You collect a random sample of 100 children and compute X¯X¯ = 47.5 inches, the average height in inches. The sample standard deviation (s) equals 6 inches. You conduct a two-sided hypothesis test...

You collect a random sample of 100 children and compute X¯X¯ = 47.5 inches, the average height in inches. The sample standard deviation (s) equals 6 inches.  You conduct a two-sided hypothesis test where H₀: μ = 46 inches. Which of the following statements are true:

                                                                         I. You reject the null hypothesis when α = 0.05

                                                                         II. You reject the null hypothesis when α = 0.01

                                                                         III. The test statistic (Z) equals Z = +2.5