question archive The compressive strength of concrete is being tested by a civilengineer
The compressive strength of concrete is being tested by a civilengineer
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The compressive strength of concrete is being tested by a civilengineer. He tests 12 specimens and obtains the following data.
2216 2237 2249 2204
2225 2301 2281 2263
2318 2255 2275 2295
a) Check the assumption that compressive strength is normallydistributed. Include a graphical display in your answer.
b) Construct a 95% two-sided confidence interval on the meanstrength.
c) Construct a 95% lower-confidence bound on the meanstrength. Compare this bound with the lower bound of thetwo-sided confidence interval and discuss why they aredifferent.
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Answer:
a) Check the assumption that compressive strength is normallydistributed. Include a graphical display in your answer.
b) Construct a 95% two-sided confidence interval on the meanstrength.
xbar= 2259.917, sd=35.57, α=0.05, t(0.025,df=n-1=11)=2.2 (check student t table),n=12
xbar±t*sd/√n
--> 2259.917±2.2*35.57/sqrt(12)
-->( 2237.327, 2282.507)
c) Construct a 95% lower-confidence bound on the meanstrength. Compare this bound with the lower bound of thetwo-sided confidence interval and discuss why they aredifferent.
α=0.05, t(0.05,df=n-1=11)=1.8 (check studentt table)
xbar-t*sd/√n =2259.917-1.8*35.57/sqrt(12)=2241.434
PFA
