Hypothesis Testing

Question 1

What are the six steps of hypothesis testing?

Answer 1

1. State hypotheses 2. Identify test statistic and distribution 3. Specify significance level (α) 4. State decision rule 5. Collect data and calculate test statistic 6. Make decision

Question 2

What is the null hypothesis (H₀)?

Answer 2

The hypothesis assumed to be true unless evidence suggests otherwise; it contains an equality (=, ≥, ≤).

Question 3

What is the alternative hypothesis (H₁ or Hₐ)?

Answer 3

The hypothesis accepted if the null hypothesis is rejected; represents the claim being tested.

Question 4

What is the significance level (α)?

Answer 4

The probability of making a Type I error (rejecting a true null hypothesis).

Question 5

What is the decision rule in hypothesis testing?

Answer 5

A rule that determines whether to reject or not reject H₀ based on the test statistic or p-value.

Question 6

What determines whether we reject the null hypothesis using a test statistic?

Answer 6

If the test statistic falls in the rejection region defined by the critical value.

Question 7

What is the structure of hypotheses in a two-tailed test?

Answer 7

H₀: μ = μ₀ ; H₁: μ ≠ μ₀

Question 8

What is the structure of hypotheses in a right-tailed test?

Answer 8

H₀: μ ≤ μ₀ ; H₁: μ > μ₀

Question 9

What is the structure of hypotheses in a left-tailed test?

Answer 9

H₀: μ ≥ μ₀ ; H₁: μ < μ₀

Question 10

What is the critical value for a two-tailed test at α = 0.05 (normal distribution)?

Answer 10

±1.96

Question 11

What is the critical value for a one-tailed test at α = 0.05 (normal distribution)?

Answer 11

1.645

Question 12

What is the Z-test statistic for a single mean?

Answer 12

Z = (X̄ − μ₀) / σₓ̄

Question 13

When is the Z-test used instead of the t-test?

Answer 13

When the population variance is known or the sample size is large.

Question 14

What is the t-test statistic for a single mean?

Answer 14

t = (X̄ − μ₀) / (s / √n)

Question 15

What is the t-test statistic for the difference in means (independent samples)?

Answer 15

t = [(X̄₁ − X̄₂) − (μ₁ − μ₂)] / √(s₁²/n₁ + s₂²/n₂)

Question 16

What is the paired sample t-test (mean difference) statistic?

Answer 16

t = (d̄ − μd₀) / (sd / √n)

Question 17

What is a Type I error?

Answer 17

Rejecting the null hypothesis when it is true.

Question 18

What is a Type II error?

Answer 18

Failing to reject the null hypothesis when it is false.

Question 19

What is the relationship between α and Type I error?

Answer 19

The significance level α equals the probability of a Type I error.

Question 20

What is the power of a test?

Answer 20

The probability of correctly rejecting a false null hypothesis (1 − Type II error).

Question 21

What is a p-value?

Answer 21

The smallest significance level at which the null hypothesis can be rejected.

Question 22

What is the decision rule using a p-value?

Answer 22

Reject H₀ if p-value ≤ α.

Question 23

What is the chi-square test used for in hypothesis testing?

Answer 23

Testing hypotheses about a single population variance.

Question 24

What is the chi-square test statistic for variance?

Answer 24

χ² = (n − 1)s² / σ₀²

Question 25

What is the F-test used for?

Answer 25

Testing the equality of two population variances.

Question 26

What is the F-test statistic?

Answer 26

F = s₁² / s₂²

Question 27

What are the degrees of freedom for a single-mean t-test?

Answer 27

n − 1

Question 28

What are the degrees of freedom for a two-sample t-test?

Answer 28

n₁ + n₂ − 2

Question 29

What are the degrees of freedom for an F-test?

Answer 29

n₁ − 1 and n₂ − 1

Question 30

What are parametric tests?

Answer 30

Tests that rely on assumptions about the population distribution and involve population parameters.

Question 31

What are nonparametric tests?

Answer 31

Tests that do not assume a specific population distribution or make minimal assumptions about the population.