Your mathematics instructor claims that, over the years, 88% of his students have said that math is their favorite subject. In this year's class, however, only 21 out of 32 students named math as their favorite class. The instructor decides to construct a confidence interval for the true population proportion based on the sample value. What's the correct value for the standard error of SE in this case?

0.045

0.057

0.064

0.088

0.084

To determine the correct value for the standard error, we need to calculate it using the given information. The standard error (SE) for a proportion is calculated using the formula:

SE = sqrt(p * (1 - p) / n)

Where:
- p is the sample proportion (21/32 in this case)
- n is the sample size (32 in this case)

Let's substitute the values into the formula:

SE = sqrt((21/32) * (1 - 21/32) / 32)

Simplifying further:

SE = sqrt((21/32) * (11/32) / 32)
= sqrt(231/1024 / 32)
= sqrt(231/32768)
≈ 0.0569 (rounded to four decimal places)

So, the correct value for the standard error (SE) in this case is approximately 0.057.

Therefore, the correct option is: 0.057.