Hypothesis Testing Questions and Answers

Answer: D

Rejecting a hypothesis that should have been accepted is a Type-I error.

A Type I error occurs when a true null hypothesis is rejected; its probability is the level of significance, alpha. A Type II error is the reverse: accepting (failing to reject) a null hypothesis that is false.

The null and alternative hypotheses are the statements being tested, not errors in deciding between them.

Answer: B

The F-test is used to find out whether there is a significant difference between the variances of two sets of observations. It takes the ratio of the two sample variances and compares it with the tabulated F value for the degrees of freedom. The t-test compares means, the chi-square test examines goodness of fit or independence between categorical data, and regression relates a dependent variable to independent variables. Neither of these tests the equality of variances.

Answer: A

The F statistic is the ratio of the sample variances each divided by its population variance.

\[ F = \frac{S_1^2 / \sigma_1^2}{S_2^2 / \sigma_2^2} \]

\[ F = \frac{8/10}{15/20} \]

\[ F = \frac{0.8}{0.75} \approx 1.07 \]

The nearest value in the options is 1, option A, which is the keyed answer. The values 2, 2.81 and 3.6 are much larger.