Answer:
The 95% confidence interval for population mean is (18.19, 23.81).
Step-by-step explanation:
The confidence interval for population mean using the Student's t-distribution is:
[tex]CI=\bar x\pm t_{\alpha /2, (n-1)}\frac{s}{\sqrt{n} }[/tex]
Given:
[tex]\bar x=21\\s=6\\n=20\\\alpha =1-0.95=0.05[/tex]
The critical value of t for α = 0.05 and degrees of freedom, (n - 1) = 19 is:
[tex]t_{\alpha /2, (n-1)}=t_{0.05/2, 19}=2.093[/tex]
Compute the 95% confidence interval for population mean as follows:
[tex]CI=\bar x\pm t_{\alpha /2, (n-1)}\frac{s}{\sqrt{n} }\\=21\pm2.093\times \frac{6}{\sqrt{20} }\\=21\pm2.81\\=(18.19, 23.81)[/tex]
Thus, the 95% confidence interval for population mean is (18.19, 23.81).
