Answer:
The Mean is not equal to $31,129.
Step-by-step explanation:
Consider the provided information.
The mean is $31129
Thus, the null hypothesis ![H_0: \mu = 31129](https://tex.z-dn.net/?f=H_0%3A%20%5Cmu%20%3D%2031129)
Alternative hypothesis ![H_a: \mu \neq 31129](https://tex.z-dn.net/?f=H_a%3A%20%5Cmu%20%5Cneq%2031129)
A random sample of 15 firstyear CMAs in Denver produces a mean salary of $32,279, with a standard deviation of $1,797.
Thus the value mean of sample is 32279, standard deviation is 1797 and number of samples are 15.
Now use the 2 sided t-test.
![t=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
Now substitute the respective values in the above formula.
![t=\frac{32279-31129}{\frac{1797}{\sqrt{15}}}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B32279-31129%7D%7B%5Cfrac%7B1797%7D%7B%5Csqrt%7B15%7D%7D%7D)
![t=\frac{1150}{464}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B1150%7D%7B464%7D)
Test Value = 2.4785 approximately
Now, find the corresponding p-value in your t-table with DF(degree of freedom) 14.
p = 0.0265
as the value of p < 0.05, so you reject null hypothesis.
Thus, the Mean is not equal to $31,129.