Statistics Quiz

True or False: Inferential statistics is used to make conclusions about a population based on data from a sample.

• True

• False

Answer explanation

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.

True or False: The alternative hypothesis typically states that there is no effect or no difference between groups or variables.

• True

• False

Answer explanation

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.

Using a lower significance level (e.g., α = 0.01 instead of 0.05) reduces the probability of a Type I error but increases the risk of a Type II error. True or False?

• True

• False

Answer explanation

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).

True or False: A one-tailed hypothesis test is appropriate when we want to detect differences in either direction (both higher or lower than the null expectation).

• True

• False

Answer explanation

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.

According to the Central Limit Theorem, the sampling distribution of the sample mean is approximately normal if the sample size is sufficiently large. True or False?

• True

• False

Answer explanation

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.

Which of the following is not a requirement for the Central Limit Theorem to apply?

• Large sample size

• Normal population distribution

• Random sampling

• Independent observations

Answer explanation

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.

A chi-square test of independence is performed on a contingency table with 4 rows and 3 columns. What is the degrees of freedom for this test?

• 5

• 12

• 6

• 9

Answer explanation

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.

Which of the following is NOT an assumption of the chi-square test?

• The data must be categorical (nominal or ordinal).

• Observations must be independent of each other.

• Expected frequencies in each cell should be at least 5 (or no more than 20% of cells should have expected counts below 5).

• The data must follow a normal distribution.

Answer explanation

• 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.

What is the purpose of the chi-square goodness-of-fit test?

• To compare means of two groups

• To test if a sample matches an expected distribution

• To determine correlation between variables

• To test variance equality

Answer explanation

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.

If a result is statistically significant, it implies that the finding is also practically significant. True or False?

• True

• False

Answer explanation

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.