Question

The state test scores for 12 randomly selected high school seniors are shown below. Assume the population is normally distributed. Find (a) the sample mean. (b) Find the sample standard deviation (c) Construct a 99% confidence interval for the population mean u

1424 1220 980
691 721 837
723 745 547
620 1450 940

(a) Find the sample mean.

x = _______

​(Round to one decimal place as​ needed.)

(b) Find the sample standard deviation.

​(c) Construct a 99​% confidence interval for the population mean μ.

Answer 1

Sample mean = (1424 + 1220 + 980 + 691 + 721 + 837 + 723 + 745 + 547 + 620 + 1450 + 940 ) /12

Sample mean = 908.2

Part B:

SD = (((1424 - 908.2)² + (1220 - 908.2)² + (980 - 908.2)² + (691 - 908.2)² + (721 - 908.2)² + (837 - 908.2)² + (723 - 908.2)² + (745 - 908.2)² + (547 - 908.2)² + (620 - 908.2)² + (1450 - 908.2)² + (940 - 908.2)²)/ 11)^0.5

SD = (1,024,730/ 11)^0.5

SD = (93,157.24)^0.5

SD = 305.22

SD = 305.2

Part C

Lower Bound Confidence Interval = 908.2 - 2.58 * 305.2

Lower Bound Confidence Interval = 120.71

Upper Bound Confidence Interval = 908.2 + 2.58 * 305.2

Upper Bound Confidence Interval = 1,695.63

Confidence Interval = (120.71, 1,695.63)