Answer: [tex](24.28,\ 27.72)[/tex]
Step-by-step explanation:
Given : Sample size : [tex]n=50[/tex]
Sample mean : [tex]\overline{x}=26[/tex]
Standard deviation : [tex]\sigma =6.2[/tex]
Significance level : [tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
Formula to find the confidence interval for population mean :-
[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=26\pm(1.96)\dfrac{6.2}{\sqrt{50}}\\\\\approx26\pm1.72\\\\=(26-1.72,\ 26+1.72)\\\\=(24.28,\ 27.72)[/tex]
Hence, a 95% confidence interval for the population mean = [tex](24.28,\ 27.72)[/tex]
