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Three kinds of sleeping pills do the trial against white mice. Recorded the time in seconds from start until the mice given the drug slept. Prove whether the effects are the same for three types of drugs Drug 1 Drug 2 Drug 3 47 55 54 53 58 50 49 54 51 50 61 51 46 62 49

Three kinds of sleeping pills do the trial against white mice. Recorded the time in seconds from start until the mice given the drug slept. Prove whether the effects are the same for three types of drugs Drug 1 Drug 2 Drug 3 47 55 54 53 58 50 49 54 51 50 61 51 46 62 49

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.6: Variation
Problem 37E
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Three kinds of sleeping pills do the trial against white mice. Recorded the time in seconds from start until the mice given the drug slept.

Prove whether the effects are the same for three types of drugs

Drug 1

Drug 2

Drug 3

47

55

54

53

58

50

49

54

51

50

61

51

46

62

49
Expert Solution
Step 1

Given Data :

  Drug 1 Drug 2 Drug 3
  47 55 54
  53 58 50
  49 54 51
  50 61 51
  46 62 49
       
Total = 245 290 255
Mean = 49 58 51
∑iXij2=\sum_i X_{ij}^2 = 12035 16870 13019
SS = 30 50 14
n = 5 5 5

Calculating Sum of Squares :

∑i,jXij=245+290+255=790\sum_{i,j} X_{ij} = {245} + {290} + {255} = 790 

∑i,jXij2=12035+16870+13019=41924\sum_{i,j} X_{ij}^2 = {12035} + {16870} + {13019} = 41924

Total sum of squares=SStotal=∑i,jXij2−1N(∑i,jXij)2=41924−790215=317.333SS_{total} = \sum_{i,j} X_{ij}^2 - \frac{1}{N} \left(\sum_{i,j} X_{ij}\right)^2 = 41924 - \frac{ 790^2}{ 15} = 317.333

Within sum of squares =  SSwithin=∑SSwithingroups=30+50+14=94SS_{within} = \sum SS_{within groups} = {30} + {50} + {14} = 94 

Between sum of squares =  SSbetween=SStotal−SSwithin=317.333−94=223.333SS_{between} = SS_{total} - SS_{within} = 317.333 - 94 = 223.333

 

Total sample size = N=15N = 15

Total degrees of freedom = dftotal=15−1=14df_{total} = 15 - 1 = 14 

Groups = k = 3

Between-groups degrees of freedom = dfbetween=3−1=2df_{between} = 3 - 1 = 2 

Within-groups degrees of freedom = dfwithin=dftotal−dfbetween=14−2=12df_{within} = df_{total} - df_{between} = 14 - 2 = 12 

 

Calculating the mean sum of squares :

MSbetween=SSbetweendfbetween=223.3332=111.667MS_{between} = \frac{SS_{between}}{df_{between}} = \frac{ 223.333}{ 2} = 111.667

MSwithin=SSwithindfwithin=9412=7.833MS_{within} = \frac{SS_{within}}{df_{within}} = \frac{ 94}{ 12} = 7.833

 

 

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