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

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.

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