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?

Question

Quizplus · Accepted Answer

We can use the formula n = (Z/ E)^2 * P * (1-P) where 
- Z is the Z-score corresponding to the desired level of confidence (2.33 for 98% confidence)
- E is the maximum error desired (0.03)
- P is the estimated proportion (0.8)

Substituting these values, we get 
n = (2.33/0.03)^2 * 0.8 * 0.2
n = 1183

Therefore, the researcher needs a sample size of 1183 to be 98% confident that the true proportion is within 3% of the estimated proportion. We can use the formula n = (Z^2 * p * (1-p)) / E^2 where:
- Z is the z-value for our level of confidence, so Z = 2.33 (z-value for 98% confidence)
- p is our estimated proportion, which is 0.8 (80%)
- E is our maximum error, which is 0.03 (3%)

Plugging in these values, we get:
n = (2.33^2 * 0.8 * (1-0.8)) / 0.03^2
n = 1182.97

Rounding up to the nearest whole number, we get n = 1183. Therefore, the best choice is C, with a necessary sample size of 1183.

The Academy of Orthopedic Surgeons States That 80% of Women