Question

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.

1285 1236 1236 1271 1268 1316 1275 1317 1275

(a) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.)

x = _____A.D.

s = _____yr

(b) 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.

Answer 1

The answers are given below. The mean and sd is found using calculator. Ti-84

Press STAT ENTER
Enter the datapoint
When done press 2nd QUIT

To find the mean
Press 2nd LIST
Move the arrow to MATH
Select mean
Press 2nd, then of list of a number will appear.
Press close parentheses and enter

We are given sample mean = = 1275.4444444 sample standard deviation o 28.8318882 n 9 Confidence interval 0.9 a/2 (1-0.9)/2= 0.05 df n 1 8 Using the Student t-table, we find the tstat for a/2 0.05 and df 8 tstat 1.859548 28.8318882 1.859548 Margin of error = ME = tstat x = 17.871427 Confidence Interval utstat x V12 1275.4444444± 17.871427 1275.4444444± 1.859548 x 28.8318882 Therefore the 90% confidence interval for the mean is (1257.573, 1293.3159)