Take this Quiz: A-Level Maths: Hypothesis Testing | Zestly

Question 1

In a hypothesis test, what does the 'significance level' represent?

Accepted Answer

The probability of rejecting the null hypothesis when it is actually true.

Question 2

A researcher tests a claim that a coin is biased towards heads. Let $p$ be the probability of landing on heads. Which pair of hypotheses is correct?

Accepted Answer

$H_0: p = 0.5, H_1: p > 0.5$

Question 3

Which of the following statements correctly describe the properties of a p-value in a hypothesis test?

Accepted Answer

It is the probability of obtaining results at least as extreme as the observed data, assuming the null hypothesis is true.

Question 4

When testing the mean $\mu$ of a Normal distribution with known variance $\sigma^2$, the test statistic $Z$ for a sample mean $\bar{X}$ of size $n$ is calculated as:

Answer

$Z = \frac{\bar{X} - \mu}{\sigma}$

Answer

$Z = \frac{\bar{X} - \mu}{\sigma^2}$

Answer

$Z = \frac{\bar{X} - \mu}{\sigma / \sqrt{n}}$

Answer

$Z = \frac{\bar{X} - \mu}{\sigma / n}$

Question 5

Which of the following are valid interpretations of 'failing to reject the null hypothesis'?

Answer

The null hypothesis has been proven true.

Answer

There is insufficient evidence to conclude that the alternative hypothesis is true.

Answer

The data is consistent with the null hypothesis.

Answer

The null hypothesis is definitely correct.