Question

Out of 8000 graduates in a town 800 are females; out of 1600 graduate
employees 120 are females. Use χ
2
(chi-squared test)to determine if any
distinction is made in appointment on the basis of sex. Value of χ
2
at 5%
level for one degree of freedom is 3.84.

Answer 1

Answer:

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Answer 2

Answer:

The Value of $x^{2}$at 5% level for one degree of freedom is 3.84 is 13.889.

Step-by-step explanation:

Given that:

Graduates in the town = 8000

Females = 800

In 1600 graduates the employees of females = 120

To find:

The value of  at 5% at level of one degree of freedom of 3.84 =?

Solution:

Now let us arrange the following in a tabular form:

                        Employment            Unemployment    total

Males                    1480                      5720                  7200

Females                   120                      680                      800

Total                       1600                      6400                  8000

Now, let us consider that,

By taking the null hypothesis of no distinction which is made by appointment on basis of both male and females.

Let us apply, the formula for X square and find the value:

$E_{11}$ = $200/8000 *1600$

        = $0.025 *1600$

        = $1440$

Now, let us again create a table related to frequency :

1440                 5760                          7200

160                     640                           800

1600                  6400                        8000

Observed frequency     Expected frequency      ($O_{i} - E_{i} ^{2}$)        

1480                                1440                                   1600

120                                     160                                   1600                  

5720                                 5760                                  1600

680                                    640                                   1600

$(o_{i} -E_{i} )^{2} / E_{i}$

1.111

10.00

0.278

2.500

__________

13.889

___________

Therefore, $x^{2}$ = 13.889

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