Answer:
|Z| = |-0.126| = 0.126 < 1.645
Null hypothesis is accepted
<em>The retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire. </em>
<em> μ = 57.5</em>
Step-by-step explanation:
<u><em>Explanation</em></u>:-
The average retirement age for a certain country was reported to be 56.4 years
<em>The mean of the sample x⁻ = 56.4</em>
<em>The standard deviation of the Population 'σ'= 55 years</em>
<em>The mean of the population μ = 57.5</em>
<em>Null hypothesis: H₀:The retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire. </em>
<em> μ = 57.5</em>
<em>Alternative Hypothesis</em> : H₁: μ ≠57.5
Test statistic
![Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7Bx%5E%7B-%7D-mean%20%7D%7B%5Cfrac%7BS.D%7D%7B%5Csqrt%7Bn%7D%20%7D%20%7D)
<u><em>critical value:</em></u>
![Z_{\frac{\alpha }{2} } = Z_{0.05} =1.645](https://tex.z-dn.net/?f=Z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%20%3D%20Z_%7B0.05%7D%20%3D1.645)
![Z = \frac{56.4-57.5 }{\frac{55}{\sqrt{40} } } = -0.126](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B56.4-57.5%20%7D%7B%5Cfrac%7B55%7D%7B%5Csqrt%7B40%7D%20%7D%20%7D%20%3D%20-0.126)
|Z| = |-0.126| = 0.126 < 1.645
<em>The null hypothesis is accepted </em>
<u><em>Conclusion</em></u>:-
The retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire.
μ = 57.5