Hypothesis Testing Concepts

How is 'significance' defined in the context of hypothesis testing?

• The quality of being statistically significant

• The probability of accepting the null hypothesis

• The degree of accuracy in a study

• The likelihood of making a correct decision

Answer explanation

In hypothesis testing, 'significance' refers to the quality of being statistically significant, indicating that the results are unlikely to have occurred by chance. This makes the first choice the correct answer.

What does the 'level of significance', denoted by alpha (α), refer to in hypothesis testing?

• The probability of making a Type II error

• The degree of significance in which we accept or reject the null hypothesis

• The confidence interval of the study

• The sample size required for the test

Answer explanation

The 'level of significance' (α) indicates the threshold for deciding whether to reject the null hypothesis. It represents the probability of making a Type I error, thus guiding the acceptance or rejection of the null hypothesis.

What is impossible when accepting or rejecting a hypothesis?

• Achieving a significance level of 0.01

• Using a two-tailed test

• 100% accuracy

• Dividing alpha by 2

Answer explanation

In hypothesis testing, achieving 100% accuracy is not possible due to the inherent uncertainty and variability in data. We can only estimate the likelihood of results, not guarantee absolute correctness.

The significance level is also described as the probability of making what type of decision?

• Making a correct decision when the null hypothesis is false

• Making the wrong decision when the null hypothesis is true

• Making a correct decision when the alternative hypothesis is true

• Making the wrong decision when the alternative hypothesis is false

Answer explanation

The significance level represents the probability of making a Type I error, which is making the wrong decision when the null hypothesis is true. This is why the correct choice is 'Making the wrong decision when the null hypothesis is true'.

What is the usual alpha (α) level in public health research?

• 0.05 or 5%

• 0.10 or 10%

• 0.01 or 1%

• 0.001 or 0.1%

Answer explanation

In public health research, the usual alpha (α) level is set at 0.05 or 5%, but a more stringent level of 0.01 or 1% is often used to reduce the risk of Type I errors, making it the correct choice here.

What is the usual alpha (α) level in social science research?

• 0.01 or 1%

• 0.10 or 10%

• 0.05 or 5%

• 0.005 or 0.5%

Answer explanation

The usual alpha (α) level in social science research is 0.05 or 5%. This level indicates a 5% risk of concluding that a difference exists when there is none, making it a standard threshold for significance.

If the alpha level is 5%, what does this imply regarding the probability of rejecting a true null hypothesis?

• There is a 1% probability

• There is a 5% probability

• There is a 10% probability

• There is a 0.5% probability

Answer explanation

An alpha level of 5% indicates that there is a 5% probability of rejecting a true null hypothesis, which is known as the Type I error rate. Therefore, the correct choice is 'There is a 5% probability'.

When should the alpha (α) level be divided by 2?

• When the null hypothesis is accepted

• When the alternative hypothesis uses the 'not equal' symbol

• When the confidence interval is 99%

• When the sample size is less than 30

Answer explanation

The alpha (α) level should be divided by 2 when the alternative hypothesis uses the 'not equal' symbol, as this indicates a two-tailed test, requiring the significance level to be split between both tails.

If α = 0.01 and the alternative hypothesis uses 'not equal', what is the value of α/2?

• 0.01

• 0.005

• 0.02

• 0.05

Answer explanation

Since the alternative hypothesis is 'not equal', we split α into two tails. Thus, α/2 = 0.01/2 = 0.005. Therefore, the correct answer is 0.005.

If α = 0.05 and the alternative hypothesis uses 'not equal', what is the value of α/2?

• 0.05

• 0.01

• 0.025

• 0.10

Answer explanation

Since the alternative hypothesis is 'not equal', we split α into two tails. Thus, α/2 = 0.05/2 = 0.025. Therefore, the correct answer is 0.025.