In a particular year, registered nurses earned an average annual salary of $52,330. A survey was conducted with48nurses from a particular state to determine if the annual salary is higher than $52,330 for that state's nurses. The sample average was$61,214with a sample standard deviation of $7,489. Conduct a hypothesis test at the 5% level.

Note: If you are using a Student'st-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

• Part (a)
• State the null hypothesis.
• H₀:
• <52,330
• H₀:
• 52,330
• H₀:
• 52,330
• H₀:
• 52,330
• Part (b)
• State the alternative hypothesis.
• H_a:
• 52,330
• H_a:
• = 52,330
• H_a:
• >52,330
• H_a:
• 52,330
• Part (c)
• In words, state what your random variableXrepresents.
• X
• represents the annual salary of a nurse.
• X
• represents the proportion of nurses that earn more than $52,330.
• X
• represents the number of registered nurses.
• X
• represents the average annual salary of nurses.
• Part (d)
• State the distribution to use for the test. (Enter your answer in the formzort_dfwheredfis the degrees of freedom.)
• Part (e)
• What is the test statistic? (Round your answer to two decimal places.)
• ---Select---
• z
• t
• =
• Part (f)
• What is thep-value? (Round your answer to four decimal places.)
• Explain what thep-value means for this problem.
• IfH₀
• is false, then there is a chance equal to thep-value that the average annual salary of a nurse is $61,214 or more.
• IfH₀
• is false, then there is a chance equal to thep-value that the average annual salary of a nurse is not $61,214 or more.
• IfH₀
• is true, then there is a chance equal to thep-value that the average annual salary of a nurse is not $61,214 or more.
• IfH₀
• is true, then there is a chance equal to thep-value that the average annual salary of a nurse is $61,214 or more.
• Part (g)
• Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to thep-value. (Upload your file below.)
• This answer has not been graded yet.
• Part (h)
• Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.
• (i) Alpha:
• =
• (ii) Decision:
• reject the null hypothesis
• do not reject the null hypothesis
• (iii) Reason for decision:
• Since<p-value, we do not reject the null hypothesis.
• Since>p-value, we do not reject the null hypothesis.
• Since<p-value, we reject the null hypothesis.
• Since>p-value, we reject the null hypothesis.
• (iv) Conclusion:
• There is sufficient evidence to conclude that the average salary of nurses in the state is more than $52,330.
• There is not sufficient evidence to conclude that the average salary of nurses in the state is more than $52,330.
• Part (i)
• Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to the nearest whole number.)