Complete Question
The options for the above question is
a There is not sufficient evidence to warrant rejection of the claim.
b There is sufficient evidence to warrant rejection of the claim.
c There is sufficient evidence to support the claim.
d There is not sufficient evidence to support the claim.
Answer:
Option A is correct
Step-by-step explanation:
From the question we are told that
The population mean is
$47,500
The sample size is ![n = 86](https://tex.z-dn.net/?f=n%20%20%3D%20%2086)
The sample mean is
$48,061
The standard deviation is
$2,351
The level of significance is ![\alpha = 0.02](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%200.02)
The null hypothesis is
$47,500
The alternative hypothesis is
$47,500
The critical value of
from the t-Distribution table is ![Z_{\frac{\alpha }{2} } = 2.326](https://tex.z-dn.net/?f=Z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%20%3D%20%202.326)
Now the test statistics is mathematically evaluated as
![t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }](https://tex.z-dn.net/?f=t%20%20%3D%20%20%5Cfrac%7B%5C%3D%20x%20-%20%20%5Cmu%20%7D%7B%20%5Cfrac%7B%5Csigma%20%7D%7B%5Csqrt%7Bn%7D%20%7D%20%20%7D)
substituting values
![t = \frac{48061 - 47500 }{\frac{2351}{\sqrt{86} } }](https://tex.z-dn.net/?f=t%20%20%3D%20%20%5Cfrac%7B48061%20%20-%20%2047500%20%7D%7B%5Cfrac%7B2351%7D%7B%5Csqrt%7B86%7D%20%7D%20%20%7D)
![t = 2.21](https://tex.z-dn.net/?f=t%20%20%3D%202.21)
Now from the values obtained we can see that
hence we fail to reject the null hypothesis
Hence there is not sufficient evidence to warrant rejection of the claim