1. When the population standard deviation is unknown and sample size is less than 30, which test statistic is used?

A. Z-test B. T-test C. F-test D. Chi-square test

2. In hypothesis testing for one sample proportion, the test statistic is \( Z = \frac{\hat{P} - P_0}{\sqrt{\frac{P_0(1-P_0)}{n}}} \). What does \( P_0 \) represent?

A. Sample proportion B. Hypothesized population proportion C. Difference between two proportions D. Standard deviation of proportion

3. Which of the following best describes the consequence of rejecting the null hypothesis when it is actually true?

A. Type II Error B. Power of a Test C. Type I Error D. Acceptance Region

4. What conclusion is drawn when |Z| > critical value at α = 0.05 in testing proportions?

A. Fail to reject H0 B. Reject H0; significant difference exists C. Increase sample size D. Accept H0 with caution

5. In testing a single proportion, what is the formula for the test statistic Z?

A. (P̂ - P0) / sqrt[P0(1 - P0)/n] B. (P̂ - P0) / sqrt[P̂(1 - P̂)/n] C. (P̂ - P0) / sqrt[(P̂ + P0)/2] D. (P̂ - P0) / sqrt[n]

6. Which of the following assumptions is critical for hypothesis testing to be valid?

A. Normality, homogeneity, randomness, independence B. Randomness and ignoring independence C. Large sample size and non-normality D. None of the above

7. Which of the following best describes a one-tailed test?

A. H1 states the population parameter is different (≠) from H0 B. H1 specifies the population parameter is greater or less than the null C. It tests for any difference in the parameter D. It is used only when n ≥ 30

8. Which of the following is NOT an assumption in hypothesis testing?

A. Independence of observations B. Random sampling C. Homogeneity of variance in some cases D. Population parameters must be known exactly

9. When testing the hypothesis for difference in two production lines, the appropriate test statistic is:

A. Z-test for two proportions B. Paired t-test C. Independent t-test for two means D. Chi-square test

10. Which is a correct interpretation if \(|Z| > Z_{\alpha/2}\) in a two-tailed test?

A. Accept H0, no significant difference B. Reject H0, significant difference exists C. Unable to conclude without more data D. Always reduce the sample size

11. The formula for the test statistic for difference of two means when population variances are unknown and n1, n2 < 30 is:

A. \( Z = \frac{(\bar{X}_1 - \bar{X}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}} \) B. \( t = \frac{(\bar{X}_1 - \bar{X}_2) - (\mu_1 - \mu_2)}{S_{\bar{X}_1 - \bar{X}_2}} \) C. \( F = \frac{S_1^2}{S_2^2} \) D. \( Z = \frac{\bar{X} - \mu_0}{\sigma / \sqrt{n}} \)

12. What is the critical value for a two-tailed test at 5% significance level?

A. 1.28 B. 1.645 C. 1.96 D. 2.58

13. What is the test statistic for difference of two proportions?

A. (P̂1 - P̂2) / sqrt[P0(1 - P0)*(1/n1 + 1/n2)] B. (P̂1 - P̂2) / sqrt[P̂1(1 - P̂1)/n1 + P̂2(1 - P̂2)/n2] C. (P̂1 - P̂2) / sqrt[(P̂1 + P̂2)/2] D. (P̂1 + P̂2) / sqrt[n1 + n2]

14. What is the purpose of statistical hypothesis testing?

A. To determine sample size B. To estimate population parameters C. To accept or reject a claim about a population parameter based on sample data D. To calculate descriptive statistics

15. When is the Z-test for population mean appropriate?

A. When population variance is unknown and sample size < 30 B. When population variance is known and sample size ≥ 30 C. When data are categorical D. For any sample size regardless of population variance knowledge

16. How is the pooled variance \( S_p^2 \) calculated for two samples?

A. \( \frac{\sum (X_1^2 + X_2^2)}{n_1 + n_2} \) B. \( \frac{(n_1 - 1)S_1^2 + (n_2 - 1)S_2^2}{n_1 + n_2 - 2} \) C. \( \sqrt{S_1^2 + S_2^2} \) D. \( S_1^2 \times S_2^2 \)

17. What does the acceptance region in hypothesis testing represent?

A. Values where H0 is rejected B. Values where H0 is accepted C. Values where data is incorrectly sampled D. Region where both hypotheses are false

18. What happens if sample size increases in relation to the test statistic for the mean?

A. The standard error increases B. The test statistic decreases C. The test statistic becomes more sensitive to differences D. The significance level increases

19. When performing hypothesis testing, why is it important to choose the significance level (α) carefully?

A. It determines the sample size only B. It controls the probability of committing Type I error C. It has no effect on decision-making D. It guarantees acceptance of the null hypothesis

20. What statistical measure can be used to test whether the average cost of seminar differs significantly from a hypothesized amount?

A. Z-test for proportions B. t-test for difference of means C. Z-test for difference of means D. F-test for variances

21. What does the pooled variance estimate (S²p) represent in testing the difference between two means?

A. The average of two population variances B. The weighted average of two sample variances C. The difference of two sample variances D. The ratio of two sample variances

22. In the formula \( Z = \frac{\bar{X} - \mu_0}{\sigma / \sqrt{n}} \), what does \(\mu_0\) represent?

A. Population variance B. Sample mean C. Hypothesized population mean D. Sample standard deviation

23. What is the relationship between type I error and the level of significance (\(\alpha\))?

A. Type I error probability = 1 - \(\alpha\) B. Type I error probability = \(\alpha\) C. Type I error probability is unrelated to \(\alpha\) D. Type I error is always double \(\alpha\)

24. For large samples (n ≥ 30) with known population variance, what test statistic is appropriate for testing means?

A. \( t = \frac{\bar{X} - \mu_0}{S / \sqrt{n}} \) B. \( Z = \frac{\bar{X} - \mu_0}{\sigma / \sqrt{n}} \) C. \( F = \frac{S_1^2}{S_2^2} \) D. \( \chi^2 = \frac{(n-1)S^2}{\sigma^2} \)

25. What is the level of significance (α) in hypothesis testing?

A. The probability of accepting a false null hypothesis B. The probability level at which the observed difference is considered unlikely due to chance C. The probability of rejecting a true alternative hypothesis D. The sample size

26. What does it mean if the null hypothesis H0: P1 = P2 is rejected?

A. There is no difference between the two population proportions B. The two sample sizes are equal C. There is a significant difference between the two population proportions D. Population proportions are both equal to zero

27. What is the "power of a test"?

A. Probability of accepting H0 when H0 is true B. Probability of rejecting H0 when H0 is true C. Probability of rejecting H0 when H0 is false D. Probability of accepting H0 when H0 is false

28. Which of these best describes Type II error in hypothesis testing?

A. Rejecting H0 when it is true B. Accepting H0 when it is false C. Rejecting H1 when it is false D. Accepting H1 when it is true

29. What is the decision if in example involving two departments, Z = 3.0861 and critical Z = 1.96?

A. Fail to reject H0 B. Reject H0 and conclude significant difference C. Collect more data before concluding D. Accept H1 as false

30. If the absolute value of the test statistic is greater than the critical value, what is the decision regarding H0?

A. Accept H0 B. Reject H0 C. Increase significance level D. Collect more data

31. What does the standard error of the difference between two proportions depend on?

A. The sample sizes only B. The population proportions only C. Both sample sizes and sample proportions D. The variance of the population means

32. A test statistic t calculated as 44.90 with a critical value t0.025(16)=2.120 leads to what conclusion?

A. Fail to reject null hypothesis B. Reject null hypothesis; significant difference exists C. Accept null hypothesis D. Increase sample size

33. When testing the difference between two means with unknown variances and small samples, which distribution is used?

A. Normal distribution B. t-distribution with pooled degrees of freedom C. Chi-square distribution D. F distribution

34. In hypothesis testing, the level of significance (α) is:

A. The probability of accepting a false null hypothesis B. The probability of rejecting a true null hypothesis C. The probability of randomly selecting data D. The probability of the alternative hypothesis being true

35. What does the alternative hypothesis (H1) represent?

A. Hypothesis that there is no difference B. Hypothesis that is expected to confirm the null hypothesis C. Hypothesis of practical interest showing difference or change D. Hypothesis that must always be rejected

36. If the test statistic \( Z = 8 \) and \( Z_{0.025} = 1.96 \), what is the inference about H0?

A. Fail to reject H0 B. Reject H0 due to significant difference C. Accept H0 without doubt D. Increase significance level

37. What is the formula for the standard error of the difference between two sample means when variances are unequal?

A. \( \sqrt{\frac{S_1^2}{n_1} + \frac{S_2^2}{n_2}} \) B. \( \frac{S_p}{\sqrt{n_1 + n_2}} \) C. \( S_1^2 + S_2^2 \) D. \( S_1^2 - S_2^2 \)

38. What is the null hypothesis (H0) in statistical hypothesis testing?

A. The hypothesis of practical interest expected to disprove the null B. A claim about the population parameter being significantly different C. A hypothesis of no significance or no change D. The hypothesis always accepted without testing

39. What test statistic is used when population variance is unknown and sample size is less than 30?

A. Z-test B. Chi-square test C. t-test D. F-test

40. What represents the formula for the \( t \)-test when population standard deviation is unknown and sample size is small?

A. \( t = \frac{\bar{X} - \mu_0}{S / \sqrt{n}} \) B. \( Z = \frac{\bar{X} - \mu_0}{\sigma / \sqrt{n}} \) C. \( t = \frac{S}{\bar{X} \sqrt{n}} \) D. \( Z = \frac{S - \mu_0}{\bar{X} / \sqrt{n}} \)

41. In the context of hypothesis testing, what does homogeneity imply?

A. Equal sample sizes B. Equal population variances C. Independent observations D. Normal distribution of data

42. The test statistic for hypothesis on the difference of two proportions \( P_1 \) and \( P_2 \) is:

A. \( t = \frac{P_1 - P_2}{\sqrt{P(1-P)(\frac{1}{n_1} + \frac{1}{n_2})}} \) B. \( Z = \frac{(\hat{P}_1 - \hat{P}_2) - (P_1 - P_2)}{\sqrt{\frac{\hat{P}_1 (1 - \hat{P}_1)}{n_1} + \frac{\hat{P}_2 (1 - \hat{P}_2)}{n_2}}} \) C. \( Z = \frac{(\hat{P}_1 - \hat{P}_2)}{S_p} \) D. \( t = \frac{(\hat{P}_1 + \hat{P}_2)}{2} \)

43. What does the null hypothesis (H0) typically represent?

A. A hypothesis of change B. A statement of no significant difference or effect C. A hypothesis that must always be accepted D. An alternative hypothesis

44. What is the critical region in hypothesis testing?

A. Range where the null hypothesis is accepted B. Range where the null hypothesis is rejected C. The range containing the mean of the sample data D. The confidence interval of the sample mean

45. What does the power of a test measure?

A. Probability of rejecting a true null hypothesis B. Probability of accepting a true null hypothesis C. Probability of rejecting a false null hypothesis D. Probability of accepting a false null hypothesis

46. How is the Z-test statistic for mean calculated when population variance is known?

A. (X̄ - μ0) / S B. (X̄ - μ0) * √n / σ C. (X̄ - μ0) / √n D. (X̄ - μ0) * σ

47. Given a sample proportion P̂ = 0.5, hypothesized proportion P0 = 0.3, and standard error 0.025, what is the Z value?

A. 4 B. 6 C. 8 D. 2

48. When performing a two-tailed test, what does the alternative hypothesis (H1) claim?

A. The parameter is greater than the hypothesized value B. The parameter is less than the hypothesized value C. The parameter is different (either greater or less) from the hypothesized value D. The parameter is equal to the hypothesized value

49. What is the formula for the standard error of the difference between two means when variances are unknown without pooling?

A. sqrt[S1²/n1 + S2²/n2] B. sqrt[(S1² + S2²)/(n1 + n2)] C. (S1 - S2) / (n1 + n2) D. (X̄1 - X̄2) / pooled variance

50. What is a Type I error in hypothesis testing?

A. Rejecting a true null hypothesis B. Accepting a false null hypothesis C. Rejecting a false alternative hypothesis D. Accepting a true null hypothesis