Question

"In R, define a function counting the values that are less than 0 for two vectors x=rnorm(50) and y=rnorm(5000) respectively. Define another function to calcute the proportion that values are less than 0 for x and y respectively. Compare calculated proportions with theoretical proportion 0.5, what conclusions can you make?"

Please help me with the source code! Thanks!  

Answer 1

R-Code

X=rnorm(50)

length(X)

Z=as.vector(Z)

# Here the Z vector is created now we count the value in X which are less than 0

# Here the R vector is created now we count the value in Y which are less than 0

#In Loop vector Z is created such that if X is less than 0 the value is added. so the last value of this vector is the total count of value in X which are less than 0ifelse(X[1]<0,Z[1]+1,Z[1]+0)

for(i in 2:50)

{

if(X[i]<0)

Z[i]=Z[i-1]+1

else

Z[i]=Z[i-1]

}

Z

Y=rnorm(5000)

R=as.vector(R)

# Here the R vector is created now we count the value in Y which are less than 0

#In Loop vector R is created such that if Y is less than 0 the value is added. so the last value of this vector is the total count of value in Y which are less than 0

ifelse(Y[1]<0,R[1]+1,R[1]+0)

for(i in 2:5000)

{

if(Y[i]<0)

R[i]=R[i-1]+1

else

R[i]=R[i-1]

}

#Here the last value from Z & R is the count of value whcih are less than 0 in X & Y respectively

# The proportion is n/N

p1=Z[50]/50

p2=R[5000]/5000

p1

p2

# Test for Proportion

#H0: p1=0.5 Vs. H1 :p1 not equal to 0.5

#H0:p2=0.5 Vs. H1 :p2 not equal to 0.5

sd=sqrt(0.5*(1-0.5)/50)

Test1=(p1-0.5)/sd

Test1

Test2=(p2-0.5)/sd

Test2

#Calculate p-value to make decision

Prob1=pnorm(Test1,0,1)

Prob2=pnorm(Test2,0,1)

The conclusion is based on pvalue for the test ad it is dependent on X & Y. and Here X & Y are random so the test statistic change every time. The output is of when the program is run.

Run the given code

Output

> X=rnorm(50)

> length(X)

[1] 50

> Z=as.vector(Z)

> # Here the Z vector is created now we count the value in X which are less than 0

> # Here the R vector is created now we count the value in Y which are less than 0

> #In Loop vector Z is created such that if X is less than 0 the value is added. so the last value of this vector is the total count of value in X which are less than 0ifelse(X[1]<0,Z[1]+1,Z[1]+0)

> for(i in 2:50)

+ {

+ if(X[i]<0)

+ Z[i]=Z[i-1]+1

+ else

+ Z[i]=Z[i-1]

+ }

> Z

[1] 0 1 1 2 2 3 3 4 4 5 6 7 8 8 9 9 10 10 10 11 11 11 11 12

[25] 12 13 14 15 15 15 16 16 17 17 17 18 19 20 21 21 21 22 23 24 24 24 25 25

[49] 25 25

> Y=rnorm(5000)

> R=as.vector(R)

> # Here the R vector is created now we count the value in Y which are less than 0

> #In Loop vector R is created such that if Y is less than 0 the value is added. so the last value of this vector is the total count of value in Y which are less than 0

> ifelse(Y[1]<0,R[1]+1,R[1]+0)

[1] 2

> for(i in 2:5000)

+ {

+ if(Y[i]<0)

+ R[i]=R[i-1]+1

+ else

+ R[i]=R[i-1]

+ }

> #Here the last value from Z & R is the count of value whcih are less than 0 in X & Y respectively

> # The proportion is n/N

> p1=Z[50]/50

> p2=R[5000]/5000

> p1

[1] 0.5

> p2

[1] 0.5014

>

> # Test for Proportion

> #H0: p1=0.5 Vs. H1 :p1 not equal to 0.5

> #H0:p2=0.5 Vs. H1 :p2 not equal to 0.5

> sd=sqrt(0.5*(1-0.5)/50)

> Test1=(p1-0.5)/sd

> Test1

[1] 0

> Test2=(p2-0.5)/sd

> Test2

[1] 0.01979899

> #Calculate p-value to make decision

> Prob1=pnorm(Test1,0,1)

> Prob2=pnorm(Test2,0,1)

> Prob1

[1] 0.5

> Prob2

[1] 0.5078981

Here for both X & Y p-value is >0.05. so we fail to reject null hypothesis than proportion is 0.5