Question

auestion 14 AND 15 please

Question 14 A medical researcher is studying the effects of a drug on blood pressure. Type numbers in the boxes Subjects in the study have their blood pressure taken at the beginning of the so points study. After being on the medication for 4 weeks, their blood pressure is taken again. The change in blood pressure is recorded and used in doing the hypothesis test. Change: Final Blood Pressure - Initial Blood Pressure The researcher wants to know if there is evidence that the drug reduces blood pressure. At the end of 4 weeks, 32 subjects in the study had an average change in blood pressure of -1.9 with a standard deviation of 4.8. Find the p-value for the hypothesis test. Your answer should be rounded to 4 decimal places. Question 15 Find the p-value for the hypothesis test. A random sample of size 51 is taken. The sample has a mean of 423 and a standard deviation of 84. Type numbers in the boxes. 10 points Ho: = 400 H: > 400 The p-value for the hypothesis test is Your answer should be rounded to 4 decimal places.

Answer 1

(14) The null and alternative hypothesis are-

Null hypothesis, , i.e., the true average blood pressure before and after taking the medication is not different.

Ho : M final – Minitial = 0

Alternative hypothesis, , i.e., the true average blood pressure after taking the medication is less than before, which means the drug reduces the blood pressure.

H : M final – Minitial < 0

Well in order to find the p-value, we have to first calculate the test-statistic and the formula for calculating the test-statistic is given by-

= 1 011-P

where, , the average change in blood pressure

d= -1.9

, standard deviation

Sd = 4.8

, From null hypothesis

Mo=0

, sample size

n = 32

d-HO -1.9 - 0 t= = -2.239171474 -2.23917 5

So, the test-statistic is calculated as

t= -2.23917

P - value:
Since we are testing a left-tailed hypothesis and the test-statistic is calculated as
t = -2.23917

p-value = P(t < -2.23917, df = 32 – 1 = 31) = 0.01623009 0.0162

So, the p-value is calculated as

p - value = 0.0162

__________________________

(15) The null and alternative hypothesis are given as
001 = 11: 'H
and
001 <11: H

To find the p-value we need to calculate the test-statistic first and which is given by

X -u t =

Given:

I = 423, s = 84, n=51

X- 423-400 t = = 1.9553911171.95539 751

So, the test-statistic is calculated as

t= 1,95539

P - value:
Since we are testing a right-tailed hypothesis and the test-statistic is calculated as
t = 1.95539

p-value = P(t > 1.95539, df = 51 - 1 = 50) = 0.02806874 -0.0281

So, the p-value is calculated as

t=0,0281