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Supposed a sample of 1453 tankers is drawn. Of these ships 989 did not have spills. Using the data construct the 99% confidence interval for the population proportion of all tankers that have spills each month. Ranch your answers to three decimal places

Supposed a sample of 1453 tankers is drawn Of these ships 989 did not have spills Using the data construct the 99 confidence interval for the population proport class=

Respuesta :

Sample: 1453

989= Without spills

99% Confidenece interval is given by:

[tex]ConfidenceInterval=Z_c*\sqrt[\placeholder{⬚}]{\frac{p(1-p)}{n}}[/tex]

For 99% confidence, the Z_c is:

[tex]Z_c=2.576[/tex]

And p is given by:

[tex]\begin{gathered} p=\frac{989}{1453}=0.68 \\ 1-p=0.319 \end{gathered}[/tex]

Substituing:

[tex]ConfidenceInterval=2.576*\sqrt[\placeholder{⬚}]{\frac{0.68*(0.319)}{1453}}=0.0315[/tex]

Finally, the way to find the intervals is given by:

[tex]p\pm ConfidenceInterval[/tex]

ANSWER:

Upper endpoint:

[tex]0.68+0.0315=0.7115\approx0.712[/tex]

Lower endpoint:

[tex]0.68-0.0315=0.6485\approx0.648[/tex]

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