Question

Please answer all questions using the last page below.

Chapter 7

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 x̅ = 29.8 inches. Assume that σ 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.

(b) Interpret the meaning of the confidence interval in the 29.8x= context of this problem.

2. Collette is self-employed and sells cookware at home parties. She wants to estimate the average amount a client spends at each party. A random sample of 35 receipts gave a mean of x̅ = $34.70 with standard deviation s = $4.85.

(a) Find a 90% confidence interval for the average amount spent by all clients.

(b) What conditions are necessary for your calculations?

(c) For a party with 35 clients, use part (a) to estimate a range of dollar values for Collette’s total sales at that party.

Answer 1

Given that n=45; x = 29.8 inches = 7.2 inches a) Here s'is known, So we have to use z critical value At x = 0.05 level 70.05 = 1.96 S.E. CF) = 0/55 = 7.21545 = 1.0733 : The 95%. C. I. for in' is ( ž + 20.05 S.E. (x) ) (29.8 I (1.96) (1.0733)) (2918 2.1037) (27.6963, 31.9039) b) 95% confident that the population mean Circumference of all blue gruce trees is lies between 27. 6963 inches and 31.9037 inches.