Answer: [tex](238.57,\ 253.43)[/tex]
Step-by-step explanation:
When population standard deviation is not given , then the formula to find the confidence interval for population mean is given by :-
[tex]\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}[/tex]
, where [tex]\overline{x}[/tex] = sample mean.
s= sample standard deviation.
n= sample size.
[tex]t_{\alpha/2}[/tex] = Critical t-value (two tailed ).
Given : n= 12 , [tex]\overline{x}=246[/tex] , s=11.7
Significance level = [tex]\alpha=1-0.95=0.05[/tex]
Degree of freedom : n- 1= 11
Using t- distribution , the critical t-value =[tex]t_{\alpha/2, df}=t_{0.025,\ 11}=2.2010[/tex]
Now, the required 95% CI for the true mean cholesterol content of all such eggs will be :-
[tex]246\pm (2.2010)\dfrac{11.7}{\sqrt{12}}\\\\=246\pm(2.2010)(3.3775)\\\\=\\\\=246\pm7.4339=(246-7.4338,\ 246+ 7.4338)\\\\=(238.5662,\ 253.4338)\approx(238.57,\ 253.43)[/tex]
Hence, the required confidence interval = [tex](238.57,\ 253.43)[/tex]
