Ultra high performance concrete UHPC is characterized by str

Ultra high performance concrete (UHPC) is characterized by strong adhesive properties with other materials. The following shows the work of adhesion measurements (in mJ.m^2) got UHPC specimens adhered to steel:

107.1 109.5 107.4 106.8 108.1

A. Calculate a two-sided 95% confidence interval for the true average work of adhesion for UHPC adhered to steel.

B. Referring to part (A) does the interval suggest that 107 is a plausible value for the true average work of adhesion for UHPC adhered to steel? What about 110?

Solution

A)
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)=107.78
Standard deviation( sd )=1.076
Sample Size(n)=5
Confidence Interval = [ 107.78 ± t a/2 ( 1.076/ Sqrt ( 5) ) ]
= [ 107.78 - 2.776 * (0.481) , 107.78 + 2.776 * (0.481) ]
= [ 106.444,109.116 ]

B)
107 is a plausible value for the true average work of adhesion for UHPC adhered to steel, as the reason it lies in the range calculated in part A.
110 is out of bound