Bridge Construction
Statistics question. The original estimate for the date of a bridge construction was 2950 B.C.?
A new sample discovered was made of nine artifacts in the bridge with a mean age dating back to 3033.1 B.C. with a standard deviation of 66.9 years. Assume the ages are normally distributed with no outliers. With a significance (alpha) level of 0.05, is there any reason to dispute the original estimate?
Any help would be great and if you could show me the steps in which to solve it that would be even more helpful.
ANSWER: Conclusion: H1 is true. Yes; there is statistically significant good reason to doubt the original estimate.
SINGLE SAMPLE TEST, ONE-TAILED, 6 - Step Procedure for t Distributions, "one-tailed test"
Step 1: Determine the hypothesis to be tested.
Lower-Tail
H0: μ ≥ μ0 H1: μ < μ0
or
Upper-Tail
H0: μ ≤ μ0 H1: μ > μ0
hypothesis test (lower or upper) = upper
Step 2: Determine a planning value for α [level of significance] =0.05
Step 3: From the sample data determine x-bar, s and n; then compute Standardized Test Statistic: t = (x-bar - μ0)/(s/SQRT(n))
x-bar: Estimate of the Population Mean (statistical mean of the sample) = 3033.1
n: number of individuals in the sample = 9
s: sample standard deviation = 66.9
μ0: Population Mean = 2950
significant digits =3
Standardized Test Statistic t = ( 3033.1 - 2950 )/( 66.9 / SQRT( 9 )) = 3.726
Step 4: Using Students t distribution, "lookup" the area to the left of t (if lower-tail test) or to the right of t (if upper-tail test) using Students t distribution Table or Excel TDIST(x, n-1 degrees_freedom, 1 tail).
=TDIST( 3.726 , 8 , 1 )
Step 5: Area in Step 4 is equal to P value = 0.003
based on n -1 = 8 df (degrees of freedom).
Table look-up value shows area under the 8 df curve to the right of t = 3.726 is (approx) probability = 0.003
Step 6: For P ≥ α, fail to reject H0; and for P < α, reject H0 with
95% confidence.
Conclusion: H1 is true
Note: level of significance [α] is the maximum level of risk an experimenter is willing to take in making a "reject H0" or "conclude H1" conclusion (i.e. it is the maximum risk in making a Type I error).
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