Question

The following hypotheses are given. HO: IT = 0.40 HAT+0.40 A sample of 120 observations revealed that p=0.30. At the 0.05 significance level, can the null hypothesis be rejected? a. State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.) Reject HO and accept H1 when z< or z> b. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) Value of the test statistic c. What is your decision regarding the null hypothesis? Reject Ho O Do not reject Ho

Answer 1

a.

$H_0: \pi = 0.40$

$H_1: \pi \neq 0.40$

Since, it is a two tailed hypothesis, at 5% significance level, the critical value of z is z_0.05 = 1.96.

So, the decision rule is:

Reject H0 and accept H1 when Z < -1.96 or Z > 1.96.

b.

Given: n = 120 and p = 0.30.

We'll do a Z-test for proportion. The value of the test statistic will be calculated as:

$Z = \frac{(p - \pi)}{\bigg[\sqrt\frac{\pi(1-\pi)}{n}\bigg]}$

  

(0.30 -0.40) 10.40(1-0.40) 120

  

(-0.1) 10.40(0.60) 120

$= \frac{(-0.1)}{\bigg[\sqrt\frac{0.24}{120}\bigg]}$

  $= \frac{(-0.1)}{0.0447213595}$

  $=-2.24$

c.

Since the calculated value of Z(-2.24) < Z critical value(-1.96), we reject the null hypothesis(H0).