Selecting, Implementing, and Communicating Inference Procedures - AP Statistics

1. What does a significant F-statistic in ANOVA indicate?

   At least one group mean is different. Not all group means are equal.

2. Identify the type of error when $H_0$ is true, but rejected.

   Type I error. Rejecting true null hypothesis incorrectly.

3. Which test checks for independence between two categorical variables?

   Chi-square test of independence. Tests if two categorical variables are related.

4. What is the alternative hypothesis for a two-tailed test?

   $H_a: \text{parameter} \neq \text{value}$. Parameter differs from specified value in either direction.

5. State the null hypothesis for a test of a single proportion.

   $H_0: p = p_0$. Tests if population proportion equals specific value.

6. Choose the correct decision rule: reject $H_0$ if p-value < $α$.

   Correct. Standard decision rule for hypothesis testing.

7. What assumption is made about variances in ANOVA?

   Homogeneity of variances. Equal variances across all groups required.

8. State the null hypothesis for an ANOVA test.

   $H_0: \text{All group means are equal}$. No difference among any group means.

9. Identify the correct interpretation of a 95% confidence interval for a mean.

   95% of such intervals contain the true population mean. Describes long-run capture rate behavior.

10. Identify the critical value for a 95% confidence interval using a z-distribution.

    1.96. Captures 95% of area under standard normal curve.

11. Choose the correct decision rule: reject $H_0$ if p-value < $\alpha$.

    Correct. Standard decision rule for hypothesis testing.

12. Identify the degrees of freedom for the numerator in an ANOVA test.

    $k - 1$. Where $k$ is number of groups compared.

13. Find the critical value for a 99% confidence interval using a t-distribution with 10 df.

    3.169. Critical value for 99% confidence with 10 degrees freedom.

14. What is the null hypothesis for a two-sample t-test?

    $H_0: \text{The two population means are equal}$. States no difference between population means.

15. Which option describes a Type II error?

    Failing to reject $H_0$ when it is false. Accepting false null hypothesis incorrectly.

16. Identify the test for comparing paired sample means.

    Paired t-test. Compares before and after measurements on same subjects.

17. Which test would you use for homogeneity of variance among groups?

    Levene's test. Tests equal variances assumption for ANOVA.

18. Identify the degrees of freedom for the denominator in an ANOVA test.

    $N - k$. Where $N$ is total sample size, $k$ is groups.

19. Identify the condition for sample proportions in hypothesis testing.

    np ≥ 10 and n(1-p) ≥ 10. Ensures normal approximation validity for proportions.

20. What is the formula for the standard error of a sample mean?

    $SE = \frac{s}{\sqrt{n}}$. Measures variability of sample mean estimates.

21. Determine the p-value given a z-score of 1.96 in a two-tailed test.

    0.05. Two-tailed area beyond $z = 1.96$ is 0.05.

22. Which test is used when comparing the variance of a sample to a known variance?

    Chi-square test. Compares sample variance to known population variance.

23. What is the formula for the chi-square statistic?

    $χ^2 = \text{Σ} \frac{(O_i - E_i)^2}{E_i}$. Compares observed frequencies to expected frequencies.

24. Which condition is checked for normality in a t-test?

    The sample data is approximately normally distributed. Required for valid t-test inference procedures.

25. State the null hypothesis for a chi-square goodness-of-fit test.

    $H_0: \text{The observed distribution fits the expected distribution}$. Tests if data follows expected distribution pattern.

26. Which test statistic is used for proportions?

    Z-test. Uses normal distribution for proportion tests.

27. What is the purpose of a confidence interval?

    Estimate a population parameter with an associated level of confidence. Provides range of plausible parameter values.

28. What is the formula for the test statistic in a one-sample t-test?

    $t = \frac{\bar{x} - \mu}{s / \sqrt{n}}$. Standardizes sample mean using sample standard deviation.

29. Which inference method is used when population variance is unknown?

    T-distribution. Used when population standard deviation unknown.

30. State the formula for the test statistic in a two-proportion z-test.

    z = \frac{\text{p}_1 - \text{p}_2}{\text{√(p(1-p)(\frac{1}{n_1} + \frac{1}{n_2}))}}. Compares two population proportions using pooled estimate.

31. Identify the alternative hypothesis for a left-tailed test.

    $H_a: \text{parameter} < \text{value}$. Parameter is less than specified value.

32. What is the test statistic formula for an ANOVA test?

    $F = \frac{\text{MSB}}{\text{MSW}}$. Ratio of between-group to within-group variance.

33. Which test would you use for comparing means of two independent samples?

    Two-sample t-test. Compares means when groups are independent.

34. What is the p-value interpretation in hypothesis testing?

    Probability of observing data as extreme as current, under $H_0$. Measures strength of evidence against null hypothesis.

35. Choose the formula for calculating a confidence interval for a mean.

    $\bar{x} \pm t* \frac{s}{\sqrt{n}}$. Uses t-distribution critical value for unknown variance.

36. What is the significance level commonly denoted as?

    $\text{α}$. Probability of Type I error threshold.

37. What is the formula for the margin of error in a confidence interval?

    $\text{ME} = z* \frac{σ}{\sqrt{n}}$. Half-width of confidence interval around estimate.

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