The durability times (in hours) of $12$ randomly selected ceiling fans have a sample standard deviation of $0.4$ hours. Assume the data come from a normally distributed population. Using an $80\%$ confidence level, construct the confidence interval for the population variance (${\sigma }^2$). Also, interpret the results.

$(0.1,0.3)$

We are $90\%$ confident that the true population variance in ceiling fan durability times is between $0.1$ and $0.3{\text{ hrs}}^{}$

$(0.1,0.3)$

We are $80\%$ confident that the true population variance in ceiling fan durability times is between $0.1$ and $0.3{\text{ hrs}}^2$

$(0.1,0.3)$

We are $80\%$ confident that the true population variance in ceiling fan durability times is greater than $0.1$ but less than $0.3{\text{ hrs}}^2$

$(10.8,26.9)$ We are $80\%$ confident that the true population variance in ceiling fan durability times is greater than $10.8$ but less than

$0.3{\text{ hrs}}^2$