Question

In a sample of 1200 people, exactly 690 are in education profession and rests are business person. Can we claim that business and education both are equally acceptable in this society? Give your conclusion at (i) 1% level of significance and (ii) 5% level of significance.

Answer 1

(i) No, at a 1% level of significance we cannot claim that the business and education both are equally acceptable in this society.

(ii) No, at a 5% level of significance we cannot claim that the business and education both are equally acceptable in this society.

Step-by-step explanation:

We are given that in a sample of 1200 people, exactly 690 are in the education profession and rests are business persons.

Let p = population proportion of people who are in the education profession

Here, the business and education both are equally acceptable in this society means that the value of p will be 50% or 0.5.

So, Null Hypothesis, $H_0$ : p = 0.50     {means that the business and education both are equally acceptable in this society}

Alternate Hypothesis, $H_A$ : p $\neq$ 0.50     {means that the business and education both are not equally acceptable in this society}

The test statistics that will be used here is One-sample z-test for proportions;

                               T.S.  =  $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$  ~  N(0,1)

where, $\hat p$ = sample proportion of people in the education profession = $\frac{690}{1200}$  = 0.575

            n = sample of people = 1200

So, the test statistics =  $\frac{0.575-0.5}{\sqrt{\frac{0.5(1-0.5)}{1200} } }$

                                     =  5.196

The value of z-test statistics is 5.196.

(i) Now, at a 1% level of significance, the z table gives a critical value of -2.58 and 2.58 for the two-tailed test.

Since the value of our test statistics doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.

Therefore, we conclude that the business and education both are not equally acceptable in this society.

(ii) Now, at a 5% level of significance, the z table gives a critical value of -1.96 and 1.96 for the two-tailed test.

Since the value of our test statistics doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.

Therefore, we conclude that the business and education both are not equally acceptable in this society.