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

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

(173.8175 , 196.1825)

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_({(\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_{(\alpha )/(2) } (S)/(√(n) ) , x^(-) + t_{(\alpha )/(2) } (S)/(√(n) ))`

`(185 - 2.2010 (17.6)/(√(12) ) , 185 + 2.2010 (17.6)/(√(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)