hypertension trial is mounted and 12 participants are randomly assigned to receive either a new treatment or a placebo.  Each participant takes the assigned medication and their systolic blood pressure (SBP) is recorded after 6 months on the assigned treatment.  The data are as follows.  PlaceboNew Treatment134114143117148121142124150122160128 Is there a difference in mean SBP between treatments? Assume equal variances.  Run the test at a 5% level of significance. Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value.

Question
Asked Nov 7, 2019

 hypertension trial is mounted and 12 participants are randomly assigned to receive either a new treatment or a placebo.  Each participant takes the assigned medication and their systolic blood pressure (SBP) is recorded after 6 months on the assigned treatment.  The data are as follows.
 

 Placebo
New Treatment
134
114
143
117
148
121
142
124
150
122
160
128

 
Is there a difference in mean SBP between treatments? Assume equal variances.  Run the test at a 5% level of significance. Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value.

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Step 1

Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If you want remaining sub-parts to be solved, then please resubmit the whole question and specify those sub-parts you want us to solve.

According to the provided information,

Placebo (X1) New Treatment (X2)
134
114
143
117
148
121
142
124
150
122
160
128
Mean
146.1666667
121
8.773064839
SD
4.979959839
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Placebo (X1) New Treatment (X2) 134 114 143 117 148 121 142 124 150 122 160 128 Mean 146.1666667 121 8.773064839 SD 4.979959839

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Step 2

1)  Hypothesis for the test is given below:

Here, and are the number of mean participants random assigned to receive Placebo and New
treatment respectively
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Here, and are the number of mean participants random assigned to receive Placebo and New treatment respectively

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Step 3

2) In order to test the difference in mean SBP between treatments. T...

(with nn2 df
t =
п,
146.1667-121
76.97 24.80
V 6
6
=6.111
Therefore, the t-statistic value is 6.11
help_outline

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(with nn2 df t = п, 146.1667-121 76.97 24.80 V 6 6 =6.111 Therefore, the t-statistic value is 6.11

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