Question

The following hypotheses are given.

H₀: π = 0.40
H₁: π ≠ 0.40

A sample of 120 observations revealed that p = 0.30. At the 0.05 significance level, can the null hypothesis be rejected?

1. State the decision rule. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

2. Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

3. What is your decision regarding the null hypothesis?

• Do not reject H₀

• Reject H₀

Answer 1

Solution:

Given:

H₀: π = 0.40
H₁: π ≠ 0.40 ( two tailed test)

n = 120

Level of significance = 0.05

Part a) State the decision rule.

Since this is two tailed, we find : Area =

Look in z table for area = 0.0250 or its closest area and find z value

Area 0.0250 corresponds to -1.9 and 0.06

thus z critical value = -1.96

Since this is two tailed test, we have two z critical values: ( -1.96 , 1.96)

Thus decision rule is:

Reject null hypothesis ,if z  test statistic value < z critical value = -1.96 or z test statistic value > z critical value =1.96 , otherwise we fail to reject H0.

that is: Reject H0 if or

Part b) Compute the value of the test statistic

Part c) What is your decision regarding the null hypothesis?

Since z  test statistic value = < z critical value = -1.96, we reject H0.

Thus correct answer is: Reject H0.