Hypothesis Testing Questions and Answers

Q: ................... means rejection of hypothesis which should have been accepted.

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.

11.

................... means rejection of hypothesis which should have been accepted.

A.Alternative Hypothesis
B.Null Hypothesis
C.Type-II error
D.Type-I error

Exam Year(s)

MH SET - 2024, SET Exam - 2024,

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.

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12.

The following statistical test is used to ascertain whether there is significant difference between the variances of two sets of observations :

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

Exam Year(s)

UGC NET - 2012,

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.

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13.

Two normal populations have variances \(\sigma_1^{2}\) = 10 and \(\sigma_2^{2}\) = 20. Two random samples of sizes 25 and 20, independently selected from these populations have variances of \(S_1^{2}\) = 8 and \(S_2^{2}\) = 15, respectively. What is the \(F_{(24, 19)}\) statistic ?

A.1
B.2
C.2.81
D.3.6

Exam Year(s)

UGC NET - 2013,

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.

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