Chapter 10.2, Problem 10.45E

(a)

To determine

To Calculate: the critical value for 99% confidence interval based on n=12 observations

Answer to Problem 10.45E

  $t^{\ast }=3.106$

Explanation of Solution

Given:

  $\begin{array}{l}n=12\\ c=99\%=0.99\end{array}$

Calculation:

The t-value by looking in the row starting with degrees of freedom $df=n-1=12-1=11$ and in the column with $p=\left(1-c\right)/2=0.005$ in the table of the Students $T$ distribution:

  $t^{\ast }=3.106$

(b)

To determine

To Calculate: the critical value for 90% confidence interval from an SRS of 30 observations.

Answer to Problem 10.45E

  $t^{\ast }=1.699$

Explanation of Solution

Given:

  $\begin{array}{l}n=30\\ c=90\%=0.90\end{array}$

Calculation:

The t-value by looking in the row starting with degrees of freedom $df=n-1=30-1=29$ and in the column with $p=\left(1-c\right)/2=0.05$ in the table of the Students $T$ distribution:

  $t^{\ast }=1.699$

(c)

To determine

To Calculate: the critical value for 95% confidence interval from a sample of size of 18.

Answer to Problem 10.45E

  $t^{\ast }=2.110$

Explanation of Solution

Given:

  $\begin{array}{l}n=18\\ c=95\%=0.95\end{array}$

Calculation:

The t-value by looking in the row starting with degrees of freedom $df=n-1=18-1=17$ and in the column with $p=\left(1-c\right)/2=0.025$ in the table of the Students $T$ distribution:

  $t^{\ast }=2.110$