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).

Group 1 Standard Treatment : 124 111 133 125 128 115 = 736

Group 2 Placebo: 134 143 148 142 150 160 = 877

Group 3 New Treatment: 114 117 121 124 122 128 = 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

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁ = u₂ = u₃

Alternative hypothesis: At-least one of the u is not equal.

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data.

F statistics is given by:-

F = 21.07

F_critical = 3.682

Reject H₀ if F > 3.68

The P-value = 0.000041

Interpret results. Since the P-value (0.000041) is less than the significance level (0.05), we have to reject the null hypothesis.

Conclusion:-

Reject H₀, There is sufficient evidence for significant differences between the three groups.

Mean of group 1 = 122.667

Mean of group 2 = 146.167

Mean of group 3 = 121

The overall mean is 129.44

SSB = 2376.778