Question

A polymer mixing process must be run until the blending is complete. A random sample of nine runs measuring the time to complete blending, were recorded as (in hours):
14.82, 13.16, 12.86, 12.4, 12.98, 12.88, 13.86, 13, 13.1.
Assuming blending times are normally distributed but sample size is too SMALL to assume s ≈ σ, construct a 90% confidence interval for the true mean blending time.

	t-values for tail area α
ν	0.100	0.050	0.025	0.010	0.005
1	3.078	6.314	12.706	31.821	63.657
2	1.886	2.920	4.303	6.965	9.925
3	1.638	2.353	3.182	4.541	5.841
4	1.533	2.132	2.776	3.747	4.604
5	1.476	2.015	2.571	3.365	4.032
6	1.440	1.943	2.447	3.143	3.707
7	1.415	1.895	2.365	2.998	3.499
8	1.397	1.860	2.306	2.896	3.355
9	1.383	1.833	2.262	2.821	3.250
10	1.372	1.812	2.228	2.764	3.169

Your answers can be rounded to three decimal digit accuracy when entered.

Lower limit is =?

Upper limit is =?

Answer 1

Level of Significance ,    α =    0.1
sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   0.708
Sample Size ,   n =    9
Sample Mean,    x̅ = ΣX/n =    13.2289

degree of freedom=   DF=n-1=   8  

α/2 = 0.05
't value='   tα/2=   1.860 [from given table]

Standard Error , SE =   s/√n =   0.2360      
margin of error ,   E=t*SE =   0.439     

confidence interval is               
Interval Lower Limit=   x̅ - E =    12.790  
Interval Upper Limit=   x̅ + E =    13.668   
confidence interval is (   12.7900   < µ <   13.6678   )