A normal population yields sample25.8,36.6,26.3,21.8,27.2. Given one-sided t critical value2.132 at 5% significance with 4 degrees of freedom, select the statement.
Correct answer: (A) Population mean≤25 with 95% confidence
Explanation
Mean=27.54 and sample standard deviation≈5.48. For $H_0:\mu\le25$, $t=(27.54-25)/(s/\sqrt5)\approx1.04<2.132$. The sample does not demonstrate μ>25 at 5% significance. The official answer is **A**, interpreted as retaining the null; failure to reject is not a proof that μ≤25 with 95% confidence. A one-sided upper95% confidence bound is about 32.76, so none of the literal confidence assertions follows as written.