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 α = 0.01, test the claim that the mean salary is $95,000. complete parts (a) through (e) below. assume the population is normally distributed.
(a) identify the claim and state ( h_0 ) and ( h_a ).
( h_0: mu = 95,000 )
( h_a: mu
eq 95,000 )
(type integers or decimals. do not round)
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 = square ).
(use a comma to separate answers as needed. round to two decimal places as needed.)

Explanation:

Step1: Determine the type of test

Since \(H_{a}:\mu
eq95000\), this is a two - tailed test.

Step2: Calculate the degrees of freedom

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

Step3: Find the critical value

For a two - tailed test with \(\alpha=0.01\) and \(df = 15\), using a t - distribution table or technology, the critical values are \(t_{0}=\pm 2.95\)

Answer:

\(t_{0}=- 2.95,2.95\)