Kindergarten children have heights that are approximately distributed normal. A random sample of size 20 is taken and the mean x and the standard deviation s are calculated ( x = 40 inches and s = 3).

Question

a. Is there sufficient evidence to indicate that the mean of kindergarten children’ height exceeds 40 inches? Perform a test
using alpha=.05.

b. What is the probability that the mean of kindergarten children’ heights would be between 39 and 42.5 inches?

Answer 1

a. In a normal distribution, 50% are above the mean. For confidence interval,

95% = mean ± 1.96 SEm

b. Z = (score-mean)/SEm

SEm = SD/√n

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability between the two Z scores.