Questions 13 through 16: The corrosion loss (in mm) was measured for eight speci
ID: 3363066 • Letter: Q
Question
Questions 13 through 16: The corrosion loss (in mm) was measured for eight specimens of a certain steel alloy (that had been immersed in brine). The qqplot and summary statistics are shown below 25% 0.3688 0.02 0.3429 0.35365 0.3709 0.3792 0.4007 8 mean S 0% 50% 751 100% n 15-1045 10 1S 13. Are the assumptions for using a t-based confidence interval satisfied for this data? Justify your response. 14. Regardless of your answer in #13, construct a 95% confidence interval for the mean corrosion loss. Give your answer to 3 decimal places. 15. Interpret your confidence interval from #14. STAT360 Exam 2 6 16. Will the 99% confidence interval be wider or narrower than the confidence interval from #147Explanation / Answer
Solution13:
Yes normality assumptions satified from qq plot.
The observations are lying on the starigh line which is theortical distribution line.
And also
mean=median
0.3688=0.3709
50% is median value
approximately equal
so follows ND
Solution14:
can construct confidence intervals
alpha=0.05
alpha/2=0.05/2=0.025
degrees of freedom=n-1=8-1=7
t crit=2.365
95% confidence inetrval for true mean is
sample mean-t crit*smaplesd/sqrt(n),sample mean+t crit*smaplesd/sqrt(n)
0.3688-2.365*0.02/sqrt(8),0.3688+2.365*0.02/sqrt(8)
0.352,0.385
lower limit=0.352
upper limit=0.385
0.352<mu<0.385
Solution15:
we are 95% confident that thetrue mean corrsoin loss lies in between 0.352 and 0.385
in 5% of the times only
Solution16:
99% CI for mean
alpha=0..01
alpha/2=0.01/2=0.005
t crit=3.499
0.3688-3.499*0.02/sqrt(8),0.3688+3.499*0.02/sqrt(8)
0.344,0.394
interval is wider
99% is wider than 95%
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