It was determined that this sample of three artifacts had a

It was determined that this sample of three artifacts had a mean age of 2193.3 B.C, with a standard deviation of 104.1 years. Assume that the ages are normally distributed with no obvious outliers. Use a significance level of 0.05 to test the claim that the population mean age of the Bluestone formations is different from Corbin’s declared mean age of the ditch, that is, 2950 B.C.

Solution

Given that   n = 3    X = 2193.3    µ₀ = 2950    = 104.1

The null hypothesis is

H₀ µ = 2950 (µ₀) i.e., to test the claim that the population mean age of the bluestone formations is different from corbin’s declared mean age of the ditch.

Against the alternative hypothesis

H₁ : µ 2950 (µ₀) i.e., to test the claim that the population mean age of the bluestone formations is not different from corbin’s declared mean age of the ditch.  

The test statistic is

t = (X -µ₀ ) / (/ n) t_(n-1)

t = (2193.3 - 2950) / (104.1/ 3) t_(3-1)

t = (-756.7) / (60.1022) t₍₂₎

t_cal    =   12.5902

Here the table value at 0.05 level of significance is t_tab = 4.303

Therefore t_cal > t_tab we reject the null hypothesis and conclude that the population mean age of the bluestone formation is not different from corbin’s declared mean age of the ditch