Question

Part 1) The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution. 1271 1299 1299 1215 1268 1316 1275 1317 1275

a) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.)

lower limit________	A.D.
upper limit________	A.D.

Part 2) How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20°F to 45°F. A random sample of prices ($) for sleeping bags in this temperature range is given below. Assume that the population of x values has an approximately normal distribution.   

50	85	120	40	65	70	30	23	100	110
105	95	105	60	110	120	95	90	60	70

a) Using the given data as representative of the population of prices of all summer sleeping bags, find a 90% confidence interval for the mean price ? of all summer sleeping bags. (Round your answers to two decimal places.)

lower limit	$ _______
upper limit	$ _______

Answer 1

Part 1)

Use a one-sample t confidence interval for the population mean (we do not know the population standard deviation and must estimate it with the sample standard deviations)

Given:

Confidence level (C) = 0.90, = 1 - C = 1 - 0.90 = 0.10, n = 9

Degrees of Freedom = n-1 = 9-1 = 8

Calculation:

Critical value:

90% Confidence interval:

Lower limit : 1262 A.D

Upper limit: 1301 A.D

Part 2)

Use a one-sample t confidence interval for the population mean (we do not know the population standard deviation and must estimate it with the sample standard deviations)

Given:

Confidence level (C) = 0.90, = 1 - C = 1 - 0.90 = 0.10, n = 20

Degrees of Freedom = n-1 = 20-1 = 19

Calculation:

Critical value:

90% Confidence interval:

Lower limit: $68.69

Upper limit: $91.61