Question: The mean number of students who get first grade in a school of 35 sections is 8 and that of 42 sections of another school is 7. If the variances are 4 and 6, then find out the p A ) 0.0001, the means differ
B ) 0.1922, the means do not differ
C ) 0.0016, the means differ
D ) 0.0488, the means differ
Steps to derive 1 H
0 : μ
1 = μ
2 and H
1 : μ
1 ≠ μ
2 [Null and Alternative hypotheses.]
2 X ‾ 1 = 8,
X ‾ 2 = 7,
n 1 = 35,
n 2 = 42,
s 1 2 = 4,
s 2 2 = 6
3 The
z score value is
4 z = 1.972
[Substitute the values in the
z score and simplify.]
5 z = 1.972 occupies an area of 0.4756 under the curve.
6 For 95% confidence level, α = 0.05.
7 P - value = 2(0.5000 - 0.4756) = 0.0488
[This is a two tailed test.]
8 Since the P value is less that the α value, we reject the null hypothesis.
9 So, there is enough evidence to prove that the mean number of students who got first grade in both the schools differ significantly.
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