Multiple Choice Questions from Statistical Inference for the preparation of exam and different statistical job tests in Government/ Semi-Government or Private Organization sectors. These tests are also helpful in getting admission in different colleges and Universities.

Most of the MCQs on this page are covered from Estimate and Estimation, Testing of Hypothesis, Parametric and Non-Parametric tests etc.

**Question 1:** In hypothesis testing, type II error is represented by $\beta$ and the power of the test is $1-\beta$ then

A) The probability of rejecting $H_0$ when $H_1$ is true

B) The probability of failing to reject $H_0$ when $H_1$ is true

C) The probability of failing to reject $H_0$ when $H_0$ is true

D) The probability of rejecting $H_0$ when $H_0$ is true

E) The probability of failing to reject $H_0$

**Question 2:** In statistical testing of hypothesis, what happens to the region of rejection when the level of significance $\alpha$ is reduced?

A) The answer depends on the value of $\beta$

B) The rejection region is reduced in size

C) The rejection region is increased in size

D) The rejection region is unaltered

E) The answer depends on the form of the alternative hypothesis

**Question 3**: Which of the following is NOT correct?

A) The probability of a type I error is controlled by the selection of the level of significance $\alpha$

B) The probability of a type II error is controlled by the sample size $(n)$

C) The power of a test depends upon the sample size and the distance between the null hypothesis and the alternative hypothesis

D) the $p$-value measures the probability that the null hypothesis is true

E) The rejection region is controlled by the $\alpha$ and the alternative hypothesis

**Question** **4:** In testing the statistical hypothesis, which of the following statement(s) is false?

A) The critical region is the values of the test statistic for which we reject the null hypothesis

B) The level of significance is the probability of type I error

C) For testing $H_0:\mu=\mu_0$, $H_1:\mu>\mu_0$, we reject $H_0$ for high values of the sample mean $\overline{X}$

D) In testing $H_0:\mu=\mu_0$, $H_1:\mu \ne \mu_0$, the critical region is two sided.

E) The $p$-value measures the probability that the null hypothesis is true

**Question** **5:** Since $\alpha=$ probability of type I error then $1-\alpha$

A) Probability of rejecting $H_0$ when $H_0$ is true

B) Probability of not rejecting $H_0$ when $H_0$ is true

C) Probability of not rejecting $H_0$ when $H_1$ is true

D) Probability of rejecting $H_0$ when $H_1$ is true

E) $1-\beta$

**Question** **6:** In statistical hypothesis test of equality of means, such as $H_0:\mu=10$, if $\alpha=5\%$

A) 95% of the time we will make an incorrect inference

B) 5% of the time we will say that there is a real difference when there is no difference (Type I error)

C) 5% of the time we will say that there is no real difference when there is a difference (Type II error)

D) 95% of the time the null hypothesis will be correct

E) 5% of the time we will make a correct inference

**Question** **7:** Which of the following statements is correct

A) An extremely small p-value indicates that the actual data different significantly from the expected if the null hypothesis is true

B) The p-value measures the probability that the hypothesis is true

C) The p-value measures the probability of making a Type II error

D) The larger the p-value, the stronger the evidence against the null hypothesis

E) A large p-value indicates that the data is consistent with the alternative hypothesis

**Question** **8:** The average growth of a certain variety of pine tree is 10.1 inches in three years. A biologist claims that a new variety will have a greater three-year growth. A random sample of 25 of the new variety has an average three-year growth of 10.8 inches and a standard deviation of 2.1 inches. The appropriate null and alternate hypotheses to test the biologist’s claim are:

A) $H: \mu = 10.8$ against $H_a: \mu > 10.8$

B) $H: \mu = 10.8$ against $H_a: \mu \ne 10.8$

C) $H: \mu = 10.1$ against $H_a: \mu > 10.1$

D) $H: \mu = 10.1$ against $H_a: \mu < 10.1$

E) $H: \mu = 10.1$ against $H_a: \mu \ne 10.1$

**Question** **9:** Since $\alpha$= probability of Type I error, then $1 -\alpha$

A) Probability of rejecting $H_0$ when $H_0$ is true

B) Probability of not rejecting $H_0$ when $H_0$ is true

C) Probability of not rejecting $H_0$ when $H_a$ is true

D) Probability of rejecting $H_0$ when $H_a$ is true

E) $1 – \beta$

**Question** **10:** The following are percentages of fat found in 5 samples of each of two brands of baby food:

A: 5.7, 4.5, 6.2, 6.3, 7.3

B: 6.3, 5.7, 5.9, 6.4, 5.1

Which of he following procedures is appropriate to test the hypothesis of equal average fat content in the two types of ice cream?

A) Paired $t$-test with 5 d.f

B) Two sample $t$-test with 8 d.f

C) Paired $t$-test with 4 d.f

D) Two sample $t$-test with 9 d.f

E) Sign test

**Download MCQ Hypothesis Testing pdf file with Answers **
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**MCQ Hypothesis Testing 83.49 KB**

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Pls post some mcq with answers on doe

Thanks for commenting.

soon will update mcqs on Design of Experiment (DOE).

Keep sharing and visiting the site.

i am appearing in cssbb exam this year.pls help me by providing questions mainly on control charts ,doe and other relavent topics

You can download all available questions. On control charts, doe I have not written any thing yet related to MCQs.

Hi sir my name is shravan kumar shukla pls send me objective problem on probability , random variable , estimation inference with solution on my gmail account.

You can download from site. approximately all are in pdf form.

Sir, kindly put up some questions regarding estimation of type I and type II error.

hope soon will update about type-I and type-II errors

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