Answer:
D) + 3.82
Z- test statistic value = 3.819≅ 3.82
Step-by-step explanation:
<em><u>Explanation</u></em>:-
Given data the sample size 'n' = 350
Population mean 'μ' = $8,500
Sample mean 'x⁻' = $8,500
The population standard deviation is 'σ' = $1,200
The level of significance ∝ =0.05
<em>The tabulated value Z₀.₉₅ = 1.96</em>
<u><em>Null hypothesis</em></u><em>: There is no significant difference between the small private liberal arts college and the financial administrator.</em>
<em> x⁻= μ</em>
<em>Alternative hypothesis: x⁻> μ</em>
<em></em>
<u><em>Test statistic </em></u>
![Z = \frac{x^{-} -mean }{\frac{S.D}{\sqrt{n} } }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7Bx%5E%7B-%7D%20-mean%20%7D%7B%5Cfrac%7BS.D%7D%7B%5Csqrt%7Bn%7D%20%7D%20%7D)
![Z = \frac{8745-8500}{\frac{1200}{\sqrt{350} } }](https://tex.z-dn.net/?f=Z%20%20%20%3D%20%20%5Cfrac%7B8745-8500%7D%7B%5Cfrac%7B1200%7D%7B%5Csqrt%7B350%7D%20%7D%20%7D)
On calculation , we get
![Z = \frac{245}{64.14} = 3.819](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B245%7D%7B64.14%7D%20%3D%203.819)
<em> Z- test statistic value = 3.819≅ 3.82</em>
<u><em>Conclusion:</em></u><em>-</em>
<em>The calculated value = 3.82 > 1.96 at 0.05 level of significance.</em>
<em>The null hypothesis is rejected </em>
<em>Alternative hypothesis is accepted</em>
<em>The financial administrator believes that the average cost is higher than the small private liberal arts college</em>