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The Academy of Orthopedic Surgeons states that 80% of women wear shoes that are too small for their feet. A researcher wants to be 98% confident that this proportion is within 3% of the true proportion. How large a sample is necessary?

  • Statistics -

    Try this formula:
    n = [(z-value)^2 * p * q]/E^2
    ...where n = sample size needed; use .8 for p and .2 for q (q = 1 - p). E = maximum error, which is .03 (3%) in the problem. Z-value is found using a z-table (for 98%, the value is 2.33). Also, ^2 means squared and * means to multiply.

    I hope this will help get you started.

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