Question

Give a 95% confidence interval, for Hi He given the following information. ny = 35, = 2.82, i = 0.59 n2 30, T2 = 3.2, s2 = 0.69 -0.74 X + -0.01 x Use Technology. Rounded to 2 decimal places.

Answer 1

For n1 + n2 - 2 = 63 degrees of freedom, we have from t distribution tables here:

P( t63 < 1.998) = 0.975

Therefore, due to symmetry, we have here:
P( - 1.998 < t63 < 1.998) = 0.95

Therefore the confidence interval here is obtained as:

$\bar X_1 - \bar X_2 \pm t^*SE$

The standard error here is computed as:

$SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} = \sqrt{\frac{0.59^2}{35} + \frac{0.69^2}{30}} = 0.1607$

Therefore, the confidence interval here is obtained as:

$2.82 - 3.2 \pm 1.998*0.1607$

$-0.38 \pm 0.32$

This is the required 95% confidence interval here.