Question

an employment information service claims the mean annual salary for senior level product engineers is $95,000. the annual salaries (in dollars) for a random sample of 16 senior level product engineers are shown in the table to the right. at \LXI0, test the claim that the mean salary is $95,000. complete parts (a) through (e) below. assume the population is normally distributed.
the claim is the null hypothesis.
(b) use technology to find the critical value(s) and identify the rejection region(s).
the critical value(s) is/are \\( t_{0}= \\) - 2.95,2.95.
(use a comma to separate answers as needed. round to two decimal places as needed.)
choose the graph which shows the rejection region.
a.
b.
c.
d.

Explanation:

Step1: Determine the type of test

Since we are testing a claim about the population mean and the population standard deviation is unknown, we use a \(t -\)test. The claim is \(\mu = 95000\), so the null hypothesis is \(H_0:\mu=95000\) and the alternative hypothesis is \(H_1:\mu
eq95000\) (two - tailed test).

Step2: Find the degrees of freedom

The degrees of freedom is \(df=n - 1\), where \(n = 16\). So \(df=16 - 1=15\).

Step3: Find the critical values

Using a \(t -\)distribution table or technology (e.g., in Excel: =T.INV.2T(0.01,15)), for a two - tailed test with \(\alpha = 0.01\) and \(df = 15\), the critical values are \(t_0=\pm 2.95\).

Step4: Identify the rejection regions

For a two - tailed \(t -\)test, the rejection regions are \(t<-t_0\) and \(t > t_0\), i.e., \(t<- 2.95\) and \(t>2.95\).

Answer:

The critical values are \(t_0=-2.95,2.95\). The rejection regions are \(t < - 2.95\) and \(t>2.95\), so the correct graph is C.