A certain injection administered to 12 patients resulted in the following changes of blood pressure 5 , 2, 8, -1, 3, 0, 6, -2, 1, 5, 0, 4. Can it be concluded that the injection will be in general accompanied by an increase in blood pressure?

First we calculate $\bar X $&$s^2$

$\bar X=2.58$

$ s^2 = \frac {\sum (x-\bar x)^2}{9}=\frac{104.96}{12}=8.74$

(i)The null hypothesis$ H_0 : \mu= 0 $

Alternative hypothesis $H_1 : \mu ≠ 0$

(ii) Calculation of test statistic: Since the sample size is small , we use t – distribution

$t=\frac{\bar X-\mu}{s/\sqrt n-1}=\frac{2.58-0}{\sqrt 8.74 / \sqrt 12-1}=2.89$

(iii)Level of significance : $\alpha=0.05$

(iv)Critical value : the value of $t_\alpha$ at 5% level of significance for ν= 12-1 =11 degrees of freedom is 2.201

(v)Decision : since the calculated value of |t| =2.89 is greater than the table value $t_\alpha=2.201$ ,the null hypothesis is rejected.