Book edition OER 2018

Author(s) Barbara Illowsky, Susan Dean

Pages 902 pages

ISBN 9781938168208

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Short Answer

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)

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Find H0 and Ha: We want to test if California registered nurses earned greater than $69,110 of an average annual salary, on average.

$H_{0} : μ = 69, 110; H_{a} : μ > 69, 110$

Step 2: Determine the distribution needed: In words, CLEARLY state what your random variable x represents.Let x = the mean salary in dollars for California registered nurses.

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

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

Step 3: Calculate the p-value using the normal distribution for mean RV

$p - v a l u e = 0.0466$

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.

Step 4: Compare α and the p-value:Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

alpha	decision	reason for decision
0.05	Reject the null hypothesis.	$p - v a l u e < 0.05$

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

Step 5: Confidence Interval

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

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Introductory Statistics

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Short Answer

Step by Step Solution

Step 1: Find H0 and Ha: We want to test if California registered nurses earned greater than $69,110 of an average annual salary, on average.

Step 2: Determine the distribution needed: In words, CLEARLY state what your random variable x represents.Let x = the mean salary in dollars for California registered nurses.

Step 3: Calculate the p-value using the normal distribution for mean RV

Step 4: Compare α and the p-value:Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

Step 5: Confidence Interval

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Introductory Statistics

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Short Answer

Step by Step Solution

Step 1: Find H0 and Ha: We want to test if California registered nurses earned greater than $69,110 of an average annual salary, on average.

Step 2: Determine the distribution needed: In words, CLEARLY state what your random variable x represents.Let x = the mean salary in dollars for California registered nurses.

Step 3: Calculate the p-value using the normal distribution for mean RV

Step 4: Compare α and the p-value:Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

Step 5: Confidence Interval

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