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Confidence Interval & Hypothesis Testing: Proportion

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The topic of my project is to find out the number of patients that have used In Home Care as their home health agency for more than 2 years. In Home Care's goal is to have over 50% of their patients be with them over 2 years which would demonstrate the staff is providing adequate and satisfying healthcare to their patients. A sample of 30 patients was obtained from the population of patients that currently use In Home Care as their home health provider which is 60 patients.10 patients states they have had In Home care home health agency for over 2 years and 20 patients state they have had In Home Care for less than 2 years.

A. Compute the proportion p (hat) for your sample. Show your computation.
B. Find a 95% confidence interval for p. What is the margin of error in this confidence interval? What is the meaning of this interval with respect to your data and project?
C. Construct and perform a hypothesis test for p at the significance level a = 0.05. What conclusions can you draw from this test?

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Solution Summary

The solution provides step by step method for the calculation of confidence interval and testing of hypothesis of population proportion. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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Estimation of a population proportion project
The topic of my project is to find out the number of patients that have used In Home Care as their home health agency for more than 2 years. In Home Care's goal is to have over 50% of their patients be with them over 2 years which would demonstrate the staff is providing adequate and satisfying healthcare to their patients. A sample of 30 patients was obtained from the population of patients that currently use In Home Care as their home health provider which is 60 patients. 10 patients states they have had In Home care home health agency for over 2 years and 20 patients state they have had In Home Care for less than 2 years.
Answers

A. Compute the proportion p (hat) for your sample. Show your computation.
Proportion, p (hat) = x/n = 10/30 = 0.3333333
B. Find a 95% confidence ...

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