Question

The effect of surfactants on the wetting behavior of super-hydrophobic surfaces was investigated. The table below lists a set of unpaired measurements for the initial contact angle and the contact angle three days after molding (in degrees): B: 3 Days A: Initial 140 143 149 144 133 A researcher wants to find the difference in contact angle over time. Assume that the angles are normally distributed, and check to see if the variances may be pooled. (Round all answers to 3 decimal places as needed) a) Find the mean and the standard deviation for the initial measurements: = b) Find the mean and the standard deviation for the measurements after three days: c) Find the standard error of the difference between the means SE d) Find the critical value from the distribution for a 90% confidence interval Calculate the 90% confidence interval for the difference in contactangle Submit

Answer 1

(a) T = 141.6 SA=5.595 ; n 5 (b) TR= 151.75 ; SB = 4.113 ; no=4 cd) A+ *0.10 + 0.05 with df = ni+n2-2 df = 5+4-2 df = 7 tcritica = 1.895 c) Standard error of the difference between mean se fessos, con SE : 3.239 (e) 90 y. confidence interval is TEA - Ig) + tarit (141.6 - 15175) † 1,895 X SE - 10.15 1.895 X 3. 239 -10.15 € 6,138 The 30% confidence (-16.288 - 4.012) interval is

#R version 3.3.2 A=c(140,143,144,133,148) length(A) mean(A) sd(A) B=c(157,149,148,153) length(B) mean(B) sd(B) Save it Put on a wall Run it (Shift+Enter) [ + ] Show input Absolute running time: 0.42 sec, cpu time: 0.74 sec, memory peak: 30 Mb, absolute service time: 0,43 sec [1] 5 [1] 141.6 [1] 5.59464 [1] 4 [1] 151.75 [1] 4.112988