Question

When finding the sample size, remember to round all answers up to the next highert whole number. Show all work for partial credit 1.) As part of an environmental studies class project, students measured the circumferences of a random sample of 45 blue spruce trees near Brainard Lake, Colorado. The sample mean circumference was r-29.8 inches. Assume that ? is known to be 7.2 inches. a ) Find a 95% confidence interval for the population mean circumference of all blue spruce trees near this lake. (12 points) b.) Interpret the meaning of the confidence interval in the context of this problem. (2 points)

Answer 1

Given that x^bar = 29.8 n = 45 sigma = 7.2 95% internal x^bar plusminus Z_alpha sigma/squareroot n = 29.8 plusminus (1.96) (7,2/squareroot 45 => C I E (298 plusminus 2. 10) => c. I E (27.7 31.9) from C.I we got in put (a) we can say that the is 95% confidence that the true average circumference lie b/w27.7 to 31.9 inches. 90% C.I is x^bar plusminu 1.645 sigma/squareroot n = 34.70 plusminus (1.645) (4.85)/squareroot 35 => C I E (34.70 plusminus 1.349) [where 1.645 is zd => C. I E (33.35 36.05) value at 90% there are 90% confidence that the true average amount spent by all clients lie b/w 33.35 to 36.05 $ from data x^bar = sigma xi/n = 267/8 = 33.38 and std deviation (s) = squareroot sigma xi - x^bar)^2/n - 1 = 6.46 25% C.I is x^bar plusminus 1.96 sigma/squareroot n = 33.38 plusminus 1.96 (6.46)/squareroot 8 => C.I E (33.38 plusminus 4.48) C.I E (28.9, 37.9)