Answer:
The significance level α is 0.02.
Step-by-step explanation:
A hypothesis test for single mean can be performed to determine whether the average starting salary for a 21-25 year old college grad exceeds $52,000 per year.
The hypothesis is defined as follows:
<em>H₀</em>: The average starting salary for a 21-25 year old college grad does not exceeds $52,000 per year, i.e. <em>µ</em> ≤ 52,000.
<em>Hₐ</em>: The average starting salary for a 21-25 year old college grad exceeds $52,000 per year, i.e. <em>µ</em> > 52,000.
The information provided is:
<em>σ</em> = $5,745
<em>n</em> = 65
Also, if
then the null hypothesis will be rejected.
Here, we need to compute the value of significance level <em>α</em>, the type I error probability.
A type I error occurs when we reject a true null hypothesis (H<em>₀</em>).
That is:
<em>α</em> = P (type I error)
<em>α</em> = P (Rejecting H<em>₀</em>| H<em>₀</em> is true)
![=P(\bar X>53460|\mu \leq 52000)](https://tex.z-dn.net/?f=%3DP%28%5Cbar%20X%3E53460%7C%5Cmu%20%5Cleq%2052000%29)
![=P[\frac{\bar X-\mu_{0}}{\sigma/\sqrt{n}}>\frac{53460-52000}{5745/\sqrt{65}}]](https://tex.z-dn.net/?f=%3DP%5B%5Cfrac%7B%5Cbar%20X-%5Cmu_%7B0%7D%7D%7B%5Csigma%2F%5Csqrt%7Bn%7D%7D%3E%5Cfrac%7B53460-52000%7D%7B5745%2F%5Csqrt%7B65%7D%7D%5D)
![=P(Z>2.05)\\=1-P(Z](https://tex.z-dn.net/?f=%3DP%28Z%3E2.05%29%5C%5C%3D1-P%28Z%3C2.05%29%5C%5C%3D1-0.97982%5C%5C%3D0.02018%5C%5C%5Capprox0.02)
*Use a <em>z</em>-table for the probability.
Thus, the significance level α is 0.02.