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Chapter 9: Q.102 (page 554)

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.

Short Answer

Expert verified

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

Step by step solution

01

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

H0:渭=69,110;Ha:渭>69,110

02

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:N69110,748941localid="1649503125769" N69110,748941

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

03

Calculate the p-value using the normal distribution for mean RV

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.

04

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.

alphadecisionreason for decision
0.05Reject 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.

05

Confidence Interval

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

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