Problem 3 The compressive strength of concrete is being test

Problem #3

The compressive strength of concrete is being tested by a civil engineer. He tests 12 specimens and obtains the following data.

2216                2237                2249                2204

2225                2301                2281                2263

2318                2255                2275                2295

a.) Compute a 90% tolerance interval on the compressive strength of the concrete that has 95% confidence.

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)=2259.917
Standard deviation( sd )=35.569
Sample Size(n)=12
Confidence Interval = [ 2259.917 ± t a/2 ( 35.569/ Sqrt ( 12) ) ]
= [ 2259.917 - 1.7959 * (10.27) , 2259.917 + 1.7959 * (10.27) ]
= [ 2241.48,2278.36 ]