Question

A Statistics professor wants to estimate the mean Math SAT score of incoming freshmen. It is known that Math SAT scores are normally distributed. In a random sample of 20 incoming freshmen, the mean Math SAT score was 527 with a standard deviation of 88. Construct a 90% confidence interval for the population mean. Use the appropriate formulas and show your work! 6.__________________________[8]

Answer 1

df = n-1 = 20 - 1 = 19

T score for 90% confidence interval = t_0.05,19 = 1.729

Confidence interval $=(\bar{X} \pm t_{0.05,19}*\frac{s}{\sqrt{n}})$

                                $=(527 \pm 1.729*\frac{88}{\sqrt{20}})$

                                $=(527 \pm 34.02)$

                                = (492.98 , 561.02)