Question

1. Given a normal population which has a mean of 140 and a standard deviation of 21, find the probability that a random sample of 100 has a mean between 138 and 145.

2. If all possible samples of size n are drawn from an infinite population with standard deviation 8, then the standard error of the sample mean equals 1.0 if the sample size is 64.

a. true

b. false

3. You have completed an hypothesis test and determine the p-value = 0.0327. If you are testing at an α
= 0.03 level, what is your test conclusion?

		Reject H0
		Do not reject H0
		Accept H1
		Reject H1
		None of these answers are correct

Answer 1

1)

Given,

= 140, = 21

Using central limit theorem,

P( < x) = P( Z < x - / ( / sqrt(n) ))

So,

P(138 < < 145) = P(Z < 145 - 140 / (21 / sqrt(100) ) ) - P(Z < 138 - 140 / (21 / sqrt(100) ) )

= P(Z < 2.38) - P(Z < -0.95)

= 0.9913 - 0.1711

= 0.8202

2)

Standard error = Standard deviation / sqrt(n)

= 8 / sqrt(64)

= 1

True

3)

Since p-value > 0.03 significance level, Do not reject H0