Question

7) When subjects were treated with a drug, their systolic blood pressure readings (in mm Hg) were measured before and after the drug was taken. Results are given in the table below. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Using a 0.05 significance level, is there sufficient evidence to support the claim that the drug is effective in lowering systolic blood pressure? 159 189 164 179 157 175 183 195 158 169 209 205 163 155 148 147 152 162 144 176 159 186 163 143 In this example, Ha is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the systolic blood pressure reading before the drug was taken Before After minus the reading after the drug was taken. a) What are the null and alternative hypotheses for the hypothesis test? b) What is the t statistic? c) What is the p-value? d) Which is greater p-value or significance level? e) What is the conclusion (ejectfail to reject) in regarding to the null hypothesis? f) Complete the following based on the analysis above There is blood pressure (The fil-in should be either sufficient or insufficient). evidence to support the claim that the drug is effective in lowering systolic

please help desperately need it

Answer 1

The following table is obtained:

	Sample 1	Sample 2	Difference = Sample 1 - Sample 2
	159	163	-4
	189	155	34
	164	148	16
	179	147	32
	157	152	5
	175	162	13
	183	144	39
	195	176	19
	158	159	-1
	169	186	-17
	209	163	46
	205	143	62
Average	178.5	158.167	20.333
St. Dev.	18.118	13.009	22.995
n	12	12	12

given :

Mean ($\large \bar d$) = 20.333

Standard deviation ( $\large S_d$ ) = 22.995

Sample size (n) = 12

a)

$\large H_0 : \mu_d = 0$

$\large H_a: \mu_d \neq 0$

b)

t - test statistic :

t = $\inline \large \frac { \bar d } { S_d /\sqrt n }$ = $\inline \large \frac { 20.333} { 22.995 /\sqrt 12 }$

t = 3.063

c)

p-value = 0.0108

d)

p-value is less than level of significance (alpha = 0.05)

i.e. level of significance greater than p-value.

e)

Conclusion :- Reject the null hypothesis (H0).

F)

There is sufficient or enough evidence to support the claim that the drug is effective in lowering systolic blood pressure.