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:
H₀: The average starting salary for a 21-25 year old college grad does not exceeds $52,000 per year, i.e. µ ≤ 52,000.
Hₐ: The average starting salary for a 21-25 year old college grad exceeds $52,000 per year, i.e. µ > 52,000.
The information provided is:
σ = $5,745
n = 65
Also, if [tex]\bar X>\$53,460[/tex] then the null hypothesis will be rejected.
Here, we need to compute the value of significance level α, the type I error probability.
A type I error occurs when we reject a true null hypothesis (H₀).
That is:
α = P (type I error)
α = P (Rejecting H₀| H₀ is true)
[tex]=P(\bar X>53460|\mu \leq 52000)[/tex]
[tex]=P[\frac{\bar X-\mu_{0}}{\sigma/\sqrt{n}}>\frac{53460-52000}{5745/\sqrt{65}}][/tex]
[tex]=P(Z>2.05)\\=1-P(Z<2.05)\\=1-0.97982\\=0.02018\\\approx0.02[/tex]
*Use a z-table for the probability.
Thus, the significance level α is 0.02.
