A valid level-0.05 test has an actual Type I error probability of 0.03 under its null model. How should this be interpreted?

• The rate must be 0.05 for the test to have that level
• The rate determines the probability that H0 is true
• The rate is permitted because it is below the level bound
• The rate is the test's power at every alternative value

H0 says a production change leaves the population mean unchanged. The mean really is unchanged, but the test rejects H0. Which outcome occurred?

• Type I error
• Type II error
• Correct rejection

For a specified true parameter in the alternative, what is the power of a test?

• Its probability of rejecting a true null
• Its probability of rejecting the false null
• Its probability that the null itself is true

A planned lower-tail test fails to reject H0, although the true population mean is below the null value. This is a Type II error.

Two designs use the same target effect and level. Their calculated powers are 0.68 and 0.83. What is the increase in rejection probability from the first design to the second?

For the same normal-mean model, sample size and statistic, α rises from 0.01 to 0.05 using nested rejection regions. What is the trade-off?

• A higher allowed Type I rate and power that cannot decrease
• A lower allowed Type I rate and power that cannot increase
• An unchanged Type I bound because sample size stays fixed
• A higher chance that H0 itself becomes true in the population

A treatment study reports p = 0.3 at planned α = 0.05. This result by itself proves that the population treatment effect is exactly zero.

A lower-tail normal-mean test uses null mean 100. Hold n, α, population variance and sampling method fixed. The true mean moves from 98 to 94. What happens to power?

• It falls as the mean moves farther into the lower alternative
• It stays fixed because the significance level has not changed
• It rises as the mean moves farther into the lower alternative

At one specified alternative, 400 simulation runs include 64 failures to reject H0. Estimate power as a decimal.

A normal-mean test has planned power 0.55 for a target effect. The team must keep α = 0.05, the target effect, population variance and sampling method fixed. Which change can raise power?

• Increase independent sample size and recalculate planned power
• Reduce independent sample size and keep the same model inputs
• Keep sample size unchanged and increase the test level to 0.5