Hypothesis Testing Quiz | Online MCQs on Statistical Inference

1. Since $\alpha$= probability of Type I error, then $1 -\alpha$

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

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

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

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

$1 – \beta$

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

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

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

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

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

The probability of failing to reject $H_0$

3. The average growth of a certain variety of pine trees is 10.1 inches in three years. A biologist claims that a new variety will have 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 alternative hypotheses to test the biologist’s claim are:

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

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

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

$H: \mu = 10.1$ against $H_a: \mu

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

4. In statistical testing of the hypothesis, what happens to the region of rejection when the level of significance $\alpha$ is reduced?

The answer depends on the value of $\beta$

The rejection region is reduced in size

The rejection region is increased in size

The rejection region is unaltered

The answer depends on the form of the alternative hypothesis

5. In testing the statistical hypothesis, which of the following statement(s) is false?

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

The level of significance is the probability of type I error

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

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

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

6. Which of the following statements is correct

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

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

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

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

A large

Hypothesis Testing Quiz 3