Math Problem Statement

The Medical Assurance Company is investigating the cost of a routine office visit to family practice physicians in the Rochester, NY area. There are 39 physicians, labeled from 00 to 38, categorized into solo practice (S), partner practice (P), and group practice (G). Tasks involve contacting physicians according to different sampling methods.

Solution

It seems you've uploaded an image that relates to a statistical question involving sampling from a group of physicians. Based on the text and table in the image, here is a breakdown of the questions:

Task Overview:

  • Objective: Investigate the cost of routine office visits for family practice physicians in the Rochester, NY area.
  • There are 39 physicians, labeled from 00 to 38, and they are either in solo practice (S), partner practice (P), or group practice (G).
  • You need to contact physicians according to various sampling methods.

Questions:

  1. (a) Which physicians should be contacted from the random numbers provided?

    • The random numbers are: 31, 94, 43, 36, 03, 24, 17.
    • Since only physicians numbered from 00 to 38 are considered, ignore numbers outside this range (e.g., 94 and 43).

    Physicians to contact based on valid random numbers:

    • 31: Mark Bertko, M.D. (P)
    • 36: Richard Molloy, M.D. (S)
    • 03: Mark D. Hilliard, M.D. (P)
    • 24: Stanford Kennedy, M.D. (S)
    • 17: Randy Myers, M.D. (S)
  2. (b) Select a random sample of four physicians using a random number table (Appendix B.4 or similar).

    • This question asks for a random sample of 4, which would be selected using a random number generator or table.
  3. (c) Use systematic random sampling:

    • Every fifth physician will be selected, starting at a random number like 02.
    • Selecting every fifth physician starting from 02: 02, 07, 12, 17, 22, 27, 32.

    Physicians selected:

    • 02: Crystal R. Gowie, M.D. (S)
    • 07: Justin Fordham, M.D. (S)
    • 12: Patrick Adams, M.D. (G)
    • 17: Randy Myers, M.D. (S)
    • 22: J. Christian Zona, M.D. (P)
    • 27: Thomas Tafelski, M.D. (P)
    • 32: Cheryl Zaborowski, M.D. (G)
  4. (d) Select a sample that includes three physicians in solo practice (S), two in partnership (P), and one in a group practice (G).

    • You would need to select based on the listed practice types, ensuring the correct distribution.

Would you like to proceed with one of these tasks or clarify anything further?

5 Related Questions:

  1. How do you compute the systematic sampling interval?
  2. What are the advantages of systematic sampling over random sampling?
  3. Can systematic sampling introduce bias, and how can that be mitigated?
  4. How would you calculate the sample mean from the charges once data is collected?
  5. What is the importance of stratified sampling in healthcare studies like this?

Tip: Always ensure that random samples are chosen without any influence, as this helps to reduce bias in statistical studies.

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Math Problem Analysis

Mathematical Concepts

Random Sampling
Systematic Sampling
Stratified Sampling

Formulas

Systematic Sampling Interval = Population Size / Sample Size

Theorems

Law of Large Numbers
Central Limit Theorem

Suitable Grade Level

Undergraduate