Answer:
For Part A:
Z>Z_{0.05} hence reject H₀ it means girls are better.Hₐ hypothesis is correct
For Part B:
Z<Z_{0.01} hence Girls are not better and Hₙ hypothesis is correct.
Step-by-step explanation:
Consider the Two Hypothesis:
H₀:[tex]u_{G}[/tex]=[tex]u_{B}[/tex]
Hₐ:[tex]u_{G}[/tex]>[tex]u_{B}[/tex]
Hₙ:[tex]u_{G}[/tex]<[tex]u_{B}[/tex]
Test Statistics:
Z=[tex]\frac{(x_{G} -x_{B} )-(u_{G}-u_{B)} }{\sqrt{\frac{S_{G} ^{2} }{n_{G} }+\frac{S_{B}^{2} }{n_{B} } } }[/tex]
Where
[tex]x_{G}[/tex] is the mean grade of girls
[tex]x_{B}[/tex] is the mean grade of boys
[tex]S_{G}[/tex] is the standard deviation of girls
[tex]S_{B}[/tex] is the standard deviation of boys
[tex]n_{G}[/tex] is the number of girls
[tex]n_{B}[/tex] is the number of boys
Z=[tex]\frac{(75 -72 )-0 }{\sqrt{\frac{6^{2} }{36 }+\frac{8^{2} }{32 } } }[/tex]
Z≅1.73
Critical Value at [tex]Z_{0.05} = 1.645\\Z_{0.01} = 2.326[/tex]
For Part A:
Z>Z_{0.05} hence reject H₀ it means girls are better.Hₐ hypothesis is correct
For Part B:
Z<Z_{0.01} hence Girls are not better and Hₙ hypothesis is correct.
