Comparing Z test and t test

When should you use a z-test instead of a t-test?

• When the population standard deviation is unknown.

• When the sample size is small (n < 30).

• When the population standard deviation is known.

• When the data is paired.

Which of the following is a key characteristic of the t-distribution compared to the z-distribution?

• The t-distribution has a smaller variance.

• The t-distribution is defined by degrees of freedom.

• The t-distribution is only used for proportions.

• The t-distribution is not bell-shaped.

For a sample size of 20 with an unknown population standard deviation, which test should be used?

• z-test

• t-test

• Chi-square test

• ANOVA

What happens to the t-distribution as the sample size increases?

• It becomes more skewed.

• It approaches the standard normal distribution.

• It becomes wider.

• It becomes discontinuous.

In a t-test, what does the degrees of freedom (d.f.) typically equal?

• n

• n-1

• n+1

• 2n

Which of the following assumptions is unique to the independent samples t-test (not required for the z-test)?

• The population standard deviation is known.

• The sample sizes must be equal.

• The variances of the two samples are approximately equal.

• The data must be normally distributed for any sample size.

When comparing two means from independent samples with known population standard deviations, which test should be used?

• Paired t-test

• z-test

• One-sample t-test

• Chi-square test

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

• ±1.96

• ±1.645

• ±2.576

• ±2.33

Which test is appropriate for analyzing the difference in means before and after a treatment in the same group of subjects?

• Independent samples t-test

• z-test

Why is the t-test considered more conservative than the z-test for small sample sizes?

• It uses a larger critical value due to greater uncertainty.

• It assumes the population standard deviation is known.

• It does not require normally distributed data.

• It ignores degrees of freedom.