Question

The weight (in pounds) for a population of school-aged children is normally distributed with a mean equal to 138 ± 23 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

Part (a)

Correct option:

H0: 138

H1: 138

Part (b):

One Tail Right Side Test

= 0.05

From Table, critical value of Z = 1.645

So,

critical value for this test: 1.645

Part (c):

The mean of the sampling distribution: 138

Part (d):

Standard error of the mean for the sampling distribution = /

                                                                               = 23/ = 2.3