According to a research report, $42 \%$ of millennials have a BA degree. Suppose we take a random sample of 400 millennials and find the proportion who have a BA degree. Complete parts (a) through ( $d$ ) below.
a. What value should we expect for our sample proportion?

We should expect a sample proportion of $42 \%$.
(Type an integer or a decimal. Do not round.)
b. What is the standard error?

The standard error is $\square$.
(Type an integer or decimal rounded to three decimal places as needed.)

Step 1 ：Given that the proportion of millennials who have a BA degree according to the research report is 42%, or 0.42, and the sample size is 400.

Step 2 ：For part a, the expected value for our sample proportion is simply the proportion of millennials who have a BA degree according to the research report, which is 0.42.

Step 3 ：For part b, the standard error can be calculated using the formula for the standard error of a proportion, which is \( \sqrt{p(1-p)/n} \), where p is the proportion (in this case, 0.42) and n is the sample size (in this case, 400).

Step 4 ：Substitute the given values into the formula, we get \( \sqrt{0.42(1-0.42)/400} \).

Step 5 ：Calculate the above expression to get the standard error, which is approximately 0.025.

Step 6 ：Final Answer: \n a. The expected value for our sample proportion is \( \boxed{0.42} \). \n b. The standard error is approximately \( \boxed{0.025} \).