The standard error is 3.7/√25=3.7/5=0.74mg. We need the critical value for this sample size and significance level of 0.05 (95% confidence level). We use the 2-tailed value because the test is for equality, which means we test for less than or greater than the claim of 3.2mg. Looking up the critical value in the test table gives us 2.064 (24 degrees of freedom=sample size 25-1).
2.064 times 0.74=1.53 approx for the margin of error: 3.7±1.53 gives us a range of 2.17 to 5.23mg, and 3.2mg lies within this range, so the claim is valid.