Question

# A polymer mixing process must be run until the blending is complete. A random sample of...

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 3.078 6.314 12.706 31.821 63.657 1.886 2.920 4.303 6.965 9.925 1.638 2.353 3.182 4.541 5.841 1.533 2.132 2.776 3.747 4.604 1.476 2.015 2.571 3.365 4.032 1.440 1.943 2.447 3.143 3.707 1.415 1.895 2.365 2.998 3.499 1.397 1.860 2.306 2.896 3.355 1.383 1.833 2.262 2.821 3.250 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 =?

#### Homework Answers

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   )

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