You are a travel agent and wish to estimate, with 95% confidence, the proportion of vacationers who plan to travel outside the United States in the next 12 months. Your estimate must be accurate within 3% of the true proportion
Find the minimum sample size needed, using a prior study that found that 26% of the respondents said they planned to travel outside the United States in the next 12 months.
To find the minimum sample size needed to estimate the proportion of vacationers who plan to travel outside the United States with a 95% confidence level and an accuracy within 3% of the true proportion, you can use the following formula:
n = (Z^2 * p * q) / E^2
Where:
n = sample size
Z = Z-score corresponding to the desired confidence level (95% confidence level corresponds to a Z-score of approximately 1.96)
p = estimated proportion from the prior study (26% or 0.26)
q = 1 - p
E = margin of error (3% or 0.03)
Now we can substitute the values into the formula to find the minimum sample size:
n = (1.96^2 * 0.26 * 0.74) / (0.03^2)
Using a calculator, the minimum sample size is approximately 1026.06. However, since the sample size must be a whole number, we round it up to the nearest whole number.
Therefore, the minimum sample size needed for this estimation is 1027.