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Svetach [21]
3 years ago
13

Stainless steels are frequently used in chemical plants to handle corrosive fluids, however, these steels are especially suscept

ible to stress corrosion cracking in certain environments. In a sample of 295 steel alloy failures that occurred in oil refineries and petrochemical plants in Japan over the last 10 tears, 118 were caused by stress corrosion cracking and corrosion fatigue (Materials Performance, 1981). Construct a 95% confidence interval for the true proportion of alloy failures caused by stress corrosion cracking.
Mathematics
2 answers:
Ira Lisetskai [31]3 years ago
6 0

Answer: 95% confidence interval would be (0.344,0.456).

Step-by-step explanation:

Since we have given that

n = 295

x = 118

so, \hat{p}=\dfrac{x}{n}=\dfrac{118}{295}=0.4

At 95% confidence, z = 1.96

So, margin of error would be

z\times \sqrt{\dfrac{p(1-p)}{n}}\\\\=1.96\times \sqrt{\dfrac{0.4\times 0.6}{295}}\\\\=0.056

so, 95% confidence interval would be

\hat{p}\pm \text{margin of error}\\\\=0.4\pm 0.056\\\\=(0.4-0.056,0.4+0.056)\\\\ =(0.344,0.456)

Hence, 95% confidence interval would be (0.344,0.456).

12345 [234]3 years ago
4 0

Answer:

<h2>95% confidence interval would be (0.344,0.456).</h2>

Step-by-step explanation:

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