Probability and Statistics

1)
a)
Number of students from Electronic and Electrical Engineering scored more than 70 % is = 37
Total students from Electronic and Electrical Engineering = n1 = 114
Proportion = p1= 37/114 = 0.325
σ 1= √ p1 ( 1− p1 )
n1
= √ 0.325 ( 1−0.325 )
114 =0.0438
b)
Number of students from Mechanical Engineering scored more than 70 % is = 48
Total students from Mechanical Engineering = n2 = 131
Proportion = p2 = 48/131 = 0.366
σ 2= √ p2 ( 1− p2 )
n2
= √ 0.3 66 (1−0.3 66 )
131 =0.04 20
c)
Pooled sample proportion
p= p1 × n1 + p2 × n2
n1 +n2
p=0.347
σ =
√ p ( 1− p )
1
1
n1
+ 1
n2
=0.0609
Hypothesis is
H0 : p1= p2
H1 : p1 ≠ p2
z= p1− p2
σ =−0.673
Cumulative probability: P (Z <-0.673)
= 0.025
Since the P value is less than 5 % then we reject the null hypothesis and we can infer that