Let [tex]\mu[/tex] be the population mean strain in a way that conveys information about precision and reliability.
The sample mean is the best point estimate of the true population mean .
As per given , we have
Sample size : n= 12
degree of freedom : [tex]df=12-1=11[/tex]
Sample mean : [tex]\overline{x}=25.0[/tex]
The true average strain in a way that conveys information about precision and reliability= 25.0
sample standard deviation : s= 3.3
Significance level : [tex]\alpha= 0.05[/tex]
Since sample population standard deviation is unknown , so we use t-test.
Critical t-value for t : [tex]t_{\alpha/2, df}=t_{0.025, 11}=2.201[/tex]
95% Confidence interval for true average strain in a way that conveys information about precision and reliability:
[tex]\overline{x}\pm t_{\alpha/2, df}\dfrac{s}{\sqrt{n}}[/tex]
[tex]25.0\pm (2.201)\dfrac{3.3}{\sqrt{12}}\\\\=\approx 25.0\pm2.10\\\\=(25.0-2.10, 25.0+2.10)=(22.9,\ 27.1)[/tex]
The 95% Confidence interval for true average strain in a way that conveys information about precision and reliability: [tex](22.9,\ 27.1)[/tex]
We 95% confident that the true population average strain in a way that conveys information about precision and reliability lies between 22.9 and 27.1 .
