Question

The weight (in pounds) for a population of school-aged children is normally distributed with a mean equal to 132 ± 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.

A.

What are the null and alternative hypotheses?

H₀: μ = 132
H₁: μ ≠ 132H₀: μ = 132
H₁: μ < 132    H₀: μ ≤ 132
H₁: μ = 132H₀: μ ≤ 132
H₁: μ > 132

B. What is the critical value for this test?

C. What is the mean of the sampling distribution?

D. What is the standard error of the mean for the sampling distribution?

Answer 1

A)

H0: = 132

H1: > 132

B)

This is one tailed test.

Critical value at 0.05 significance level = 1.645

c)

Mean of sampling distribution = = = 132

d)

Standard deviation of sampling distribution of mean = = / sqrt(n)

= 24 / sqrt(100)

= 2.4