The method of tree ring dating gave the following years AD f

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.

(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.)

(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.)

Solution

Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=1291.778 ~ 1292
Standard deviation( sd )=23.874 ~ 24
Sample Size(n)=9

Confidence Interval = [ 1292 ± t a/2 ( 24/ Sqrt ( 9) ) ]
= [ 1292 - 1.86 * (8) , 1292 + 1.86 * (8) ]
= [ 1277.12,1306.88 ] ~ [ 1278,1307]