Question

In: Statistics and Probability

The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly...

The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.40. Construct a 95% two-sided confidence interval for σ. Assume population is approximately normally distributed.

Round your answers to 4 decimal places.

Solutions

Expert Solution

Solution :

Given that,

s = 0.40

s2 = 0.6325

n = 51

Degrees of freedom = df = n - 1 = 51 - 1 = 50

At 95% confidence level the 2 value is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

1 - / 2 = 1 - 0.025 = 0.975

2L = 2/2,df = 71.420

2R = 21 - /2,df = 32.357

The 95% confidence interval for is,

(n - 1)s2 / 2/2 < < (n - 1)s2 / 21 - /2

(50)(0.6325) / 71.420 < < (52)(0.6325) / 32.357

0.6654 < < 0.9886

(0.6654 , 0.9886)

orchestra answered 3 years ago
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