Question

Suppose a hypertension trial is mounted and 18 participants are randomly assigned to one of the comparison treatments. Each participant takes the assigned medication and their systolic blood pressure (SBP) is recorded after 6 months on the assigned treatment. The data are presented in the table below. Compute the totals for each column (1pt).

Standard Treatment Placebo New Treatment

124 134 114

111    143 117

133    148 121

125 142 124

128 150    122

115 160 128

Total: 736 877 726

Is there a difference in mean SBP among treatments at a 5% significance level?

Indicate the correct competing hypotheses:

1. H₀: The means are not all equal.

H₁: The means are all equal.

2. H₀: Treatment group and SBP are independent.

H₁: The null hypothesis is false.

3. H₀: The means are all equal.

H₁: The means are not all equal.

4. H₀: Treatment group and SBP are not independent.

H₁: The null hypothesis is false.

Indicate the decision rule.

1. Reject H₀ if F > 3.68
2. Reject H₀ if F < 3.68
3. Reject H₀ if F > 3.16
4. Reject H₀ if F < 3.16
5. Some other answer; indicate:

Indicate the mean of Group 1.

Indicate the mean of Group 2.

Indicate the mean of Group 3.

Indicate the overall mean.

Indicate the Between Groups Sums of Squares (SSB,).

Answer 1

Applying ANOVA on above data:

Groups	Count	Sum	Average	Variance
Standard Treatment	6	736	122.667	67.467
Placebo	6	877	146.167	76.967
New Treatment	6	726	121.000	24.800

Source of Variation	SS	df	MS	F	P-value
Between Groups	2376.778	2	1188.39	21.07	0.0000
Within Groups	846.167	15	56.41
Total	3222.944	17

correct competing hypotheses:

H₀: The means are all equal.

H₁: The means are not all equal

decision rule. Reject H₀ if F > 3.68

mean of Group 1 =122.667

mean of Group 2 =146.167

mean of Group 3=121.000

overall mean =129.944

Between Groups Sums of Squares =2376.778