Question

A random sample of 395 people was surveyed and each person was asked to report the highest education level they obtained. It is expected that there is no gender dependency in the education level. The Observed data that resulted from the survey are summarized in the following table:

High School Bachelors Masters Ph.d. Total
Female 60 54 46 41 201
Male 40 44 53 57 194
Total 100 98 99 98 395
What is the value of LaTeX: \chi^2?

[Hint: calculate the expected values and then use the LaTeX: \chi^2 formula]

Answer 1

Answer:

8.006

Step-by-step explanation:

the answer is available on online stat

Answer 2

The value of  $\chi^{2}$ is  8.006.

Given,

395 people sample was surveyed.

To Find,

The value of $\chi^{2}$.

Solution,

Here, given that 395 samples were taken.

First, we need to find out the expected values from the given table.

First, females 60 for high school.

To find the expected values for this, the total of a row * a total of a column / n is the formula.

So, for the female high school row total is 201

and column total is 100.

Here, n is the total number of samples, 395.

(201 * 100) / 395 = 50.886.

Like this, we need to find out the expected values for all the groups.

Female

i. Highschool = 50.886.

ii. Bachelors = (201*98)/395

 = 49.868.

iii. Masters = (201*99)/395

=50.377.

iv. Ph.D. = (201* 98)/395

= 49.868.

Male

i. Highschool = (194*100)/395

= 49.114.

ii. Bachelors = ( 194* 98) / 395

= 48.132

iii. Masters = ( 194 *99)/395

=  48.623.

iv. Ph.D. = (194* 98) /395

=48.132.

$\chi^{2}$ =    $\frac{(60-50886)^{2} }{50.886} +\frac{(54-49.868)^{2} }{49.868}+\frac{((46-50.377)^{2} }{50.377} +......................+\frac{(57-48.132)^{2} }{48.132}$

$\chi^{2}$ = 8.006.

Hence, the $\chi^{2}$ value is 8.006.

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