Step 1 :Given the state test scores for 12 randomly selected high school seniors are: 1421, 1230, 981, 697, 726, 839, 721, 744, 541, 627, 1447, 946.
Step 2 :To find the sample mean, we need to sum up all the scores and divide by the number of scores. The sample mean is given as \(\bar{x}=910.0\).
Step 3 :To find the sample standard deviation, we need to subtract each score from the mean, square the result, sum up these squared results, divide by the number of scores minus 1 (this is called the variance), and finally take the square root of the variance.
Step 4 :Subtracting each score from the mean and squaring the result gives us the variance, which is 92910.90909090909.
Step 5 :Taking the square root of the variance gives us the sample standard deviation, which is 304.81290834036065.
Step 6 :Rounding to one decimal place, the sample standard deviation is \(\boxed{304.8}\).