A Study Was Conducted to Determine If Patients Recovering from Knee

question 9

Multiple Choice

A study was conducted to determine if patients recovering from knee surgery should receive physical therapy two or three times per week. Suppose $p _ { 1 }$ represents the proportion of patients who showed improvement after one month of therapy three times a week and $p _ { 2 }$ represents the proportion of patients who showed improvement after one month of therapy twice a week. A $90 \%$ confidence interval for $p _ { 1 } - p _ { 2 }$ is $( 0.12,0.38 )$ . Give an interpretation of this confidence interval.

• A) We are \(90 \%\) confident, based on the data, that patients who receive therapy three times per week show between \(12 \%\) and \(38 \%\) more improvement after one month than patients who receive therapy twice a week.
• B) We know that \(90 \%\) of all knee-surgery patients will show between \(12 \%\) and \(38 \%\) more improvement with therapy three times per week instead of twice a week.
• C) We are \(90 \%\) confident, based on the data, that the proportion of patients who show improvement with therapy three times per week is between \(12 \%\) and \(38 \%\) higher than the proportion who show improvement with therapy twice a week.
• D) We know that \(90 \%\) of all knee-surgery patients will show between \(12 \%\) and \(38 \%\) more improvement with therapy twice a week instead of three times per week.
• E) We are \(90 \%\) confident, based on the data, that the proportion of patients who show improvement with therapy three times per week is between \(12 \%\) and \(38 \%\) lower than the proportion who show improvement with therapy twice a week.

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