Question

The weight (in pounds) for a population of school-aged children is normally distributed with a mean equal to 138 ± 24 pounds (μ ± σ). Suppose we select a sample of 100 children (n = 100) to test whether children in this population are gaining weight at a 0.05 level of significance. Part (a) What are the null and alternative hypotheses? H0: μ = 138 H1: μ ≠ 138 H0: μ ≤ 138 H1: μ > 138 H0: μ ≤ 138 H1: μ = 138 H0: μ = 138 H1: μ < 138 Part (b) What is the critical value for this test? Part (c) What is the mean of the sampling distribution? lb Part (d) What is the standard error of the mean for the sampling distribution? lb

Answer 1

a) H₀: $\dpi{120} \mu$< 138

H₁: $\dpi{120} \mu$ > 138

b) At 0.05 significance level the critical value is z_0.95 = 1.645

c) $\dpi{120} \mu_{\bar x}$ = 138

d) SE = $\dpi{120} \sigma/\sqrt n$

= 24/$\dpi{120} \sqrt {100}$

= 2.4