Statistics Quiz

True. Inferential statistics allows us to draw conclusions about a larger population by analyzing data collected from a smaller sample, making it essential for research and decision-making.

The alternative hypothesis posits that there is an effect or a difference between groups or variables, contrary to the null hypothesis, which states there is no effect. Therefore, the statement is False.

True. A lower significance level (α = 0.01) decreases the chance of a Type I error (false positive) but makes it harder to reject the null hypothesis, thus increasing the risk of a Type II error (false negative).

False. A one-tailed hypothesis test is used to detect differences in only one direction (either higher or lower), not both. For detecting differences in either direction, a two-tailed test is appropriate.

True. The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the population's distribution.

The Central Limit Theorem does not require a normal population distribution; it applies to large samples regardless of the population's distribution shape, as long as the sample size is sufficiently large.

The degrees of freedom for a chi-square test of independence is calculated as (rows - 1) * (columns - 1). Here, it is (4 - 1) * (3 - 1) = 3 * 2 = 6. Thus, the correct answer is 6.

• Chi-square tests (both goodness-of-fit and test of independence) do not require the data to be normally distributed.

• Instead, the main assumptions are:
  ✅ The data are categorical (A).
  ✅ Observations are independent (B).
  ✅ Expected frequencies in cells should be ≥5 (C).

• Normality is an assumption for parametric tests like the t-test or ANOVA, but not for chi-square tests.

The chi-square goodness-of-fit test is used to determine if the observed sample data matches an expected distribution. This helps assess how well the sample fits a theoretical model.

False. Statistical significance indicates that a result is unlikely to have occurred by chance, but it does not guarantee that the finding has practical importance or relevance in real-world applications.