Statistics Flashcards

In a simple linear regression equation ŷ = 3 + 2x, if x increases by 1, ŷ:

Answer: Increases by 2

The slope coefficient (2) indicates the change in ŷ for each one-unit increase in x.

The Central Limit Theorem states that the sampling distribution of the sample mean approaches normality as:

Answer: Sample size increases

As n increases (generally n ≥ 30), the distribution of sample means approximates a normal distribution regardless of the population shape.

Which statistic is used to measure the spread of data around the regression line?

Answer: Standard error of the estimate

The standard error of the estimate (Sₑ) measures the average distance of observed values from the regression line.

When two events are mutually exclusive, P(A or B) equals:

Answer: P(A) + P(B)

Mutually exclusive events cannot occur together, so P(A and B) = 0 and P(A or B) = P(A) + P(B).

A researcher increases the alpha level from 0.01 to 0.05. This change:

Answer: Increases the probability of a Type I error

Alpha is the Type I error rate; raising it from 0.01 to 0.05 increases the chance of incorrectly rejecting a true null.

Which of the following is an example of a discrete random variable?

Answer: The number of defects in a batch of 100 items

Count data (number of defects) can only take whole-number values, making it discrete.

In a two-tailed hypothesis test with α = 0.05, each tail contains:

Answer: 2.5% of the rejection region

For a two-tailed test, α is split equally between both tails, placing 0.025 (2.5%) in each.