Respuesta :
Answer:
There is not enough evidence to conclude that average starting salary for clerical employees in the state is less than $35,000 per year.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 35,000 dollars per year
Sample mean, [tex]\bar{x}[/tex] = 34,700 dollars per year
Sample size, n = 100
Alpha, α = 0.10
Population standard deviation, σ = 3,500 dollars per year
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 35,000\text{ dollars per year}\\H_A: \mu < 35,000\text{ dollars per year}[/tex]
We use one-tailed z test to perform this hypothesis.
Formula:
[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]z_{stat} = \displaystyle\frac{34700 - 35000}{\frac{3500}{\sqrt{100}} } = -0.8571[/tex]
Now, [tex]z_{critical} \text{ at 0.10 level of significance } = -1.28[/tex]
Since,
[tex]z_{stat} > z_{critical}[/tex]
We fail to reject the null hypothesis and accept the null hypothesis.
Thus, there is not enough evidence to conclude that average starting salary for clerical employees in the state is less than $35,000 per year.
