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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Definitions:

Innovation

The process of translating an idea or invention into a good or service that creates value or for which customers will pay.

Volume Density

Volume density, in logistics and material science, relates to the mass of an object or substance per unit volume, influencing shipping costs, storage requirements, and handling methods.

Transportation Costs

Expenses related to the movement of goods or materials from one location to another, including costs for shipping, freight, fuel, and warehousing.

Remanufacturing

The process of restoring used products to a condition of quality comparable to that of new products, often involving disassembly, cleaning, repair, and reassembly.