Problem 1 (20 points). You randomly sample 25 fifth-graders from a population an

Question

Problem 1 (20 points). You randomly sample 25 fifth-graders from a population and estimate each child's height. The average height (u) of the population of fifth-graders is unknown, but the standard is known and equals 4.0 inches. You calculate X for your sample and obtain X-58 inches. deviation (a) Conduct a two-sided hypothesis test for Ho: -60 for -0.05. Compute the resulting p-value. State whether you would reject Ho and why a) b) Create a 95% confidence interval for the parameter , with what level of confidence can you conclude that does not equal 60 inches?

Explanation / Answer

A)
test statistics, t = (58 - 60)/(4/sqrt(25) = -2.5

df = 24

p-value = 0.0197

As p-value is less than 0.05, we reject the null hypothesis.

B)

We are 95% confident that mu is not equals to 60

CI for 95% n 25 mean 58 t-value of 95% CI and df = 24 2.0639 std. dev. 4 SE = std.dev./sqrt(n) 0.80000 ME = t*SE 1.65112 Lower Limit = Mean - ME 56.34888 Upper Limit = Mean + ME 59.65112 95% CI (56.3489 , 59.6511 )

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