Hypothesis Testing Flashcards

A school claims its average SAT score is 1100. A sample of 36 students yields x̄ = 1080 and s = 90. What is the test statistic for a one-sample t-test?

Answer: t = −1.33

t = (1080 − 1100) / (90 / √36) = −20 / 15 ≈ −1.33.

Which statement about p-values is correct?

Answer: A p-value is the probability of obtaining results as extreme or more extreme, assuming H₀ is true.

The p-value measures how likely the observed data (or more extreme) would be if H₀ were true, not the probability that H₀ is true.

For a chi-square goodness-of-fit test, the degrees of freedom equal:

Answer: Number of categories − 1

Degrees of freedom for a goodness-of-fit test = k − 1, where k is the number of categories.

A significance test yields z = 2.45 for a right-tailed test. The p-value is approximately:

Answer: 0.007

For z = 2.45 in a right-tailed test, p = P(Z > 2.45) ≈ 0.007.

Which condition is necessary for a two-sample t-test to be valid?

Answer: The two samples must be independent of each other.

Independence between the two groups is a required condition; normality is only needed if sample sizes are small.

A researcher uses α = 0.05 and obtains p = 0.048. A critic argues the result could be due to chance. Which response best addresses this?

Answer: There is about a 4.8% chance of results this extreme if H₀ is true, so we reject H₀ but cannot rule out chance entirely.

Statistical significance means the result is unlikely under H₀ but does not eliminate the possibility of a Type I error.

In a chi-square test of independence, H₀ states that:

Answer: The two categorical variables are independent.

H₀ for a chi-square test of independence asserts no association — the two variables are independent.