Question

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 1

Answer:

the 95% confidence interval to estimate the population mean is between  1.62 and 6.50

Step-by-step explanation:

given data

distribution = 4.5, 6.4, 2.3, 1.8, 5.3

so n = 5

confidence interval = 95%

to find out

the population mean is between

solution

first we calculate the mean i.e.

mean =  $\frac{1}{n}\sum_{i=1}^{n}x(i)$

mean =  4.5+ 6.4+ 2.3+ 1.8+ 5.3 / 5

mean = 4.06

now we calculate the standard deviation i.e.

standard deviation =   $\sqrt{\frac{1}{n-1}\sum (x(i)-mean)^2}$

standard deviation =   $\sqrt{\frac{1}{5-1}\sum (x(i)-mean)^2}$

standard deviation =   $\sqrt{\frac{1}{5-1} (4.5-5)^2+(6.4-5)^2 +(2.3-5)^2+(1.8-5)^2+(5.3-5)^2}$

standard deviation =   $\sqrt{\frac{1}{4} (4.5-5)^2+(6.4-5)^2 +(2.3-5)^2+(1.8-5)^2+(5.3-5)^2}$

standard deviation =  2.226544

so 95 % confidence interval is i.e. mean +/- t(5) * standard deviation/ $\sqrt{n}$

here t(5) will be 2.45

so

95 % confidence interval=  4.06 +/- 2.45 * 2.226 / $\sqrt{5}$

95 % confidence interval= 1.62 and 6.50