Question

Please answer these questions in detail. With formulas

A new blood clotting drug has been developed and researcher are interested to see if the new drug out performs the most commonly used treatment. 6 patients were given the new drug and 7 patients were given the old drug. The clotting times were recorded (lower times are better). The data are:

new drug		old drug
8.8		9.9
8.4		9
7.9		11.1
8.7		9.6
9.1		8.7
9.6		10.4
		9.5

1: What is the null hypothesis?

a: there is no difference in clotting times

b: the old drug clots faster

c: the new drug clots faster

d: there is a difference in clotting times

2: What is the value of the test statistic?

3: How many degrees of freedom are there?

4: What we conclude if we ran a two tailed test?

a: there is no evidence of a difference in clotting times

b: there is evidence that the new drug results in faster clotting

c: there is evidence that the old drug results in faster clotting

5: What would we conclude if we had instead used a one-tailed test?

a: there is no evidence of a difference in clotting times

b: there is evidence that the new drug results in faster clotting

c: there is evidence that the old drug results in faster clotting

Answer 1

Answer 1: Option a: there is no difference in clotting times

Explanation: The null hypothesis states that there is no difference between the two population means. In this case, we are interested in mean clotting times for the old and new drugs.

Answer 2:

The value of the test statistic is calculated assuming equal variance:

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

The value of the test statistic is -2.477

Answer 3

Degrees of freedom = n1 + n2 - 2 = 6 + 7 - 2 = 13 - 2

Degrees of freedom = 11

Answer 4

P-value corresponding to t = -2.477 and df = 11 for two tailed test is 0.0308

Since, p-value less than 0.05, we reject null hypothesis.

Thus, conclusion is as follows:

Please not correct conclusion for two tailed test should be that there is evidence of a difference in clotting times but this option is not given in list provided.

Answer 5

P-value corresponding to t = -2.477 and df = 11 for one tailed test is 0.0154

Since, p-value less than 0.05, we reject null hypothesis.

Thus, conclusion is as follows:

Option b: there is evidence that the new drug results in faster clotting