Respuesta :
Answer:
Critical value for the rejection region if the level of significance is 5% = 1.645
We conclude that the average starting salary of graduates is more than 85,000$.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 85,000$
Sample mean, [tex]\bar{x}[/tex] = 88,000$
Sample size, n = 64
Alpha, α = 0.05
Population standard deviation, σ = 10,000
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 85,000\text{ dollars}\\H_A: \mu > 85,000\text{ dollars}[/tex]
We use One-tailed(right) 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{88000 - 85000}{\frac{10000}{\sqrt{64}} } = 2.4[/tex]
Now, [tex]z_{critical} \text{ at 0.05 level of significance } = 1.64[/tex]
Since,
[tex]z_{stat} > z_{critical}[/tex]
We reject the null hypothesis and accept the alternate hypothesis.
Thus, we conclude that the average starting salary of graduates is more than 85,000$.
