Final answer:
To be 95% confident that the sample proportion does not differ from the true proportion of households with two cars by more than 6%, a sample size calculation using a standard formula shows that approximately 268 households need to be surveyed.
Step-by-step explanation:
A researcher who wants to estimate the number of households with two cars and to be 95% confident that the sample proportion will not differ from the true proportion by more than 6% can use a sample size formula for a proportion. The formula is n = (Z^2 * p * (1-p)) / E^2, where Z is the Z-score corresponding to the desired confidence level (1.96 for 95% confidence), p is the estimated proportion of the population with the characteristic, and E is the margin of error.
Substituting the values: n = (1.96^2 * 0.23 * (1-0.23)) / 0.06^2, we calculate the sample size needed.
When calculating, we find that the sample size needed is approximately 267 households. Since we cannot survey a fraction of a household, we round up to the next whole number, resulting in a required sample size of 268 households. Sample size, confidence interval, and margin of error are crucial in this calculation.