Final answer:
The standard deviation of the sampling distribution of the proportion of adults who do not own a credit card in a simple random sample of 700 adults is approximately 0.016. The correct answer is option D) 0.016.
Step-by-step explanation:
To determine the standard deviation of the sampling distribution of the proportion (σp) of adults in the simple random sample who do not own a credit card, we can use the formula for the standard deviation of the sampling distribution of a proportion given by:
σp = √[p(1 - p) / n]
Where:
- σp is the standard deviation of the sampling distribution of the sample proportion p.
- p is the population proportion (25% or 0.25 in this case).
- n is the sample size (700 in this case).
Inserting the given values:
σp = √[0.25(1 - 0.25) / 700]
σp = √[0.25(0.75) / 700]
σp = √[0.1875 / 700]
σp = √[0.00026785714]
σp ≈ 0.01636
The closest answer among the provided options is D) 0.016, so that would be the choice we select as the standard deviation of the sampling distribution of p.