Respuesta :
Answer:
a) The Z -value 2.397 < 2.576 at 99% or 0.01% level of significance
Null hypothesis is accepted at 0.01% level of significance
They score is above 24 on the math portion of the exam
b)
Null Hypothesis: There is no significance difference between the college level mathematics and math courses in high school
H₀: μ = 24
Alternative Hypothesis: H₁: μ ≠ 24
Step-by-step explanation:
Step(i):-
Given random sample 'n' = 250
Given data sample mean x⁻ = 24.5
Standard deviation = 3.3
Null Hypothesis: There is no significance difference between the college level mathematics and math courses in high school
H₀: μ = 24
Alternative Hypothesis: H₁: μ ≠ 24
test statistic
[tex]Z = \frac{x^{-} - mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{24.5 - 24}{\frac{3.3}{\sqrt{250} } } = \frac{0.5}{0.2087} = 2.397[/tex]
a) 99% or 0.01% level of significance
Level of significance ∝ = 0.01
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01}{2} } = Z_{0.005} =2.576[/tex]
The Z -value 2.397 < 2.576 at 99% or 0.01% level of significance
Null hypothesis is accepted at 0.01% level of significance
They score is above 24 on the math portion of the exam
b) 95% or 0.05% level of significance
Level of significance ∝ = 0.05
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96[/tex]
The Z -value 2.397 > 1.96 at 95% or 0.05% level of significance
Null hypothesis is Rejected at 0.05% level of significance
They score is below 24 on the math portion of the exam
