What % of hospitals provide at least some charity care? Thefollowing problem is

Question

What % of hospitals provide at least some charity care? Thefollowing problem is based on information taken from state healthcare data: Utilizationi , spending, and characteristics (AmericanMedical Association) Based on a random sample of hospital reportsfrom eastern states, the following information was obtained (unitsin % of hospitals providing at least some charity care: 57.1   56.2   53.0  66.1   59.0   64.7   70.1  64.7    53.5    78.2                                                                                                                    _ Use a calculator with mean and sample stardard deviation keysto verify that x ˜ 62.3% and s ˜ 8.0%. Find a 90%confidence interval for the population average of thepercentage of hospitals providing at least some charity care. What % of hospitals provide at least some charity care? Thefollowing problem is based on information taken from state healthcare data: Utilizationi , spending, and characteristics (AmericanMedical Association) Based on a random sample of hospital reportsfrom eastern states, the following information was obtained (unitsin % of hospitals providing at least some charity care: 57.1   56.2   53.0  66.1   59.0   64.7   70.1  64.7    53.5    78.2                                                                                                                    _ Use a calculator with mean and sample stardard deviation keysto verify that x ˜ 62.3% and s ˜ 8.0%. Find a 90%confidence interval for the population average of thepercentage of hospitals providing at least some charity care.

Explanation / Answer

Based on arandom sample of hospital reports from eastern states, thefollowing
data was obtained (units in %) of hospitals providing at least somecharity care: 57.1   56.2   53.0  66.1   59.0   64.7   70.1  64.7    53.5    78.2

a. Use a calculator with mean and samplestandard deviation keys to verify from
above data that sample mean X_bar ˜ 62.3% and sample standarddeviation s ˜8.0%.
   {Sample Mean} = (X_bar) = 62.26
     {Sample Standard Deviation} = s = 8.018

b. Find a 90% confidence interval for thepopulation average of the percentage
of hospitals providing at least some charitycare.
   {Sample Mean} = (X_bar) = 62.26
     {Sample Standard Deviation} = s = 8.018
     {Sample Size} = N = 10
     {Degrees Of Freedom} = df = N - 1 = (10) - 1 = 9
     {"t" Value For 90% Confidence Interval,df=9} = (t_90) = 1.833
     {90%Confidence Interval For Population Mean""} =
          = { (X_bar) -(t_90)*s/Sqrt[N] < < (X_bar) + (t_90)*s/Sqrt[N] }
          = {(62.26) -(1.833)*(8.018)/Sqrt[10] < < (62.26) +(1.833)*(8.018)/Sqrt[10] }
          = { (57.61) < < (66.91)}

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.