In: Statistics and Probability
As part of a study, two fabric types are tested for flammability at the National Bureau of Standards. Burn times in seconds are recorded after a paper tab is ignited on the center of a piece of fabric. Forty five (45) 3-foot-square pieces of Fabric A are burned with a mean burn time of 12.3 seconds with standard deviation of 1.1 seconds. Fifty five (55) 3-foot-square pieces of Fabric B are burned and have mean burn time of 13.6 seconds with standard deviation of 1.5 seconds. Calculate a test statistic that you could use to test the alternative hypothesis that there is a difference in mean burn time between Fabric A and Fabric B.
Answer)
Null hypothesis Ho : u1 = u2
Alternate hypothesis Ha : u1 not equal to u2
N1 = 45, x1 = 12.3, s1 = 1.1
N2 = 55, x2 = 13.6, s2 =1.5
As the population s.d is unknown and we are given with sample s.d as the best estimate we will use t distribution to conduct the test
Test statistics t = (x1-x2)/standard error
Standard error = √{(s1^2/n1) + (s2^2/n2)}
t = -4.993
Degrees of freedom is = smaller of n1-1, n2-1 = 44
For 44 dof and -4.993 test statistics
P-value from t distribution is = 0
As the obtained P-value is extremely less
We reject the null hypothesis Ho
We have enough evidence to conclude that difference exists