The weight (in pounds) for a population of school-aged children is normally dist

Question

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

123 ± 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.

Part (a)

What are the null and alternative hypotheses?

H0: = 123
H1: > 123 H0: = 123
H1: < 123     H0: < 123
H1: = 123 H0: = 123
H1: 123

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

Explanation / Answer

Hypothesis:

Ho: u>123

Ha: u <=123

test statistic z = 123 -123 / 20/sqrt(100) = 0

b)

critical value : z < 1.96

since z < critical value , we reject null hypothesis

c)

mean = 123

d)

standard error = 20/sqrt(100) = 2

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