Statistical Significance and P Values Quiz

1. A p-value should be interpreted as:

The probability that the alternative hypothesis is true

The probability of observing the data under the null hypothesis

The effect size of the study

The confidence level of the estimate

2. A p-value of 0.50 in a hypothesis test suggests:

Strong evidence against the null hypothesis

Weak evidence against the null hypothesis

The null hypothesis is definitely true

The sample size is too large

3. The null hypothesis is rejected when the test statistic falls in the:

Acceptance region

Critical region

Confidence interval

Standard error

4. Which statement about p-values is correct?

A larger p-value provides stronger evidence against the null

P-values range from 0 to 1

P-values are always normally distributed

P-values depend only on the sample size

5. A confidence interval and hypothesis test are related because:

They use the same sample data and significance level

A 95% CI corresponds to a two-tailed test at α = 0.05

Both estimate the population parameter

They always produce the same conclusion

6. In a one-tailed test with α = 0.05, the critical region is entirely in:

Both tails equally

One tail only

The center of the distribution

Neither tail

7. The relationship between p-value and significance level is:

P-value is independent of α

Result is significant if p-value < α

α is always 0.05 regardless of p-value

P-value and α must be equal

8. A Type II error (β) occurs when:

We reject a true null hypothesis

We fail to reject a false null hypothesis

We set the significance level too high

The sample is not random

9. Statistical significance indicates that:

The result is practically important

The observed effect is unlikely due to chance alone

The null hypothesis is definitely false

The sample size is appropriate

10. If the p-value equals 0.06 and α = 0.05, you should:

Reject the null hypothesis

Fail to reject the null hypothesis

Accept the null hypothesis

Increase the sample size and retest

11. A p-value of 0.03 in a hypothesis test means:

There is a 3% probability the null hypothesis is true

There is a 3% probability of observing this data (or more extreme) if the null hypothesis is true

The alternative hypothesis is 97% likely to be correct

The sample mean differs from the population mean by 3%

12. Which factor increases the power of a hypothesis test?

Decreasing the sample size

Increasing the significance level α

Using a one-tailed test when appropriate

All of the above

13. The power of a statistical test is the probability of:

Rejecting a true null hypothesis

Rejecting a false null hypothesis

Correctly accepting the null hypothesis

Obtaining a p-value less than 0.05

14. A statistically significant result at p = 0.001 compared to p = 0.04 indicates:

Much stronger evidence against the null hypothesis

A larger effect size

A more important practical finding

A larger sample size was used

15. In a two-tailed test with α = 0.05, the critical region is split into:

0.05 in one tail only

0.025 in each tail

0.10 in each tail

0.05 in the center

16. A 95% confidence interval that does not contain the hypothesized value suggests:

The result is not statistically significant at α = 0.05

The result is statistically significant at α = 0.05

The sample size was too small

The population parameter equals the hypothesized value

17. Which p-value provides stronger evidence against the null hypothesis?

P = 0.15

P = 0.08

P = 0.02

P = 0.12

18. The significance level (α) represents:

The probability of making a Type II error

The maximum acceptable probability of making a Type I error

The strength of the relationship between variables

The sample size needed for the study

19. A Type I error occurs when: