Answer: (3.3, 3.5)
Step-by-step explanation:
The formula to calculate the confidence interval is given by :-
[tex]\overline{x}\pm z^* \dfrac{\sigma}{\sqrt{n}}[/tex]
, where [tex]\overline{x}[/tex] = sample mean.
z* = critical value.
[tex]\sigma[/tex] = Population standard deviation.
n= Sample size.
As per given , we have
[tex]\overline{x}=3.4[/tex]
[tex]\sigma=0.5[/tex]
n= 217
By using z-table , the critical value for 95% confidence level : z* = 1.96
Now, the 95% confidence interval for the mean consumption of meat among males over age 50 will be :
[tex]3.4\pm (1.96) \dfrac{0.5}{\sqrt{217}}[/tex]
[tex]3.4\pm (1.96) \dfrac{0.5}{14.73091986}[/tex]
[tex]3.4\pm (1.96) 0.0339422[/tex]
[tex]3.4\pm 0.066526712\approx3.4\pm 0.1=(3.4-0.1,\ 3.4+0.1)=(3.3,\ 3.5)[/tex]
Hence, the 95% confidence interval for the mean consumption of meat among males over age 50 =(3.3, 3.5)
