Suppose a test procedure about the population mean μ is performed,when the population is normal with an unknown variance.If a sample of size 16 is drawn from the population and the alternative hypothesis is H₁ : μ ≠ μ₀,the null hypothesis is rejected at a level α = 0.05 if either t 2.131.

Question

Suppose a test procedure about the population mean μ is performed,when the population is normal with an unknown variance.If a sample of size 16 is drawn from the population and the alternative hypothesis is H₁ : μ ≠ μ₀,the null hypothesis is rejected at a level α = 0.05 if either t < -2.131 or t > 2.131.

Quizplus · Accepted Answer

This is true based on the information given. The test procedure is for the population mean μ, the population is assumed to be normal with an unknown variance, a sample of size 16 is drawn, and the alternative hypothesis is a two-sided alternative (μ can be less than or greater than the hypothesized value). The critical values for a two-tailed test with α = 0.05 and degrees of freedom = 15 are -2.131 and 2.131, which are provided in the statement of the problem. Therefore, if the calculated t-value falls outside of this range, the null hypothesis is rejected at the 0.05 level.

Suppose a Test Procedure About the Population Mean μ Is