Answer:
The 80% confidence interval for the population mean is 19.48 or 20.52
Step-by-step explanation:
Given that ;
the random sample size n = 81
mean [tex]\bar x[/tex] = 20
median = 21
mode = 22
standard deviation σ = 3.6
The 80% confidence interval for the population mean can be calculated as follows:
Firstly; the degree of freedom df = n - 1
df = 81 - 1
df = 80
At 80% confidence interval the critical value is z = [tex]t_{0.1, 80} = 1.292[/tex]
The 80% confidence interval for the population mean is = [tex]\bar x \pm \dfrac{ z \times \sigma }{\sqrt{n}}[/tex]
[tex]= 20 \pm \dfrac{ 1.292 \times 3.6 }{\sqrt{81}}[/tex]
[tex]=20 \pm \dfrac{ 4.6512 }{9}[/tex]
[tex]= {20 \pm 0.5168 }[/tex]
= 19.4832 or 20.5168
[tex]\approx[/tex] 19.48 or 20.52
