Question

An article in IEEE International Symposium on Electromagnetic Compatibility (Vol. 2, 2002, pp. 667-670) describes the quantification of the absorption of electromagnetic energy and the resulting thermal effect from cellular phones. The experimental results were obtained from in vivo experiments conducted on rats. The arterial blood pressure values (mmHg) for the control group (8 rats) during the experiment are x1= 90, s1= 5 and for the test group (9 rats) x2= 115, s2= 10. Assume that both populations are normally distributed
Required:
Calculate a 95% 2-sided confidence interval for μ1-μ2.

Answer 1

Answer:

The answer is "$(-33.9218,-16.0782)$".

Step-by-step explanation:

Calculating the critical value:

Freedom Degree= 7.

The significance level, $\alpha= 0.05$

Using excel function the critical value:

$\to t_{\frac{\alpha}{2} (df)}=t_{\frac{0.05}{2},7}\\\\=T.INV.2T(0.05,7)\\\\=\pm 2.3646$

When $95\%$ of the confidence intervals for the difference of means:

$\to (\bar{x_1}-\bar{x_2}) \pm t_{\frac{\alpha}{2}}\sqrt{\frac{S_1^2}{n_1}+\frac{S_2^2}{n_2}}\\\\=(90-115) \pm 2.3646 \sqrt{\frac{5^2}{8}+\frac{102^2}{9}}\\\\=-25 \pm 2.3646 (3.773077)\\\\=(-33.9218,-16.0782)$