Hypothesis Testing Flashcards

A researcher tests 20 independent hypotheses at α = 0.05 and finds 2 significant results. What concern does this raise?

Answer: Multiple comparisons inflate the chance of at least one Type I error.

Testing many hypotheses at α = 0.05 means about 5% will appear significant by chance alone, raising false-positive concerns.

The conditions for a two-sample z-test for proportions include all of the following EXCEPT:

Answer: The populations are normally distributed.

For proportions, normality of the population is not required; the large-counts condition ensures normality of the sampling distribution.

For a left-tailed test with test statistic t = −2.1 and df = 24, which p-value range is correct?

Answer: 0.01 < p < 0.025

Using a t-table with df = 24, t = −2.1 falls between critical values for 0.025 and 0.01 in the left tail.

A researcher increases the sample size of a study without changing any other aspect. Which of the following is most likely to occur?

Answer: The p-value for a true effect will decrease.

Larger samples produce smaller standard errors and larger test statistics for true effects, leading to smaller p-values.

Which is the correct set of hypotheses to test whether a new drug reduces average recovery time below 10 days?

Answer: H₀: μ = 10, Hₐ: μ < 10

The research claim (reduces time below 10) becomes the one-sided alternative Hₐ: μ < 10, with H₀ as the status quo.

A chi-square test statistic is always:

Answer: Non-negative.

Chi-square statistics are computed as sums of squared terms divided by expected values, so they are always ≥ 0.

A 95% confidence interval for the difference in two proportions is (0.03, 0.17). What does a two-sided test at α = 0.05 conclude about H₀: p₁ − p₂ = 0?

Answer: Reject H₀ because 0 is not in the interval.

Because 0 lies outside the 95% CI (0.03, 0.17), we reject H₀ at α = 0.05 — the proportions differ significantly.