assignment 1f

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 mu=170; sigma=8.2; 

x=zeros(136,50); x=randn(136,50).*sigma +mu; y=mean(x); z=var(y) hist(y); title('Distribution of the means'); ylabel('Frequency'); xlabel('Mean height(cm)'); 

mu=170; sigma=8.2; x=zeros(136,50); x=normrnd(mu,sigma,136,50); y=mean(x); z=var(y) hist(y); title('Distribution of the means'); 

ylabel('Frequency'); xlabel('Mean height(cm)'); 

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 rpois(n, lambda)

n= number of random values to return.

 Lambda= mean.

I used the following code to find out mean & variance under Poisson assumption.

> a<-rpois(7,78.3)

> mean(a);var(a)

Mean Variance

80.85714 69.14286

74.42857 88.619048

78.42857 126.285784.71429 92.2381

79.14286 101.1429

82.71429 76.90476

81.28571 50.57143

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73.14286 137.8095

75.57143 62.9524

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Question 3(Solved using R)

0 20 40 60 80 100

   2

   4

   6

   8

   1   0

   1   2

df

 q t ( 0 . 9 7 5 , d f )

   1 .   0

   1 .   5

   2 .

   0

   2 .

   5

log(df)

   l  o  g   (  q   t   (   0 .   9

   7   5 ,

   d   f   )   )

1 2 3 4 5 7 9 12 17 23 31 42 57 77

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Question 4

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Question 4

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 function f=two1

# H0: There is no significant difference between the data points of the same treatment.

# There is no significant difference between control and treatment1.

# H1: There is significant difference between the data points of the same treatment.

# There is significant difference between control and treatment1.

a=[4.17 5.58 5.18 6.11 4.5 4.61 5.17 4.53 5.33 5.14];b=[4.81 4.17 4.41 3.59 5.87 3.83 6.03 4.89 4.32 4.69];

r=[a;b];

 p=size(r,1);

q=size(a,2);

 x=mean(a);

y=mean(b);

m=[x y];

r_avg=mean(r);

gmean=mean([a b])

SSA=q*sum((m-gmean).^2)MSA=(SSA/(p-1))

SSB=p*(sum((r_avg-gmean).^2))

MSB=(SSB/(q-1))

SSE=sum((a-x-r_avg+gmean).^2)+sum((b-y-r_avg+gmean).^2)

MSE=SSE/((p-1)*(q-1))

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 function f=two2

# H0: There is no significant difference between the data points of the same treatment.

# There is no significant difference between control and treament2.

# H1: There is significant difference between the data points of the same treatment.# There is significant difference between control and treament2.

a=[4.17 5.58 5.18 6.11 4.5 4.61 5.17 4.53 5.33 5.14];

c=[6.31 5.12 5.54 5.5 5.37 5.29 4.92 6.15 5.8 5.26];

r=[a;c];

 p=size(r,1);

q=size(a,2);

 x=mean(a);

 z=mean(c);m=[x z];

r_avg=mean(r);

gmean=mean([a c])

SSA=q*sum((m-gmean).^2)

 MSA=(SSA/(p-1))

SSB=p*(sum((r_avg-gmean).^2))

 MSB=(SSB/(q-1))

SSE=sum((a-x-r_avg+gmean).^2)+sum((c-z-r_avg+gmean).^2)

 MSE=SSE/((p-1)*(q-1))

F1=MSA/MSE;

F2=MSB/MSE;

test_statistic1=F1

test_statistic2=F2

if (test_statistic1>finv(0.95,(p-1),(p-1)*(q-1)))

 printf ("There is significant difference between the data points of the same treatment\n")

else

 printf ("There is no significant difference between the data points of the same treatment\n")

endif 

if (test_statistic2>finv(0.95,(q-1),(p-1)*(q-1))) printf ("There is significant difference between control and treament2\n")

else

 printf ("There is no significant difference between control and treament2\n")

endif 

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test_statistic1=F1

test_statistic2=F2

if (test_statistic1>finv(0.95,(p-1),(p-1)*(q-1)))

 printf ("There is significant difference between the data points of the same treatment\n")

else

 printf ("There is no significant difference between the data points of the same treatment\n")

endif 

if (test_statistic2>finv(0.95,(q-1),(p-1)*(q-1)))

 printf ("There is significant difference between treatment1 and treatment2.\n")

else

 printf ("There is no significant difference between treatment1 and treatment2.\n")

endif