Question

Below, 25 and 50 mg / ml doses of a drug were given to subjects with the same properties and small blood pressure values were measured. Are the effects of doses different? Find with the error of 5% (The distribution of the data you will use is normal, the samples are sufficient and the variances are homogeneous)

	1	2	3	4	5	6	7	8	9
25 mg/ml doses	7	8	6	6	8	9	5	6	8
50 mg/ml doses	9	9	8	10	9	11	7	9

Answer 1

Null hypothesis:

there is no difference n the lower blood pressure after administration of 25 mg/ ml and 50 mg/ml of the drug soluton

Alternate hypothesis:

there is difference n the lower blood pressure after administration of 25 mg/ ml and 50 mg/ml of the drug soluton

For 25mg/ml,

If we calculate the mean and variance of all the 9 sample:

mean = 7

Variance = 1.75

For 50mg/ml,

If we calculate the mean and variance of all the 9 sample:

mean = 9

Variance = 1.4285

Now for two sample t test

t = (mean of 50 mg/ml -mean of 25 mg/ml) / sqrt (sum of (variance /number of sample)

t = (9-7)/sqrt(1.75/9 + 1.4285/8)

t = 2/sqrt(0.1944+0.1785))

t =3.2746

If we look at the t table and measure the critical value at 0.05 for 15 (9+8-1-1) degree of freedom for two tail:

2.1319

So calcuated t value is higher than the critical value so we reject the null hypothesis and accpet the alternate hypothesis and can say that there is a difference in lower blood pressure between the 25mg/ml dose and 50 mg/ml dose

So there is a differnece in lower blood pressure for 25 mg/ml and 50 mg/ml dose at 95% CI