Answer to Question #252533 in Statistics and Probability for Joacquin

Question

Patients (20) with high blood pressure were randomly assigned into two groups, a placebo group and a treatment group. The placebo group received conventional treatment while the treatment group received a new drug that is expected to lower blood pressure. After treatment for a couple of months, blood pressures of the patients were measured.

Determine if the new drug had a significant effect on high blood pressure.

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    Blood Pressure (systolic)

Placebo Group New Drug Group

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90 71

95 79

67 69

120 98

89 91

92 85

100 89

83 75

79 78

85 80

Answer 1

The hypothesis to be tested for this case is,

$H_0:\mu_1=\mu_2$

$Against$

$H_1:\mu_1\lt\mu_2$

To perform this hypothesis test, we use the $p-value$ method. The obtained $p-value$ is then compared with the default $\alpha=0.05$ since we are not given the level of significance.

Applying the 2 sample t-test in $R$, the test can be performed by keying in the following commands,

x=c(90,95,67,120,89,92,100,83,79,85)

y=c(71,79,69,98,91,85,89,75,78,80)

t. test(x, y)

Running these commands gives us the following output,

 Welch Two Sample t-test

data: x and y

t = 1.6081, df = 15.569, p-value = 0.1279

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

 -2.730473 19.730473

sample estimates:

mean of x mean of y 

   90.0   81.5 

The $p-value$ from this output is divided by 2 since the test we are conducting is one sided.

Therefore, $p-value=0.1279/2=0.06395$ and the null hypothesis is rejected if $p-value\lt\alpha$ .

Since $p-value=0.06395\gt\alpha=0.05,$ we fail to reject the null hypothesis and conclude that there is no sufficient evidence to show that the new drug had a significant effect on high blood pressure as compared to placebo at $\alpha=0.05$ level of significance.