The weight in pounds for a population of schoolaged children

The weight (in pounds) for a population of school-aged children is normally distributed with a mean equal to 135+/- 20 pounds. 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?
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?

Solution

Let X be the weight of population of school aged children

X is Normal (135, 20)

Sample size n =100

Std error of sample = 20/rt 100 = 2

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A) H0: mu1 = mu2

    Ha: mu1 < mu2

(where mu1 is the initial average and mu2 average after a certain time.)

B) Critical values are = (-3, 1.64)

C) Mean = 135 pounds

D) std error = 2.