An existing inventory for a test measuring self-esteem indicates that the scores have a standard deviation of

12

. A psychologist gave the self-esteem test to a random sample of

80

individuals, and their mean score was

63

. Construct a

95%

confidence interval for the true mean of all test scores. Then give its lower limit and upper limit.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)