o check pain-relieving medications for potential side effects on blood pressure, it is decided to give equal doses of each of four medications to test subjects. To control for the potential effect of weight, subjects are classified by weight groups. Subjects are approximately the same age and are in general good health. Two subjects in each category are chosen at random from a large group of male prison volunteers. Subjects’ blood pressures 15 minutes after the dose are shown below. Research question: Is mean blood pressure affected by body weight and/or by medication type? Systolic Blood Pressure of Subjects (mmHg) Ratio of Subject’s Weightto Normal Weight MedicationM1 MedicationM2 MedicationM3 MedicationM4 Under 1.1 131 146 140 130 135 136 132 125 1.1 to 1.3 136 138 134 131 145 145 147 133 1.3 to 1.5 145 149 146 139 152 157 151 141 correct row of hypothesis a. H0: A1 ≠ A2 ≠ A3 ≠ 0 ⇐⇐ Weight means differ H1: All the Aj are equal to zero ⇐⇐ Weight means are the same correct column of Hypothesis H0: B1 ≠ B2 ≠ B3 ≠ 0 ⇐⇐ Medication means differ H1: All the Bk are equal to zero ⇐⇐ Medication means are the same correct interaction-effect hypotheses H0: Not all the ABjk are equal to zer ⇐⇐ there is an interaction effect H1: All the ABjk are equal to zero ⇐⇐ there is no interaction effect (b) Fill in the missing data. (Round your table of means values to 1 decimal place, SS and F values to 2 decimal places, MS values to 3 decimal places, and p-values to 4 decimal places.) Table of Means Means: Factor 2 (Medication) Factor 1 (Weight) Med 1 Med 2 Med 3 Med 4 Total 1.1 or Less 1.1 to 1.3 1.3 to 1.5 Total ANOVA TABLE Source SS df MS F p-value Factor 1 (Weight) Factor 2 (Medication) Interaction Error Total

o check pain-relieving medications for potential side effects on blood pressure, it is decided to give equal doses of each of four medications to test subjects. To control for the potential effect of weight, subjects are classified by weight groups. Subjects are approximately the same age and are in general good health. Two subjects in each category are chosen at random from a large group of male prison volunteers. Subjects’ blood pressures 15 minutes after the dose are shown below. Research question: Is mean blood pressure affected by body weight and/or by medication type? Systolic Blood Pressure of Subjects (mmHg) Ratio of Subject’s Weightto Normal Weight MedicationM1 MedicationM2 MedicationM3 MedicationM4 Under 1.1 131 146 140 130 135 136 132 125 1.1 to 1.3 136 138 134 131 145 145 147 133 1.3 to 1.5 145 149 146 139 152 157 151 141 correct row of hypothesis a. H0: A1 ≠ A2 ≠ A3 ≠ 0 ⇐⇐ Weight means differ H1: All the Aj are equal to zero ⇐⇐ Weight means are the same correct column of Hypothesis H0: B1 ≠ B2 ≠ B3 ≠ 0 ⇐⇐ Medication means differ H1: All the Bk are equal to zero ⇐⇐ Medication means are the same correct interaction-effect hypotheses H0: Not all the ABjk are equal to zer ⇐⇐ there is an interaction effect H1: All the ABjk are equal to zero ⇐⇐ there is no interaction effect (b) Fill in the missing data. (Round your table of means values to 1 decimal place, SS and F values to 2 decimal places, MS values to 3 decimal places, and p-values to 4 decimal places.) Table of Means Means: Factor 2 (Medication) Factor 1 (Weight) Med 1 Med 2 Med 3 Med 4 Total 1.1 or Less 1.1 to 1.3 1.3 to 1.5 Total ANOVA TABLE Source SS df MS F p-value Factor 1 (Weight) Factor 2 (Medication) Interaction Error Total

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Description: o check pain-relieving medications for potential side effects on blood pressure, it is decided to give equal doses of each of four medications to test subjects. To control for the potential effect of weight, subjects are classified by weight groups.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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Systolic Blood Pressure of Subjects (mmHg)
Ratio of Subject’s Weight to Normal Weight	Medication M1	Medication M2	Medication M3	Medication M4
Under 1.1	131	146	140	130
	135	136	132	125
1.1 to 1.3	136	138	134	131
	145	145	147	133
1.3 to 1.5	145	149	146	139
	152	157	151	141

correct row of hypothesis

a.	H₀: A₁ ≠ A₂ ≠ A₃ ≠ 0	⇐⇐ Weight means differ
	H₁: All the A_j are equal to zero	⇐⇐ Weight means are the same

correct column of Hypothesis

H₀: B₁ ≠ B₂ ≠ B₃ ≠ 0	⇐⇐ Medication means differ
	H₁: All the B_k are equal to zero	⇐⇐ Medication means are the same

correct interaction-effect hypotheses

H₀: Not all the AB_jk are equal to zer	⇐⇐ there is an interaction effect
	H₁: All the AB_jk are equal to zero	⇐⇐ there is no interaction effect

(b) Fill in the missing data. (Round your table of means values to 1 decimal place, SS and F values to 2 decimal places, MS values to 3 decimal places, and p-values to 4 decimal places.)

Table of Means
Means:	Factor 2 (Medication)
Factor 1 (Weight)	Med 1	Med 2	Med 3	Med 4	Total
1.1 or Less
1.1 to 1.3
1.3 to 1.5
Total

ANOVA TABLE
Source	SS	df	MS	F	p-value
Factor 1 (Weight)
Factor 2 (Medication)
Interaction
Error
Total

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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