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# Probability and Statistics MCQ – Testing of Hypothesis Concerning Single Population Mean

What is the assumption made for performing the hypothesis test with T distribution?

a) the distribution is non-symmetric

b) the distribution has more than one modal class

c) the distribution has a constant variance

d) the distribution follows a normal distribution

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Answer: d

Explanation: For testing of Hypothesis with T distribution it is assumed that the distribution follows a normal distribution. The region is identified and hence based on the normal variate Hypothesis is accepted or rejected.

If a hypothesis is rejected at 0.6 Level of Significance then ______________

a) it will be rejected at any level

b) it must be rejected at 0.5 level

c) it may be rejected at 0.5 level

d) it cannot be rejected at 0.5 level

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Answer: c

Explanation: If the hypothesis is rejected at 0.6 Level of Significance then p < 0.6. Hence p can be less than 0.5 also. Therefore it may be rejected at 0.5 Level of Significance.

In a two tailed test when a Null Hypothesis is rejected for a True Alternative Hypothesis then it has ____________

a) Type 1 error

b) Type 2 error

c) No error

d) Many errors

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Answer: c

Explanation: In Testing of Hypothesis Type 1 error occurs when we reject a true Null Hypothesis. On the contrary a Type 2 error occurs when we accept a false Null Hypothesis. Hence if the Alternative Hypothesis is true and Null Hypothesis is rejected then no error occurs.

In a hypothesis test, what does the p value signify?

a) smallest level of significance for rejection of Null Hypothesis

b) largest level of significance for rejection of Null Hypothesis

c) smallest level of significance for acceptance of Null Hypothesis

d) smallest level of significance for acceptance of Null Hypothesis

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Answer: a

Explanation: In a Hypothesis, the p value signifies the smallest level of significance for rejection of Null Hypothesis. Below this value, for every value the hypothesis is rejected.

A Null Hypothesis has Level of Significance 9%. For what values of Level of Significances it will be rejected?

a) 0.99

b) 0.009

c) 0.099

d) 0.9

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Answer: b

Explanation: The Level of Significance of Null Hypothesis is 0.09. Hence the hypothesis will be rejected at values less than 0.09.

Consider a trial of a criminal. If a type 1 error has occurred in thee judgement then which of the following statement is true?

a) a guilty person is set free

b) an innocent person is convicted

c) a guilty person is convicted

d) an innocent person is set free

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Answer: b

Explanation: Type 1 error occurs when the Null hypothesis is True but rejected. Considering Null hypothesis as innocent person and setting free as acceptance an innocent person getting convicted is a type 1 error.

If a Null Hypothesis is accepted then the value of Test statistic lies in the ____________

a) Acceptance region

b) Rejection region

c) Critical region

d) Sample region

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Answer: a

Explanation: If a Null Hypothesis is accepted then the value of Test statistic lies in the Acceptance region. For a rejected Null Hypothesis the value lies in the Rejection region.

The Test Statistic for a Hypothesis testing is given by the formula ____________

a) Sample-Population/Standard Error

b) Sample statistic-Parameter/Standard Error

c) Sample mean-Population mean/Population standard deviation

d) Statistic-E(statistic)/Variance

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Answer: b

Explanation: The Test Statistic of a hypothesis is given as the Sample statistic-Parameter/Standard Error.

The Test statistic provides a basis for testing a Null Hypothesis.

The range of Level of Significance lies between ____________

a) -∞ and 0

b) -∞ and ∞

c) 0 and ∞

d) 0 and 1

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Answer: d

Explanation: The Level of Significance lies between 0 and 1. The 0 signifies the test is least significant and 1 signifies the test is most significant.

The effect of rejection of a hypothesis with decrease in sample size ____________

a) decreases

b) increases

c) remains constant

d) fluctuates

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Answer: b

Explanation: If n decreases then the value of Level of Significance of each sample α decreases. Hence 1-α increases which are called the rejection of test sample increases.

The composite hypothesis holds true when?

a) ϕ > ϕ0

b) ϕ < ϕ0 c) ϕ = ϕ0 d) ϕ >> ϕ0

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Answer: c

Explanation: The composite hypothesis holds true when the Null Hypothesis is equal to the Alternative Hypothesis. Hence ϕ = ϕ0. Here the value of α is 0.5.

A paired T test consists of n pairs of observations. What is the number of degrees of freedom of the test?

a) 2n-1

b) 2n

c) n-1

d) n

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Answer: c

Explanation: For a paired T distribution the no of degrees of Freedom are n-1 where n denotes the number of pairs of samples in the test.

Which of the following represents the Confidence coefficient?

a) 1-α

b) β

c) 1-β

d) α

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Answer: a

Explanation: The level of Confidence is represented by 1-α. It signifies the chance of the Alternative Hypothesis.

The independent values in a set of values of a test is called as?

a) Degrees of freedom

b) Test Statistic

c) Level of Significance

d) Level of Confidence

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Answer: a

Explanation: In a test, the number of individual samples is called as Degrees of Freedom. If a sample has n values then the Degrees of Freedom are n-1.

A T-test sample has 7 pairs of samples. The distribution should contain ____________

a) 16 degrees of freedom

b) 15 degrees of freedom

c) 5 degrees of freedom

d) 6 degrees of freedom

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Answer: d

Explanation: Here the number of samples, n is 7. Hence total degrees of Freedom is n-1 that is 7-1 = 6.