Page 1 of 12 Page 3 of 12 2. (20 points). The tensile strength measurements for
ID: 3326556 • Letter: P
Question
Page 1 of 12 Page 3 of 12 2. (20 points). The tensile strength measurements for two sample batches of rope using Method 1 and Method 2 (both made from hemp) are displayed below: Test 16 16 15 14 18 Method 1 Method 2 16 12 15 4 14 17 (a ) Calculate a 95% confidence interval for the mean difference in tensile strength between ropes (b) Calculate a 95% confidence again, but consider the data as two independent random samples. (c) Extra Credit: (5 points) Compare and contrast the results of the two data analysis methods i.e made by the two methods. briefly explain the assumptions needed to apply which method (in two sentences).Explanation / Answer
Q.2 (a) FIrst we will take 95% confidence interval for paired data sample.
95% confidence interval = dbar +- tdf,0.05 (sd/ n)
where n = 5
dF = 5 -1 = 4
and t4,0.05 = 2.7764
for dbar and sd the table is given below.
95% confidence interval = dbar +- tdf,0.05 (sd/ n)
= -0.6 +- 2.7764 * (1.8166/5)
= -0.6 + 2.256
= (-2.856, 1.656)
(b) Here now we will take it as indendent samples
so here degree of freeom = n1 + n2 -2 = 5 + 5 -2 = 8
The mean and standard deviation of both the samples are
We will assume equal variance here
so pooled standard deviation sp = sqrt [{(n1-1)s12 + (n2 -1)s22 }/ (n1 + n2 -2)] = sqrt [(5 + 1.3)/2] = 1.775
so
95% confidence interval = (x1 - x2) +- tdf,0.05 sp * sqrt [1/n1 + 1/n2]
= (15 - 15.6) +- 2.306 * 1.775 * sqrt (2/5)
= -0.6 +- 2.588
= (-3.188, 1.988)
(c) There is significant variation in the result of both confidence interval. THe second confidence interval has more width. Here the independent samples must use the confidence interval 2 and the dependent samples when paired data is used shall use the confidence interval 1.
Rope Method1 Method2 Difference (d) 1 14 16 -2 2 12 15 -3 3 18 17 1 4 16 16 0 5 15 14 1 Average -0.6 Std. dev. 1.8166Related Questions
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