a politician claims that the mean salary for managers in his state is more than the national mean, $83,000. assume the the population is normally distributed and the population standard deviation is $7700. the salaries (in dollars) for a random sample of 30 managers in the state are listed. at $ \alpha = 0.07 $, is there enough evidence to support the claim? use technology

$ \begin{array} { | c | c | c | c | c | c | c | c | c | c | } \hline 78,945 & 83,509 & 89,466 & 79,248 & 98,556 & 80,394 & 76,746 & 75,022 & 88,173 & 81,659 \\ \hline 77,028 & 87,817 & 83,225 & 97,502 & 85,025 & 82,636 & 81,053 & 91,161 & 71,290 & 81,179 \\ \hline 72,479 & 86,600 & 81,846 & 75,618 & 89,265 & 70,529 & 88,004 & 87,083 & 78,496 & 98,930 \\ \hline \end{array} $

(b) identify the standardized test statistic.
$ z = $
(round the final answer to two places as needed. round all intermediate values to three places as needed.)
(c) find the p-value. use technology.
(round to three decimal places as needed.)
(d) decide whether to reject or fail to reject the null hypothesis.
$ \bigcirc $ a. fail to reject $ h _ { 0 } $. there is not sufficient evidence to $ \bigcirc $ b. reject $ h _ { 0 } $. there is sufficient evidence to support
support the claim that managers mean salary is
the claim that managers mean salary is more than
more than the national mean.
the national mean.
$ \bigcirc $ c. reject $ h _ { 0 } $. there is not sufficient evidence to $ \bigcirc $ d. fail to reject $ h _ { 0 } $. there is sufficient evidence to
support the claim that managers mean salary is
support the claim that managers mean salary is
more than the national mean.
more than the national mean.

Question

a politician claims that the mean salary for managers in his state is more than the national mean, $83,000. assume the the population is normally distributed and the population standard deviation is $7700. the salaries (in dollars) for a random sample of 30 managers in the state are listed. at $ \alpha = 0.07 $, is there enough evidence to support the claim? use technology

$ \begin{array} { | c | c | c | c | c | c | c | c | c | c | } \hline 78,945 & 83,509 & 89,466 & 79,248 & 98,556 & 80,394 & 76,746 & 75,022 & 88,173 & 81,659 \\ \hline 77,028 & 87,817 & 83,225 & 97,502 & 85,025 & 82,636 & 81,053 & 91,161 & 71,290 & 81,179 \\ \hline 72,479 & 86,600 & 81,846 & 75,618 & 89,265 & 70,529 & 88,004 & 87,083 & 78,496 & 98,930 \\ \hline \end{array} $

(b) identify the standardized test statistic.
$ z = $
(round the final answer to two places as needed. round all intermediate values to three places as needed.)
(c) find the p-value. use technology.
(round to three decimal places as needed.)
(d) decide whether to reject or fail to reject the null hypothesis.
$ \bigcirc $ a. fail to reject $ h _ { 0 } $. there is not sufficient evidence to $ \bigcirc $ b. reject $ h _ { 0 } $. there is sufficient evidence to support
support the claim that managers mean salary is
the claim that managers mean salary is more than
more than the national mean.
the national mean.
$ \bigcirc $ c. reject $ h _ { 0 } $. there is not sufficient evidence to $ \bigcirc $ d. fail to reject $ h _ { 0 } $. there is sufficient evidence to
support the claim that managers mean salary is
support the claim that managers mean salary is
more than the national mean.
more than the national mean.

Accepted Answer

# Explanation:
## Step1: Recall the decision rule for hypothesis testing
If $P - value\geq\alpha$, fail to reject $H_0$. If $P - value<\alpha$, reject $H_0$. Here, $\alpha = 0.07$ and $P - value=0.417$.
## Step2: Compare the $P - value$ and $\alpha$
Since $0.417\geq0.07$ (i.e., $P - value\geq\alpha$).

# Answer:
A. Fail to reject $H_0$. There is not sufficient evidence to support the claim that managers mean salary is more than the national mean.

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the decision rule for hypothesis testing

Step2: Compare the \(P - value\) and \(\alpha\)

Answer: