A recent study indicated that 26% of the 173 women over age 55in the study were widows. Round up your answers to the next whole number for the following questions. If no estimate of the sample proportion is available, how large should the sample be?

To determine how large the sample should be when no estimate of the sample proportion is available, we use the formula for sample size calculation:

\[
n = \frac{{Z^2 \cdot p \cdot (1 - p)}}{{E^2}}
\]

Where:
- \( Z \) is the z-score corresponding to the desired confidence level.
- \( p \) is the estimated proportion of the population (in this case, 26% or 0.26).
- \( E \) is the margin of error (typically given, but it hasn't been provided here, so I'll assume one for the calculation unless you provide one).

If no estimate of the proportion is available, the safest choice is to use \( p = 0.5 \), since it maximizes the required sample size and provides the most conservative estimate.

To proceed with the calculation, we need the margin of error (E) and the confidence level (which gives us \( Z \)).

Could you please confirm the margin of error and confidence level you'd like to use?

Alternatively, I can assume a typical margin of error (say 5%) and confidence level (say 95%) to calculate the sample size.

A recent study indicated that 26% of the 173 women over age 55 in the study were widows. Round up your answers to the next whole number for the following questions. If no estimate of the sample proportion is available, how large should the sample be?

Learn how to calculate the sample size required for estimating a population proportion when no prior estimate is available. This example uses data from a study where 26% of 173 women over age 55 were widows. Suitable for students learning statistics and sample size determination. Includes key statistical concepts and the formula for sample size calculation.

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