Question

Do A students tend to sit in a particular part of the classroom? To answer this question, the locations of the students who received A grades was recorded. The results were that 17 sat in the front, 9 sat in the middle, and 5 sat in the back of the classroom. Test the claim that the A students are not evenly distributed throughout the classroom.

What are the null and alternative hypotheses for this test?

Provide the chi-square test statistic.

What do you conclude regarding the null? Use a p-value to justify your decision.

Answer 1

Claim :

Do A students tend to sit in a particular part of the classroom?

To answer this question, the locations of the students who received A grades was recorded.

The results were that 17 sat in the front, 9 sat in the middle, and 5 sat in the back of the classroom.

Test the claim that the A students are not evenly distributed throughout the classroom.

## What are the null and alternative hypotheses for this test?

Ho : the A students are evenly distributed throughout the classroom.

H1 : the A students are not evenly distributed throughout the classroom.

## chi-square test statistic.

Chi square test statistics =  Σ ( Oi - Ei) ^2 / Ei

where Oi is observed frequency and Ei is expected frequency .

here Ei = [ 17 + 9 + 5 ] /3 = 31 / 3 = 10.333

χ2   = [ ( 17 - 10.333)^2 + ( 9 - 10.333)^2 + ( 5 - 10.333)^2 ] / 10.333

= [44.4444 + 1.7768 + 28.440 ] / 10.333

= 74.661 / 10.33

= 7.2255

degree of freedom = ( k - 1) here k = 3  

= 2 is degree of freedom

here we dont have given alpha vlaue assume it 5 % = 0.05

critical value = 5.9914 ( from statistical table )

Decision : we reject Ho if chi square test statistics is greater than critical value here chi square test statistics is greater than chi square critical value here we reject Ho at given alpha level . ( using critical value approach )

Conclusion : there is sufficient evidene to conclude that the A students are not evenly distributed throughout the classroom.

## What do you conclude regarding the null? Use a p-value to justify your decision.

p value = 0.0269 ( from statistical table )

Decision : we reject Ho if p value is less than alpha value using p value approach here p value is less than alpha value we reject Ho at given level of significance .

Conclusion : there is sufficient evidene to conclude that the A students are not evenly distributed throughout the classroom.