Question

Use the given degree of confidence and sample data to construct a confidence interval for the population mean mu.Assume that the population has a normal distribution.A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with sequals17.6milligrams. Construct a​ 95% confidence interval for the true mean cholesterol content of all such eggs.

Answer 1

Answer:

95% confidence interval for the true mean cholesterol content of all such eggs.

(173.8175 , 196.1825)

Step-by-step explanation:

Step(i):-

Given mean of the sample  x⁻ = 185 milligrams

Given standard deviation of the sample 'S' = 17.6 milligrams

Level of significance

                 ∝ = 0.05

$t_({\frac{\alpha }{2} , n-1 }) = t_{0.025 ,11} = 2.2010$

Step(ii):-

95% confidence interval for the true mean cholesterol content of all such eggs.

$(x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} })$

$(185 - 2.2010 \frac{17.6}{\sqrt{12} } , 185 + 2.2010 \frac{17.6}{\sqrt{12} })$

( 185 - 11.1825 , 185 + 11.1825)

(173.8175 , 196.1825)

Final answer:-

95% confidence interval for the true mean cholesterol content of all such eggs.

(173.8175 , 196.1825)