Question 1

In hypothesis testing, what does the p-value represent?

Accepted Answer

The probability of observing data as extreme as the sample, assuming the null hypothesis is true.

Question 2

Why do statisticians say 'fail to reject' the null hypothesis ($$H_0) $$instead of 'accept' it?

Accepted Answer

Because the test may lack power to detect a real effect, so we cannot confirm $$H_0 is $$true.

Question 3

A researcher obtains a p-value of $$0.044 in a $$test with $$\alpha = 0.05. $$What is the correct interpretation?

Accepted Answer

The result is statistically significant, and we reject $$H_0.$$

Question 4

Which of the following best describes the difference between p-value and effect size?

Accepted Answer

P-value measures statistical significance; effect size measures the magnitude of the effect.

Question 5

A study with a large sample size ($$n) $$finds a very small p-value. What is a potential misconception about this result?

Accepted Answer

A small p-value may result from a large sample size, not necessarily a large effect.

Question 6

What is the formula for the power of a statistical test?

Accepted Answer

$$\text{Power} = 1 - \beta$$

Question 7

In a medical study, the probability of incorrectly rejecting the null hypothesis ($$H_0) is $$called:

Accepted Answer

Type I error ($$\alpha)$$

Question 8

If the p-value is less than the significance level ($$\alpha$$), what should you do?

Accepted Answer

Reject the null hypothesis.

Question 9

Which statement about p-values is FALSE?

Accepted Answer

A p-value tells you the probability that $$H_0 is $$true.

Question 10

A pharmaceutical company tests a new drug and gets a p-value of $$0.051$$ with $$\alpha = 0.05. $$What is the correct statistical decision?

Accepted Answer

Fail to reject the null hypothesis.

Question 11

Which of the following best describes the relationship between sample size ($$n) $$and statistical power?

Accepted Answer

Increasing $$n$$ increases power.

Question 12

In hypothesis testing, what is the consequence of setting a very low significance level ($$\alpha$$)?

Accepted Answer

It decreases the probability of Type I error but may increase Type II error.

Question 13

A researcher is confused between p-value and power. Which statement clarifies their difference?

Accepted Answer

P-value is calculated under $$H_0$$; power is calculated under $$H_1.$$

Question 14

Which scenario illustrates a Type II error ($$\beta$$)?

Accepted Answer

A test fails to reject $$H_0$$ when $$H_1 is $$actually true.

Question 15

In a Z-test, which formula correctly calculates the Z statistic for a sample mean?

Accepted Answer

$$Z = \frac{\bar{X} - \mu_0$}{\frac{\sigma}{\sqrt{n}}}$$

Question 16

A scientist claims that a p-value of $$0.01$$ means the effect is large. What is the flaw in this reasoning?

Accepted Answer

A small p-value only indicates statistical significance, not effect size.

Question 17

Which of the following is NOT a reason why a p-value just below $$\alpha (e.g$$., $$0.044 vs$$ $$0.051) $$should be interpreted with caution?

Accepted Answer

A p-value below $$\alpha$$ always means a large effect.

Question 18

In a clinical trial, what does 'power' ($$1 - \beta) $$represent?

Accepted Answer

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

Question 19

A researcher increases the sample size in an experiment. What is the most likely effect on the p-value and power?

Accepted Answer

The p-value decreases and power increases.

Question 20

Which of the following best explains why a p-value is not the probability that the null hypothesis is true?

Accepted Answer

The p-value is calculated assuming the null hypothesis is true.

Hypothesis Testing: Understanding p-values, Alpha, and Power

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