Significance Test Basics

The mean time it takes for a person to experience pain relief from aspirin is 25 minutes. A new ingredient is added to help speed up relief. Let µ denote the mean time to obtain pain relief with the new product. An experiment is conducted to verify if the new product works more quickly. What are the null and alternative hypotheses for the appropriate test of significance?

• H0 : µ = 25 vs. Ha : µ ≠ 25

• H0 : µ = 25 vs. Ha : µ < 25

• H0 : µ < 25 vs. Ha : µ = 25

• H0 : µ < 25 vs. Ha : µ > 25

• H0 : µ = 25 vs. Ha : µ > 25

A test of H₀: µ=60 versus H_a: µ≠60 produces a sample mean of x-bar = 58 and a P-value of 0.04. At an α = 0.05 level, which of the following is an appropriate conclusion?

• There is sufficient evidence to conclude that µ < 60.

• There is sufficient evidence to conclude that µ = 60.

• There is insufficient evidence to conclude that µ = 60.

• There is insufficient evidence to conclude that µ ≠ 60

• There is sufficient evidence to conclude that µ ≠ 60.

When performing a significance test, we're looking for convincing evidence to __________ the null hypothesis in favor of the alternative hypothesis.

• refute

• dispute

• reject

• accept

Small p-values mean that our sample was very unlikely if the null hypothesis is true. Therefore, small p-values are ________________ that the null hypothesis is wrong.

• convincing evidence

• believable proof

• reliable information

• justifiable inference

Whatever probability we choose as the cutoff for what is small is what we call the ____________________.

• importance level

• significance level

• meaningfulness level

• insightfulness level

The symbol for the significance level is ____.

• fail to reject, statistically significant

• reject, statistically significant

• fail to reject, not statistically significant

• reject, not statistically significant

Which of the following best describes a Type I error?

• The null is true, but we mistakenly reject it.
• The null is false and we reject it.
• The null is false, but we fail to reject it.
• The null is true but we fail to reject it.

What is the null hypothesis

• H_o: p = .39

• H_o: p < .39

• H_o: p > .39

• H_o: p ≠ .39

What is the alternative hypothesis?

• H_o: p = .39

• H_o: p < .39

• H_o: p > .39

• H_o: p ≠ .39