For both A and B problems, please follow the 5 step hypothesis testing procedure

Question

For both A and B problems, please follow the 5 step hypothesis testing procedure as explained in the textbook.

The five steps are as follows:

Step 1: Set up hypothesis and determine the level of significance

Step 2: Select appropriate test statistic

Step 3: Set up the decision rule

Step 4: Compute the test statistic

Step 5: Conclusion

A) The following data were collected in an experiment designed to investigate the
impact of different positions of the mother during ultrasound on fetal heart rate.
Fetal heart rate is measured by ultrasound in beats per minute. The study includes
20 women who are assigned to one position and have the fetal heart rate measured
in that position. Each woman is between 28-32 weeks gestation. The data are
shown below.
Back Side Sitting Standing
140 141 144 147
144 143 145 145
146 145 147 148
141 144 148 149
139 136 144 145
Mean = 142.0 Mean = 141.8 Mean = 145.6 Mean =146.8
Is there a significant difference in mean fetal heart rates by position? Run the test
at a 10% level of significance.

B) Suppose a hypertension trial is mounted and 21 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 as follows.

Standard Treatment

124, 111, 133, 125, 128, 115, 120.

Placebo

134, 143, 148, 142, 150, 160, 150.

New Treatment

114, 117, 121, 124, 122, 128, 130.

Is there a difference in mean SBP among treatments? Run the appropriate test at =0.05.

Explanation / Answer

A:

Hypotheses are:

H0: The mean fetal heart rates by position is same.

Ha: The mean fetal heart rates is different for at least one position.

Since we need to compare more than 2 means so one way ANOVA will be use. Following is the output of one way ANOVA generated by excel:

The p-value is 0.0163

Since p-value is less than 0.10 so we reject the null hypothesis. There is a significant difference in mean fetal heart rates by position.

-----------------------------

B:

Hypotheses are:

H0: The mean SBP among treatments is same.

Ha: The mean SBP among treatments is different for at least one treatment.

Since we need to compare more than 2 means so one way ANOVA will be use. Following is the output of one way ANOVA generated by excel:

Since p-value is less than 0.05 so we reject the null hypothesis. There is a significant difference in mean fetal heart rates by position.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Back 5 710 142 8.5 Side 5 709 141.8 12.7 Sitting 5 728 145.6 3.3 Standing 5 734 146.8 3.2 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 96.15 3 32.05 4.628159 0.016297433 2.461811 Within Groups 110.8 16 6.925 Total 206.95 19

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