The accompanying table gives summary data on cube compressive strength (N/mm2) f
ID: 3313462 • Letter: T
Question
The accompanying table gives summary data on cube compressive strength (N/mm2) for concrete specimens made with a pulverized fuel-ash mix. Sample SD 4.84 6.49 Sample Age (days) Sample Size 69 74 Mean 25.95 35.79 28 Calculate a 99% CI for the difference between true average 7-day strength and true average 28-day strength. (Use Ho: 7-128 places.) 0. Round your answers to two decimal N/mm2 Interpret your 99% CI with 99% confidence, we can say that the true difference falls between these values. with 99% confidence, that the true difference falls below the lower bound with 99% confidence, that the true difference falls outside these values. with 99% confidence, that the true difference falls above the upper bound You may need to use the appropriate table in the Appendix of Tables to answer this question.Explanation / Answer
TRADITIONAL METHOD
given that,
mean(x)=25.95
standard deviation , s.d1=4.84
number(n1)=69
y(mean)=35.79
standard deviation, s.d2 =6.49
number(n2)=74
I.
stanadard error = sqrt(s.d1^2/n1)+(s.d2^2/n2)
where,
sd1, sd2 = standard deviation of both
n1, n2 = sample size
stanadard error = sqrt((23.4256/69)+(42.1201/74))
= 0.9533
II.
margin of error = t a/2 * (stanadard error)
where,
t a/2 = t -table value
level of significance, = 0.01
from standard normal table, two tailed and
value of |t | with min (n1-1, n2-1) i.e 68 d.f is 2.6501
margin of error = 2.65 * 0.9533
= 2.5261
III.
CI = (x1-x2) ± margin of error
confidence interval = [ (25.95-35.79) ± 2.5261 ]
= [-12.3661 , -7.3139]
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DIRECT METHOD
given that,
mean(x)=25.95
standard deviation , s.d1=4.84
sample size, n1=69
y(mean)=35.79
standard deviation, s.d2 =6.49
sample size,n2 =74
CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
where,
x1,x2 = mean of populations
sd1,sd2 = standard deviations
n1,n2 = size of both
a = 1 - (confidence Level/100)
ta/2 = t-table value
CI = confidence interval
CI = [( 25.95-35.79) ± t a/2 * sqrt((23.4256/69)+(42.1201/74)]
= [ (-9.84) ± t a/2 * 0.9533]
= [-12.3661 , -7.3139]
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interpretations:
1. we are 99% sure that the interval [-12.3661 , -7.3139] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 99% of these intervals will contains the true population proportion
with 99% confidence the true diffrence falls below the lower bound
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