Question

Find the critical value needed to construct a confidence interval of the given level with the given sample size. Round the answers to three decimal places.
Part 1 of 4
(a) For level 95% and sample size 7.
Part 2 of 4
(b) For level 98% and sample size 12.
Part 3 of 4
(c) For level 99% and sample size 27.
Part 4 of 4
(d) For level 98% and sample size 14.

Answer 1

Answer:

a) $t_{\alpha/2}=\pm 2.447$

b) $t_{\alpha/2}=\pm 2.718$

c) $t_{\alpha/2}=\pm 2.779$

d) $t_{\alpha/2}=\pm 2.650$

Step-by-step explanation:

Part a

The degrees of freedom are given by:

$df=n-1= 7-1=6$

The confidence is 95% or 0.95 the significance would be $\alpha=0.05$ and the critical values would be:

$t_{\alpha/2}=\pm 2.447$

Part b

The degrees of freedom are given by:

$df=n-1=12-1=11$

The confidence is 98% or 0.98 the significance would be $\alpha=0.02$ and the critical values would be:

$t_{\alpha/2}=\pm 2.718$

Part c

The degrees of freedom are given by:

$df=n-1=27-1=26$

The confidence is 99% or 0.99 the significance would be $\alpha=0.01$ and the critical values would be:

$t_{\alpha/2}=\pm 2.779$

Part d

The degrees of freedom are given by:

$df=n-1=14-1=13$

The confidence is 98% or 0.98 the significance would be $\alpha=0.02$ and the critical values would be:

$t_{\alpha/2}=\pm 2.650$