Statistics Flashcards

A linear regression model gives ŷ = 3 + 2x. For x = 5, the observed value is y = 14. What is the residual?

Answer: 1

Predicted value ŷ = 3 + 2(5) = 13; residual = observed − predicted = 14 − 13 = 1.

A fair six-sided die is rolled. Given that the result is even, what is the probability it is greater than 4?

Answer: 1/3

Even outcomes are {2, 4, 6}; of these, outcomes greater than 4 are {6}, giving P = 1/3.

A frequency distribution has class intervals of width 5. The frequency for the interval [20, 25) is 12 and the total frequency is 60. What is the relative frequency for that class?

Answer: 0.20

Relative frequency = frequency / total = 12/60 = 0.20.

X ~ N(μ, σ²). If Z = (X − μ)/σ, which distribution does Z follow?

Answer: N(0, 1)

Standardizing a normal variable by subtracting its mean and dividing by its standard deviation produces a standard normal Z ~ N(0,1).

The cumulative distribution function (CDF) of a random variable X gives F(x). Which statement correctly describes F(x)?

Answer: F(x) = P(X ≤ x)

By definition, the CDF F(x) gives the probability that the random variable X takes a value less than or equal to x.

A data set has n = 9 values with Σx = 45 and Σx² = 261. What is the variance?

Answer: 4

Mean = 45/9 = 5; variance = Σx²/n − (mean)² = 261/9 − 25 = 29 − 25 = 4.

A Type I error in hypothesis testing occurs when:

Answer: H₀ is true and we reject it

A Type I error (false positive) is rejecting H₀ when H₀ is actually true; its probability equals the significance level α.