Question

A sample analysis of examination results of 500 students was made. It was found that 220 students have failed, 170 have secured a third class, 90 have secured a second class and the rest, a first class. Do these figures, support the general belief that the above categories are in the ratio 4:3:2:1 respectively?​

Answer 1

Answer:

200,100,20 ,10avanaajsvshklqkavags

Answer 2

Answer: The result is not in ratio 4 : 3 : 2 : 1

Step-by-step explanation:

Given : Total number of students given = 500

            Number of students failed = 220

            Number of students who have secured third class = 170

            Number of students who have secured second class is 90

            It is general belief that these categories are in the ratio 4:3:2:1

To Find : Do these figures support the general belief that these          

              categories are in the ratio 4:3:2:1

Concept : Testing of Hypothesis - In statistics, testing of hypothesis is used  to check the result of a survey or experiment to see if they have meaningful results.

Solution :

Number of students who secured first class = 500 - 220 - 170 - 90 = 20

The expected frequencies of the 4 classes are : 200, 150, 100, 50

$X^{2} =$∑$[\frac{(O - E)^{2} }{E} ]$

Under $H_{0}$, the test statistic is :

O            E             (O - E)             $(O - E)^{2}$            $\frac{(O - E)^{2} }{E}$

220       200            20                   400                  2

170        150             20                  400                   2.667

90         100            - 10                   100                   1

20         50             - 30                   900                  18

$X^{2}$ = 23.67

Number of degree of freedom (v) = n - 1 = 4 - 1 = 3

For v = 3, the table value of $X^{2}$ at 5% level is 7.815

Since, the calculated value of $X^{2}$ > the table value of $X^{2}$,  the result is not in ratio 4 : 3 : 2 : 1

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Related links :

Usually concerned with generating hypothesis from data rather than testing a hypothesis​ ?

https://brainly.in/question/41577498

For testing the hypothesis Ho: oº = 5 versus H :o?> 5. Suppose the degrees of

freedom is 9. Then, the find the critical value at 5% significance level.

a.6.919

b.3.325

c.19.023

d.2.7​

https://brainly.in/question/21489905

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