Question

Hi, can you help me answer this question please, thank you

Answer 1

Considering the t-distribution, to find the critical value you have to use to construct the confidence interval for the population mean you have to determine the degrees of freedom of the distribution and the corresponding probability:

`t_{n-1;1-(\alpha)/(2)}`

"n-1" is the degrees of freedom of the distribution

"1-α/2" represents the corresponding probability

Considering a sample with size n=25, the degrees of freedom are:

`n-1=25-1=24`

Using the confidence level of 95% you can determine the probability:

`\begin{gathered} 1-\alpha=0.95 \\ \alpha=1-0.95 \\ \alpha=0.05 \\ (\alpha)/(2)=(0.05)/(2)=0.025 \\ 1-(\alpha)/(2)=1-0.025=0.975 \end{gathered}`

The critical t value corresponds to a distribution with 24 degrees of freedom and accumulates 0.975 of probability. Use the distribution tables to determine the said value:

`t_(24;0.975)=2.064`

The critical t value is ± 2.064