Question

Directions: Create a PowerPoint with presenter’s notes describing your research project. A minimum of 10 slides is required, including a title and References slide. The presentation should address the following:

1. Describe the techniques and procedures that will be used.
2. State the hypothesis.
3. State general equipment that will be necessary and their intended use.
4. Describe type of data that will be collected and measurements that will be made.
5. Define and describe experimental units and be specific.
6. Define the population for generalization.
7. Define sampling technique and randomization, and include rationale.

Describe the topic and why it is important to your field of study.	10	Click here to enter text.
Describe the techniques and procedures that will be used.	4
State the hypothesis.	4
State the general equipment that will be necessary and its intended use.	4
Describe type of data that will be collected and measurements that will be made.	4
Define and describe experimental units and be specific.	4
Define the population for generalization.	4
Define sampling technique and randomization, and include rationale.	4
Reference slide included.	2
	Total Points (40)

Answer 1

Statistical Testing Procedure using R

Statistical inference is not useful just for evaluating estimators, it is also possible to conduct tests of a statistic when one has not able to find a test statistic which free of parameters. Hence, using this we test if the statistic from the observed data is consistent with the statistics calculated from data generated under the null hypothesis. In hypothesis, we mainly find

1. Test statistic value
2. P-value
3. Power of a test

Steps: Under certain null hypothesis for a particular model
1 Generate random sample X1 , X2, . . . , Xn from the null distribution or model
2 Compute the test statistic.
3 Repeat S times: T (1 ), T(2), . . . , T(S)
4 check rejection criterion at significance level α.
5 Draw conclusion with varying sample size.

Example: Generate a sample from normal random variable N(10, 25). Consider the hypothesis test defined by H0 : = 10 against H1 : . Evaluate the type I error using 500 simulation at 5% significance level.

rm(list=ls(all=TRUE))
n=c(10,50)                   # sample size
mu=10                        # true value of a parameter
sig=5                        # true value of a parameter
Sim=1000                     # Set the number of simulations
P=matrix(nrow=Sim, ncol=length(n))
for (j in 1:length(n)){
for(i in 1:Sim){             # simulation loop
y=rnorm(n[j], mu, sig)       # generate normal random number
sig_y=sqrt(var(y)/n[j])      # compute standard error
mu_y=sum(y)/n[j]             # compute estimator
tobs=(mu_y-10)/sig_y         # compute test statistic
P[i,j]=pnorm(tobs)           # p-value          
}
}
par(mfrow=c(1,2))
plot(P[,1], xlab="no. of simulation", ylab="p-value", main="n=10")
abline(h=0.025, lty=2, col="red",lwd=2)
abline(h=0.975,lty=2, col="red",lwd=2)
plot(P[,2], xlab="no. of simulation", ylab="p-value",main="n=50")
abline(h=0.025, lty=2, col="red",lwd=2)
abline(h=0.975,lty=2, col="red",lwd=2)

On the basis of plot, concluded that rejection of the p-value is more when sample size is small. As sample size increases,
rejection of null hypothesis is decreases at 5 % level of significance.