Question

It is claimed that the mean of a population equals 200. You test this claim by taking a sample of size n = 144. The mean of the sample is calculated to equal 205. Somehow, it is known that the standard deviation of the population of interest is 15. Does the evidence from the sample support the claim, or does it appear that the population mean is not equal to 200? Test at the five percent level.

a.) Test this hypothesis using the 5-step approach (Below) Be sure to do the decision rule using the critical value approach (4a) and the p-value approach (4b).

b.) Interpret your result.

Template

1. State the null and alternative hypotheses.

2. State the level of significance.

3. Choose and calculate the appropriate test statistic.

4a. State the decision rule using the critical value approach.

4b. State the decision rule using the p-value approach.

5. Make and interpret the decision.

Answer 1

(1)

H0: Null Hypothesis: = 200

HA: Alternative Hypothesis: 200

(2)

Level of Significance = = 0.05

(3)

SE = /

= 15/ = 1.25

Test statistic is:
Z = (205 - 200)/1.25 = 4

(4a)

FromTable, critical values of Z = 1.96

Decision Rule:
Reject H0:

if Z < - 1.96

OR

Z > 1.96

Since calculated value of Z is greater than critical value of Z Reject null hypothesis.

(4b)

Table of Area Under Standard Normal Curve gives area for Z = 4 as area = 0.49997

So,

P-value = (0.5 - 0.49997) X 2 = 0.00006

Since P-value is less than , Reject null hypothesis.

(5)

The data do not support the claim that the mean of a population equals 200.