Question

An experiment about the gender success in Math courses is performed and the following results are obtained. 150 out of 270 male participants could get a grade above 50. On the other hand 135 out of 228 female participants obtained a score above 50. Design and perform a test to see if the difference is statistically significant.

Answer 1

p₁: Proportion of males who could get a grade above 50

p₂ : Proportion of females who could get a grade above 50

Null hypothesis H₀ : Difference in Proportion of grades above 50 between males and females is zero(not significant)

H₀ : p₁ - p₂ = 0

Alternate hypothesis H_{a :} Difference in Proportion of grades above 50 between males and females is not zero(significant)

H₁: p₁ - p₂ 0 - two tailed test

Given,

Given
n1 : Sample Size of Sample 1: Number of male participants in the sample	270
n2 : Sample Size of Sample 2 : Number of Female participants in the sample	228
x1 : Number male participants from the sample who could get a grade above 50	150
x2 : Number female participants from the sample who could get a grade above 50	135
: Sample Proportion of male participants from the sample who could get a grade above 50 = 150/270	0.5556
: Sample Proportion of female participants from the sample who could get a grade above 50 = 135/228	0.5921
Level of Significance	5%

test statistic z = -0.8202

For two tailed test :

As P-Value i.e. is greater than Level of significance i.e (P-value:0.4121 > 0.05:Level of significance); Fail to Reject Null Hypothesis
There is no sufficient evidence to conclude there is a significant difference in Proportion of grades above 50 between males and females