region depends on:

(a) Type-I error

(b) Size of β

(b) Type-II error

(c) Test-statistic

(c) Unbiased decision

(d) Number of values

(d) Difficult to tell

The size of alfa is based on the level of confidence we want to achieve.

It’s the most tragic error, and it happens when we accept something wrong as correct.

(a) Size of α

MCQ 13.29

MCQ 13.25

Size of critical region is known as:

A passing student is failed by an examiner, it is an example of:

(a) β

(a) Type-I error

(c) Critical value

(b) Type-II error

(d) Size of the test

(b) 1 - β

The size of the test is where we can accept the null hypothesis.

As the level of significance is a probability, the level o significance must lie between 0 and 1.

MCQ 13.30

MCQ 13.34

A null hypothesis is rejected if the value of a test statistic lies in the:

Critical region is also called:

(a) Rejection region (b) Acceptance region (c) Both (a) and (b) (d) Neither (a) nor (b)

(a) Acceptance region (b) Rejection region (c) Confidence region (d) Statistical region

The rejection region is were alfa is.

The rejection region goes from the critical value to infinite.

MCQ 13.31

MCQ 13.35

The test statistic is equal to:

The probability of rejecting Ho when it is false is called:

(a)

𝑠𝑎𝑚𝑝𝑙𝑒−𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑒𝑟𝑟𝑜𝑟

(a) Power of the test

𝒔𝒂𝒎𝒑𝒍𝒆 𝒔𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄𝒔−𝒑𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏

(b) 𝒔𝒕𝒂𝒏𝒅𝒂𝒓𝒅 𝒆𝒓𝒓𝒐𝒓 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄𝒔 (c)

𝑠𝑎𝑚𝑝𝑙𝑒 𝑚𝑒𝑎𝑛 −𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑚𝑒𝑎𝑛

(b) Size of the test (c) Level of confidence

𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑒𝑟𝑟𝑜𝑟 𝑆𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐𝑠−𝐸(𝑆𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐𝑠)

(d) 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑆𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐𝑠

(d) Confidence coefficient

The test statistics is divided over the standard error of the statistics.

The power of a test is also called statistical power and it refers to the probability the test correctly rejects the null hypothesis.

MCQ 13.32

MCQ 13.36

Level of significance is also called: (a) Power of the test (b) Size of the test (c) Level of confidence (d) Confidence coefficient The size of the test tells us how big is going to be the rejection area.

MCQ 13.33 Level of significance α lies between: (a) -1 and +1 (b) 0 and 1 (c) 0 and n (d) -∞ to +∞

Power of a test is related to: (a) Type-I error (b) Type-II error (c) Both (a) and (b) (d) Neither (a) and (b) Because as we reject Ho when its false we assure to prove correct Ha. MCQ 13.37 In testing hypothesis α + β is always equal to: (a) One (b) Zero (c) Two (d) Difficult to tell

The two types of errors are complements.

MCQ 13.42

MCQ 13.38

The chance of rejecting a true hypothesis decreases when sample size is:

The significance level is the risk of: (a) Rejecting Ho when Ho is correct (b) Rejecting Ho when H1 is correct (c) Rejecting H1 when H1 is correct (d) Accepting Ho when Ho is correct. As the significance level goes narrower, the probability of having the first type of error increases. MCQ 13.39 An example in a two-sided alternative hypothesis is:

(a) Decreased (b) Increased (c) Constant (d) Both (a) and (b) As we get more data, we can get closer to the parameters. MCQ 13.43 The equality condition always appears in:

(a) H1: μ < 0

(a) Null hypothesis

(b) H1: μ > 0

(b) Simple hypothesis

(c) H1: μ ≥ 0

(c) Alternative hypothesis

(d) H1: μ ≠ 0

(d) Both (a) and (b)

The two sided hypothesis is used when an equality is tested.

My teacher told me. MCQ 13.44

MCQ 13.40

Which hypothesis is always in an inequality form?

If the magnitude of calculated value of t is less than the tabulated value of t and H1 is two-sided, we should:

(a) Null hypothesis

(a) Reject Ho (b) Accept H1 (c) Not reject Ho (d) Difficult to tell

(b) Alternative hypothesis (c) Simple hypothesis (d) Composite hypothesis If the null hypothesis is always is presented as the equality, the alternative hypothesis must the contrary.

We cannot reject Ho because it would lie in the test region.

MCQ 13.45

MCQ 13.41

(a) μ ≥ μo

Accepting a null hypothesis Ho:

(b) μ ≤ μo

(a) Proves that Ho is true

(c) μ = μo

(b) Proves that Ho is false

(d) μ ≠ μo

(c) Implies that Ho is likely to be true (d) Proves that μ ≤ 0 In fact, we don’t really know if it’s true, we only know that Ha is false. If we want to prove otherwise we would have to test Ha and Ho the other way around.

Which of the following is composite hypothesis?

The composite hypothesis is used when we want to partitionate the parameter space. MCQ 13.46 P (Type I error) is equal to:

(a) 1 – α

MCQ 13.51

(b) 1 – β

Student’s t-test is applicable only when:

(c) α

(a) n≤30 and σ is known

(d) β

(b) n>30 and σ is unknown

Alfa also means level of signifance which is related to the type one error.

(c) n=30 and σ is known

MCQ 13.47 P (Type II error) is equal to: (a) α (b) β (c) 1 – α (d) 1 – β MCQ 13.48 The power of the test is equal to: (a) α (b) β

(d) All of the above If the variance known, we should use Z. MCQ 13.52 Student’s t-statistic is applicable in case of: (a) Equal number of samples (b) Unequal number of samples (c) Small samples (d) All of the above We must use t-statistics when the n is very low. MCQ 13.53

(c) 1 – α

Paired t-test is applicable when the observations in the two samples are:

(d) 1 – β

(a) Equal in number

The power of a test is the probability of rejecting Ho when its false.

(b) Paired

MCQ 13.49 The degree of confidence is equal to: (a) α

(c) Correlation (d) All of the above MCQ 13.54

(b) β

The degree of freedom for paired t-test based on n pairs of observations is:

(c) 1 – α

(a) 2n - 1

(d) 1 – β

(b) n - 2

MCQ 13.50

(c) 2(n - 1)

α / 2 is called:

(d) n – 1

(a) One tailed significance level

v= n-1

(b) Two tailed significance level

MCQ 13.55

(c) Left tailed significance level

The test-statistic has df = ________:

(d) Right tailed significance level

(a) n

α / 2 is for two tailed tests because the significance level must be shared between the two critical values.

(b) n - 1

(c) n - 2

(d) Coefficient of variation

(d) n1 + n2 – 2

The standard error is the standard deviation over the n root squared.

v = n-1 MCQ 13.56 In an unpaired samples t-test with sample sizes n1= 11 and n2= 11, the value of tabulated t should be obtained for:

MCQ 13.60 Student’s t-distribution has (n-1) d.f. when all the n observations in the sample are: (a) Dependent

(a) 10 degrees of freedom

(b) Independent

(b) 21 degrees of freedom

(c) Maximum

(c) 22 degrees of freedom

(d) Minimum

(d) 20 degrees of freedom

MCQ 13.61

Only if the variances are equal.

The number of independent values in a set of values is called:

MCQ 13.57 In analyzing the results of an experiment involving seven paired samples, tabulated t should be obtained for: (a) 13 degrees of freedom (b) 6 degrees of freedom (c) 12 degrees of freedom (d) 14 degrees of freedom v=n-1=7-1=6 MCQ 13.58 The mean difference between 16 paired observations is 25 and the standard deviation of differences is 10. The value of statistic-t is: (a) 4 (b) 10 (c) 16 (d) 25 MCQ 13.59 Statistic-t is defined as deviation of sample mean from population mean μ expressed in terms of: (a) Standard deviation (b) Standard error (c) Coefficient of standard deviation

(a) Test-statistic (b) Degree of freedom (c) Level of significance (d) Level of confidence The degree of freedom is v=n-1 MCQ 13.62 The purpose of statistical inference is: (a) To collect sample data and use them to formulate hypotheses about a population (b) To draw conclusion about populations and then collect sample data to support the conclusions (c) To draw conclusions about populations from sample data (d) To draw conclusions about the known value of population parameter We can estimate the parameters from the sample data. MCQ 13.63 Suppose that the null hypothesis is true and it is rejected, is known as: (a) A type-I error, and its probability is β (b) A type-I error, and its probability is α (c) A type-II error, and its probability is α

(d) A type-Il error, and its probability is β It’s alfa because it correponds to he first error. MCQ 13.64 An advertising agency wants to test the hypothesis that the proportion of adults in Pakistan who read a Sunday Magazine is 25 percent. The null hypothesis is that the proportion reading the Sunday Magazine is:

(d) As the t-distribution with n1 + n2 - 2 degrees of freedom When two populations are normal, the difference between them is also going to be normal. MCQ 13.67 If the population proportion equals po, then is distributed:

(a) Different from 25%

(a) As a standard normal variable, if n > 30

(b) Equal to 25%

(b) As a Poisson variable

(c) Less than 25 %

(c) As the t-distribution with v= n 1 degrees of freedom

(d) More than 25 % As the alternative hypothesis never carries the equality, the null must be equal to 25%.

(d) As a distribution with v degrees of freedom If the variance is unknown, we could use t.

MCQ 13.65

MCQ 13.68

If the mean of a particular population is μo, is distributed:

When σ is known, the hypothesis about population mean is tested by:

(a) As a standard normal variable, if the population is non-normal

(a) t-test

(b) As a standard normal variable, if the sample is large

(c) χ2-test

(c) As a standard normal variable, if the population is normal (d) As the t-distribution with v = n - 1 degrees of freedom According to the central limit theorem, if any sample is big enough it would be destributed normal.

(b) Z-test

(d) F-test If unknown we use t. MCQ 13.69 Given μo = 130, 𝑥̅ = 150, σ = 25 and n = 4; what test statistics is appropriate? (a) t

MCQ 13.66

(b) Z

If μ1 and μ2 are means of two populations, is distributed:

(c) χ2

(a) As a standard normal variable, if both samples are independent and less than 30

Because we know the variance

(b) As a standard normal variable, if both populations are normal (c) As both (a) and (b) state

(d) F

MCQ 13.70 Given Ho: μ = μo, H1: μ ≠ μo, α = 0.05 and we reject Ho; the absolute value of the Z-statistic must have equaled or been beyond what value? (a) 1.96 (b) 1.65

(c) 2.58 (d) 2.33 z(alfa/2)=t(.025)=2.58

MCQ 13.71 If 𝜋1 and 𝜋2 are not identical, then standard error of the difference of proportions (𝜋1 − 𝜋2 ) is: 𝜎∆𝜋 = √

𝑝𝑞 𝑝𝑞 + 𝑛 𝑛

MCQ 13.72 Under the hypothesis 𝐻0 : 𝜋1 = 𝜋2 , the formula for the standard error of the difference between proportions (𝜋1 − 𝜋2 ) is: 1 1 𝜎∆𝜋 = √𝑝𝑞( + ) 𝑛 𝑛

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MCQ 13.4

A statement about a population developed for the purpose of testing is called:

Any statement whose validity is tested on the basis of a sample is called:

(a) Hypothesis

(a) Null hypothesis

(b) Hypothesis testing

(b) Alternative hypothesis

(c) Level of significance

(c) Statistical hypothesis

(d) Test-statistic

(b) Simple hypothesis

The hypothesis is the supposition that we want to test.

In the statistical hypothesis we receive most of the parameters, so we can test a sample within those parameters.

MCQ 13.2 Any hypothesis which is tested for the purpose of rejection under the assumption that it is true is called:

MCQ 13.5

(a) Null hypothesis

(a) Research hypothesis

(b) Alternative hypothesis

(b) Composite hypothesis

(c) Statistical hypothesis

(c) Simple hypothesis

(d) Composite hypothesis

(d) Statistical hypothesis

The Null hypothesis serves as counter-weight in order to prove the alternative hypothesis.

A statistical hypothesis is an assumption about a population parameter

MCQ 13.3

MCQ 13.6

A statement about the value of a population parameter is called:

A statement that is accepted if the sample data provide sufficient evidence that the null hypothesis is false is called:

(a) Null hypothesis

A quantitative statement about a population is called:

(b) Alternative hypothesis

(a) Simple hypothesis

(c) Simple hypothesis

(b) Composite hypothesis

(d) Composite hypothesis

(c) Statistical hypothesis

In the null hypothesis we do not have all the parameters so we try to approximate it.

(d) Alternative hypothesis The alternative hypothesis is the one that we want prove

(d) None of the above

The alternative hypothesis is also called:

It’s simple hypothesis because in its included a parameter in the statement

(a) Null hypothesis

MCQ 13.11

(b) Statistical hypothesis

A hypothesis may be classified as:

MCQ 13.7

(c) Research hypothesis

(a) Simple

(d) Simple hypothesis

(b) Composite

The research hypothesis is the assumption upon the outcome of an experiment.

(c) Null

MCQ 13.8

The simple and the composite are types of hypothesis based on the information used in the statement.

A hypothesis that specifies all the values of parameter is called: (a) Simple hypothesis (b) Composite hypothesis (c) Statistical hypothesis (d) None of the above

(d) All of the above

MCQ 13.12 The probability of rejecting the null hypothesis when it is true is called: (a) Level of confidence (b) Level of significance

From the simple hypothesis we can prove samples.

(c) Power of the test

MCQ 13.9

(d) Difficult to tell

The hypothesis μ ≤ 10 is a:

The level of confidence is used to calculate the critical value.

(a) Simple hypothesis (b) Composite hypothesis (c) Alternative hypothesis (d) Difficult to tell.

MCQ 13.13 The dividing point between the region where the null hypothesis is rejected and the region where it is not rejected is said to be:

Because in order to describe the hypothesis we must have more information.

(a) Critical region

MCQ 13.10

(c) Acceptance region

If a hypothesis specifies the population distribution is called:

(d) Significant region

(b) Critical value

(a) Simple hypothesis

The critical value defines the regions of acceptance and rejection.

(b) Composite hypothesis

MCQ 13.14

(c) Alternative hypothesis

If the critical region is located equally in both sides of the sampling distribution of test-statistic, the test is called:

(d) All of the above

(a) One tailed

As we base our decisions in the alternative hypothesis, the value that we want to test is on the left side.

(b) Two tailed

MCQ 13.18

(c) Right tailed

Testing Ho: μ = 25 against H1: μ ≠ 20 leads to:

(d) Left tailed

(a) Two-tailed test

We use two tail when our null hypothesis states an (b) Left-tailed test equality. (c) Right-tailed test MCQ 13.15 (d) Neither (a), (b) and (c) The choice of one-tailed test and two-tailed test depends upon:

As we are testing an equality, we must search for the experimental value in both sides.

(a) Null hypothesis

MCQ 13.19

(b) Alternative hypothesis (c) None of these

A rule or formula that provides a basis for testing a null hypothesis is called:

(d) Composite hypotheses

(a) Test-statistic

In the alternative we base our decisions because it’s the one that we want to succeed.

(b) Population statistic

MCQ 13.16

(d) None of the above

Test of hypothesis Ho: μ = 50 against H1: μ > 50 leads to:

It’s also called hypothesis test, and it helps us to know if our approximation is correct.

(a) Left-tailed test

MCQ 13.20

(b) Right-tailed test

The range of test statistic-Z is:

(c) Two-tailed test

(a) 0 to 1

(d) Difficult to tell

(b) -1 to +1

Because we want to know if the value is going to be beyond the critical value on the right side.

(c) 0 to ∞

MCQ 13.17 Test of hypothesis Ho: μ = 20 against H1: μ < 20 leads to:

(c) Both of these

(d) -∞ to +∞ The tails never touch the x vertex. MCQ 13.21

(a) Right one-sided test

The range of test statistic-t is:

(b) Left one-sided test

(a) 0 to ∞

(c) Two-sided test

(b) 0 to 1

(c) -∞ to +∞

(c) Best decision

(d) -1 to +1

(d) All of the above

The t student follows the same principle of that of the Z.

Is when we do not accept as correct that in fact is correct.

MCQ 13.22

MCQ 13.26

If Ho is true and we reject it is called:

1 – α is also called:

(a) Type-I error (b) Type-II error (c) Standard error (d) Sampling error

(a) Confidence coefficient (b) Power of the test (c) Size of the test (d) Level of significance

Is the alfa error

The confidence coefficient is the complement of the level of significance.

MCQ 13.23

MCQ 13.27

The probability associated with committing type-I error is:

1 – α is the probability associated with:

(a) β

(a) Type-I error (b) Type-II error

(b) α

(c) Level of confidence

(c) 1 – β

(d) Level of significance

(d) 1 – α

The level of confidence is calculated as 1 minus alfa.

MCQ 13.24

MCQ 13.28

A failing student is passed by an examiner, it is an example of:

Area of the rejection region depends on:

(a) Type-I error

(b) Size of β

(b) Type-II error

(c) Test-statistic

(c) Unbiased decision

(d) Number of values

(d) Difficult to tell

The size of alfa is based on the level of confidence we want to achieve.

It’s the most tragic error, and it happens when we accept something wrong as correct.

(a) Size of α

MCQ 13.29

MCQ 13.25

Size of critical region is known as:

A passing student is failed by an examiner, it is an example of:

(a) β

(a) Type-I error

(c) Critical value

(b) Type-II error

(d) Size of the test

(b) 1 - β

The size of the test is where we can accept the null hypothesis.

As the level of significance is a probability, the level o significance must lie between 0 and 1.

MCQ 13.30

MCQ 13.34

A null hypothesis is rejected if the value of a test statistic lies in the:

Critical region is also called:

(a) Rejection region (b) Acceptance region (c) Both (a) and (b) (d) Neither (a) nor (b)

(a) Acceptance region (b) Rejection region (c) Confidence region (d) Statistical region

The rejection region is were alfa is.

The rejection region goes from the critical value to infinite.

MCQ 13.31

MCQ 13.35

The test statistic is equal to:

The probability of rejecting Ho when it is false is called:

(a)

𝑠𝑎𝑚𝑝𝑙𝑒−𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑒𝑟𝑟𝑜𝑟

(a) Power of the test

𝒔𝒂𝒎𝒑𝒍𝒆 𝒔𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄𝒔−𝒑𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏

(b) 𝒔𝒕𝒂𝒏𝒅𝒂𝒓𝒅 𝒆𝒓𝒓𝒐𝒓 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄𝒔 (c)

𝑠𝑎𝑚𝑝𝑙𝑒 𝑚𝑒𝑎𝑛 −𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑚𝑒𝑎𝑛

(b) Size of the test (c) Level of confidence

𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑒𝑟𝑟𝑜𝑟 𝑆𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐𝑠−𝐸(𝑆𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐𝑠)

(d) 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑆𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐𝑠

(d) Confidence coefficient

The test statistics is divided over the standard error of the statistics.

The power of a test is also called statistical power and it refers to the probability the test correctly rejects the null hypothesis.

MCQ 13.32

MCQ 13.36

Level of significance is also called: (a) Power of the test (b) Size of the test (c) Level of confidence (d) Confidence coefficient The size of the test tells us how big is going to be the rejection area.

MCQ 13.33 Level of significance α lies between: (a) -1 and +1 (b) 0 and 1 (c) 0 and n (d) -∞ to +∞

Power of a test is related to: (a) Type-I error (b) Type-II error (c) Both (a) and (b) (d) Neither (a) and (b) Because as we reject Ho when its false we assure to prove correct Ha. MCQ 13.37 In testing hypothesis α + β is always equal to: (a) One (b) Zero (c) Two (d) Difficult to tell

The two types of errors are complements.

MCQ 13.42

MCQ 13.38

The chance of rejecting a true hypothesis decreases when sample size is:

The significance level is the risk of: (a) Rejecting Ho when Ho is correct (b) Rejecting Ho when H1 is correct (c) Rejecting H1 when H1 is correct (d) Accepting Ho when Ho is correct. As the significance level goes narrower, the probability of having the first type of error increases. MCQ 13.39 An example in a two-sided alternative hypothesis is:

(a) Decreased (b) Increased (c) Constant (d) Both (a) and (b) As we get more data, we can get closer to the parameters. MCQ 13.43 The equality condition always appears in:

(a) H1: μ < 0

(a) Null hypothesis

(b) H1: μ > 0

(b) Simple hypothesis

(c) H1: μ ≥ 0

(c) Alternative hypothesis

(d) H1: μ ≠ 0

(d) Both (a) and (b)

The two sided hypothesis is used when an equality is tested.

My teacher told me. MCQ 13.44

MCQ 13.40

Which hypothesis is always in an inequality form?

If the magnitude of calculated value of t is less than the tabulated value of t and H1 is two-sided, we should:

(a) Null hypothesis

(a) Reject Ho (b) Accept H1 (c) Not reject Ho (d) Difficult to tell

(b) Alternative hypothesis (c) Simple hypothesis (d) Composite hypothesis If the null hypothesis is always is presented as the equality, the alternative hypothesis must the contrary.

We cannot reject Ho because it would lie in the test region.

MCQ 13.45

MCQ 13.41

(a) μ ≥ μo

Accepting a null hypothesis Ho:

(b) μ ≤ μo

(a) Proves that Ho is true

(c) μ = μo

(b) Proves that Ho is false

(d) μ ≠ μo

(c) Implies that Ho is likely to be true (d) Proves that μ ≤ 0 In fact, we don’t really know if it’s true, we only know that Ha is false. If we want to prove otherwise we would have to test Ha and Ho the other way around.

Which of the following is composite hypothesis?

The composite hypothesis is used when we want to partitionate the parameter space. MCQ 13.46 P (Type I error) is equal to:

(a) 1 – α

MCQ 13.51

(b) 1 – β

Student’s t-test is applicable only when:

(c) α

(a) n≤30 and σ is known

(d) β

(b) n>30 and σ is unknown

Alfa also means level of signifance which is related to the type one error.

(c) n=30 and σ is known

MCQ 13.47 P (Type II error) is equal to: (a) α (b) β (c) 1 – α (d) 1 – β MCQ 13.48 The power of the test is equal to: (a) α (b) β

(d) All of the above If the variance known, we should use Z. MCQ 13.52 Student’s t-statistic is applicable in case of: (a) Equal number of samples (b) Unequal number of samples (c) Small samples (d) All of the above We must use t-statistics when the n is very low. MCQ 13.53

(c) 1 – α

Paired t-test is applicable when the observations in the two samples are:

(d) 1 – β

(a) Equal in number

The power of a test is the probability of rejecting Ho when its false.

(b) Paired

MCQ 13.49 The degree of confidence is equal to: (a) α

(c) Correlation (d) All of the above MCQ 13.54

(b) β

The degree of freedom for paired t-test based on n pairs of observations is:

(c) 1 – α

(a) 2n - 1

(d) 1 – β

(b) n - 2

MCQ 13.50

(c) 2(n - 1)

α / 2 is called:

(d) n – 1

(a) One tailed significance level

v= n-1

(b) Two tailed significance level

MCQ 13.55

(c) Left tailed significance level

The test-statistic has df = ________:

(d) Right tailed significance level

(a) n

α / 2 is for two tailed tests because the significance level must be shared between the two critical values.

(b) n - 1

(c) n - 2

(d) Coefficient of variation

(d) n1 + n2 – 2

The standard error is the standard deviation over the n root squared.

v = n-1 MCQ 13.56 In an unpaired samples t-test with sample sizes n1= 11 and n2= 11, the value of tabulated t should be obtained for:

MCQ 13.60 Student’s t-distribution has (n-1) d.f. when all the n observations in the sample are: (a) Dependent

(a) 10 degrees of freedom

(b) Independent

(b) 21 degrees of freedom

(c) Maximum

(c) 22 degrees of freedom

(d) Minimum

(d) 20 degrees of freedom

MCQ 13.61

Only if the variances are equal.

The number of independent values in a set of values is called:

MCQ 13.57 In analyzing the results of an experiment involving seven paired samples, tabulated t should be obtained for: (a) 13 degrees of freedom (b) 6 degrees of freedom (c) 12 degrees of freedom (d) 14 degrees of freedom v=n-1=7-1=6 MCQ 13.58 The mean difference between 16 paired observations is 25 and the standard deviation of differences is 10. The value of statistic-t is: (a) 4 (b) 10 (c) 16 (d) 25 MCQ 13.59 Statistic-t is defined as deviation of sample mean from population mean μ expressed in terms of: (a) Standard deviation (b) Standard error (c) Coefficient of standard deviation

(a) Test-statistic (b) Degree of freedom (c) Level of significance (d) Level of confidence The degree of freedom is v=n-1 MCQ 13.62 The purpose of statistical inference is: (a) To collect sample data and use them to formulate hypotheses about a population (b) To draw conclusion about populations and then collect sample data to support the conclusions (c) To draw conclusions about populations from sample data (d) To draw conclusions about the known value of population parameter We can estimate the parameters from the sample data. MCQ 13.63 Suppose that the null hypothesis is true and it is rejected, is known as: (a) A type-I error, and its probability is β (b) A type-I error, and its probability is α (c) A type-II error, and its probability is α

(d) A type-Il error, and its probability is β It’s alfa because it correponds to he first error. MCQ 13.64 An advertising agency wants to test the hypothesis that the proportion of adults in Pakistan who read a Sunday Magazine is 25 percent. The null hypothesis is that the proportion reading the Sunday Magazine is:

(d) As the t-distribution with n1 + n2 - 2 degrees of freedom When two populations are normal, the difference between them is also going to be normal. MCQ 13.67 If the population proportion equals po, then is distributed:

(a) Different from 25%

(a) As a standard normal variable, if n > 30

(b) Equal to 25%

(b) As a Poisson variable

(c) Less than 25 %

(c) As the t-distribution with v= n 1 degrees of freedom

(d) More than 25 % As the alternative hypothesis never carries the equality, the null must be equal to 25%.

(d) As a distribution with v degrees of freedom If the variance is unknown, we could use t.

MCQ 13.65

MCQ 13.68

If the mean of a particular population is μo, is distributed:

When σ is known, the hypothesis about population mean is tested by:

(a) As a standard normal variable, if the population is non-normal

(a) t-test

(b) As a standard normal variable, if the sample is large

(c) χ2-test

(c) As a standard normal variable, if the population is normal (d) As the t-distribution with v = n - 1 degrees of freedom According to the central limit theorem, if any sample is big enough it would be destributed normal.

(b) Z-test

(d) F-test If unknown we use t. MCQ 13.69 Given μo = 130, 𝑥̅ = 150, σ = 25 and n = 4; what test statistics is appropriate? (a) t

MCQ 13.66

(b) Z

If μ1 and μ2 are means of two populations, is distributed:

(c) χ2

(a) As a standard normal variable, if both samples are independent and less than 30

Because we know the variance

(b) As a standard normal variable, if both populations are normal (c) As both (a) and (b) state

(d) F

MCQ 13.70 Given Ho: μ = μo, H1: μ ≠ μo, α = 0.05 and we reject Ho; the absolute value of the Z-statistic must have equaled or been beyond what value? (a) 1.96 (b) 1.65

(c) 2.58 (d) 2.33 z(alfa/2)=t(.025)=2.58

MCQ 13.71 If 𝜋1 and 𝜋2 are not identical, then standard error of the difference of proportions (𝜋1 − 𝜋2 ) is: 𝜎∆𝜋 = √

𝑝𝑞 𝑝𝑞 + 𝑛 𝑛

MCQ 13.72 Under the hypothesis 𝐻0 : 𝜋1 = 𝜋2 , the formula for the standard error of the difference between proportions (𝜋1 − 𝜋2 ) is: 1 1 𝜎∆𝜋 = √𝑝𝑞( + ) 𝑛 𝑛

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