The latest antidepressant produced is currently involved in the testing process. Eight subjects have joined the testing process where the mean number of days taken before side effects disappeared is being examined. The results are as follows.

$16,10,6,23,12,21,25,26$

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$($a$)$

How many degrees of freedom are present in this study?

$($b$)$

What is the point estimate $($in days$)?$

days

What is the standard deviation $($in days$)$ of the sample? $($Round your answer to four decimal places.$)$

days

$($c$)$

What is the $95\%$ confidence interval $($in days$)$ for the population mean? $($Use a table or technology. Round your answers to three decimal places.$)$

$,$

days

$($d$)$

Interpret the $95\%$ confidence interval for the population mean.

We are $95\%$ confident that the true mean is contained in the interval.

We know that $95\%$ of the results will be in the interval.

We are $95\%$ confident all results are in this interval.

Ninety$-$five percent of the data are outside of the interval.