Question

20. A sample size of 600 persons selected at random from a large city shows that the percentage
of males in a sample is 53. It is believed that the ratio of males to total population in the city is
1/2 Test whether this belief is confirmed by the observations.​

Answer 1

Answer:

Not confirmed

Step-by-step explanation:

Suppose the Total population is 1000

According to the observation, in this total population males will be 53% which 530, that means females will be 470 (the remaining number)

We can see that males are not exactly the half of total population hence the belief is mo confirmed

Answer 2

Answer:

No the belief is not confirmed by the observation at all.

Step-by-step explanation:

Number of persons selected Randomly(n) = 600

In this sample percentage of males (m%) = 53 %

So number of males (m) :

$m = m\% \: of \: n \: persons \\ = (\frac{m}{100} ) \times n \: males \\ = ( \frac{53}{100}) \times 600 \: males \\ = 318 \: males$

But if it is true that the ratio of males to total population in the city is 1/2 ;

From the random sample of 600 persons we should get:

$m \prime \: = \frac{1}{2} \times n \\ = \frac{1}{2} \times 600 \: males \\ = 300 \: males$

But in fact we have got 318 males insted of 300 males. In this observation we get 18 numbers of males additional that is not matching with the belived ratio.

So it's not true that the ratio of males to total population in the city is 1/2 .

Hence from this observation the belief "the ratio of males to total population in the city is 1/2" is not confirmed.