In a hypothesis test for the population variance,the hypotheses are H₀: σ² = 30 vs.H₁: σ²

Question

In a hypothesis test for the population variance,the hypotheses are H₀: σ² = 30 vs.H₁: σ² < 30.If the sample size is 20 and the test is being carried out at the 5% level of significance,the null hypothesis is rejected if: A)χ² < 30.144. B)χ² > 10.851. C)χ² < 10.117. D)χ² > 31.410.

Quizplus · Accepted Answer

Since the alternative hypothesis is left-tailed (σ < 30), the critical value for rejection of the null hypothesis is obtained from the chi-square distribution table at 19 degrees of freedom and 5% level of significance as 10.117. Therefore, if the calculated chi-square value is less than 10.117, we reject the null hypothesis. Option A, B, and D are incorrect as they do not respect the direction of the alternative hypothesis or the critical value.

In a Hypothesis Test for the Population Variance,the Hypotheses Are