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Q.102

Expert-verifiedFound in: Page 554

Book edition
OER 2018

Author(s)
Barbara Illowsky, Susan Dean

Pages
902 pages

ISBN
9781938168208

Registered nurses earned an average annual salary of $69,110. For that same year, a survey was conducted of 41 California registered nurses to determine if the annual salary is higher than $69,110 for California nurses. The sample average was $71,121 with a sample standard deviation of $7,489. Conduct a hypothesis test.

CI: ($68,757, $73,485)

${H}_{0}:\mu =69,110;{H}_{a}:\mu >69,110$

Normal: $N\left(69110,\frac{7489}{\sqrt{41}}\right)$localid="1649503125769" $N\left(69110,\frac{7489}{\sqrt{41}}\right)$

Test Statistic: $t=1.719$localid="1649503135603" $t=1.719$

$p-value=0.0466$

In one to two complete sentences, explain what the p-value means for this problem.

If the null hypothesis is true (the mean salary is 69110), then there is a 0.0466 probability that the sample (estimated) mean salary is 71121 or more.

alpha | decision | reason for decision |

0.05 | Reject the null hypothesis. | $p-value<0.05$ |

Conclusion: At the 5% significance level, there is sufficient evidence to conclude that the mean salary of California registered nurses exceeds $69,110.

CI: ($68,757, $73,485)

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