Final answer:
The standard error of the sample proportion is found using the formula sqrt[(p(1 - p)) / n], and for a proportion of 0.34 and sample size of 231, the standard error is approximately 0.0311, rounded to four decimal places.
Step-by-step explanation:
To find the standard deviation of the sampling distribution of the sample proportion (often referred to as the standard error), we can use the formula:
Standard Error (SE) = sqrt[(p(1 - p)) / n]
where p is the proportion of defective parts in the population, and n is the sample size. Given that p=0.34 and n=231, we can calculate the standard error as follows:
SE = sqrt[(0.34(1 - 0.34)) / 231]
SE = sqrt[(0.34 * 0.66) / 231]
SE = sqrt[(0.2244) / 231]
SE = sqrt[0.000971]
SE ≈ 0.0311
Therefore, the standard error of the sample proportion is approximately 0.0311, rounded to four decimal places.