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In: Statistics and Probability

A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 230...

A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 230 milligrams with s = 11.3 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

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Expert Solution


Solution :

Given that,

= 230

s = 11.3

n = 12

Degrees of freedom = df = n - 1 = 12 - 1 = 11

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,11 =2.201

Margin of error = E = t/2,df * (s /n)

= 2.201 * (11.3 / 12)

= 7.18

Margin of error = 7.18

The 95% confidence interval estimate of the population mean is,

- E <  < + E

230 - 7.18 < < 230 + 7.18

222.82 < < 237.18

(222.82, 237.18 )

orchestra answered 2 years ago
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