The following random sample was selected from a normal distribution: 4.5, 6.4, 2.3, 1.8, 5.3, then the 95% confidence interval to estimate the population mean is between __________.

Answer:the 95% confidence interval to estimate the population mean is between  1.62 and 6.50Step-by-step explanation:given data distribution = 4.5, 6.4, 2.3, 1.8, 5.3so n = 5 confidence interval = 95%to find out the population mean is between solutionfirst we calculate the mean i.e.mean =  [tex]\frac{1}{n}\sum_{i=1}^{n}x(i)[/tex] mean =  4.5+ 6.4+ 2.3+ 1.8+ 5.3 / 5mean = 4.06now we calculate the standard deviation i.e.standard deviation =   [tex]\sqrt{\frac{1}{n-1}\sum (x(i)-mean)^2}[/tex]standard deviation =   [tex]\sqrt{\frac{1}{5-1}\sum (x(i)-mean)^2}[/tex]standard deviation =   [tex]\sqrt{\frac{1}{5-1} (4.5-5)^2+(6.4-5)^2 +(2.3-5)^2+(1.8-5)^2+(5.3-5)^2}[/tex]standard deviation =   [tex]\sqrt{\frac{1}{4} (4.5-5)^2+(6.4-5)^2 +(2.3-5)^2+(1.8-5)^2+(5.3-5)^2}[/tex]standard deviation =  2.226544so 95 % confidence interval is i.e. mean +/- t(5) * standard deviation/ [tex]\sqrt{n}[/tex]here t(5) will be 2.45so 95 % confidence interval=  4.06 +/- 2.45 * 2.226 / [tex]\sqrt{5}[/tex]95 % confidence interval= 1.62 and 6.50