If 52% of the customers at a certain grocery store regularly use coupons, what is the approximate standard deviation of the sampling distribution of the proportion for samples of size 240?
2.1%
3.2%
4.7%
10.4%
Well, the standard deviation of the sampling distribution of a proportion depends on the population proportion and the sample size.
Since 52% of the customers regularly use coupons, that would be the population proportion.
And for a sample size of 240, we can calculate the standard deviation of the sampling distribution using the formula:
Standard Deviation = sqrt((p * (1 - p)) / n),
where p is the population proportion and n is the sample size.
Plugging in the values, we get:
Standard Deviation = sqrt((0.52 * (1 - 0.52)) / 240)
= sqrt((0.52 * 0.48) / 240)
= sqrt(0.2496 / 240)
= sqrt(0.00104)
= 0.0322 (approximately)
So the approximate standard deviation of the sampling distribution of the proportion for samples of size 240 is 3.22%.
Therefore, the closest answer choice is 3.2%.
The approximate standard deviation of the sampling distribution of the proportion can be found using the formula:
Standard Deviation = sqrt(p*(1-p)/n)
where p is the proportion of customers who regularly use coupons (52% = 0.52) and n is the sample size (240).
Using this formula, we can calculate the standard deviation as follows:
Standard Deviation = sqrt(0.52*(1-0.52)/240) ≈ 0.032 (or 3.2%)
Therefore, the approximate standard deviation of the sampling distribution of the proportion for samples of size 240 is 3.2%. So, the correct answer is 3.2%.
To find the approximate standard deviation of the sampling distribution of the proportion, we can use the following formula:
Standard Deviation = sqrt( (p * (1 - p)) / n ),
where:
- p is the proportion of customers who regularly use coupons (in decimal form)
- n is the sample size
In this case, p is given as 52%, which is 0.52 in decimal form, and n is 240.
So, let's plug in the values:
Standard Deviation = sqrt( (0.52 * (1 - 0.52)) / 240 )
Calculating this expression:
Standard Deviation = sqrt( (0.52 * 0.48) / 240 )
Standard Deviation = sqrt( 0.2496 / 240 )
Standard Deviation = sqrt( 0.00104 )
Standard Deviation ≈ 0.0322
Converting this value to a percentage, we get approximately 3.22%.
Therefore, the correct answer is 3.2%.