Question

It is believed that the average starting salary for a 21-25 year old college grad exceeds $52,000 per year. Hence, it is desired to test H0: µ ≤ 52,000 versus H1 : µ > 52,000. Assume σ = $5,745 and a SRS of size 65 is taken. We reject H0 when X > 53,460. The significance level α is:

Answer 1

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 $\bar X>\ 53,460$ 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)

   $=P(\bar X>53460|\mu \leq 52000)$

   $=P[\frac{\bar X-\mu_{0}}{\sigma/\sqrt{n}}>\frac{53460-52000}{5745/\sqrt{65}}]$

   $=P(Z>2.05)\\=1-P(Z$

*Use a z-table for the probability.

Thus, the significance level α is 0.02.