OneSampleTest: One-Sample Tests
In Harrindy/StatEngine: An R Package for the UofSC Course STAT 509 "Statistics for Engineers"

Description Usage Arguments Details Value Note Author(s) References Examples

Conduct hypothesis testing on population mean, population variance, and population proportion. Compute power of a test, and calculate the required sample size for a desired power.

#Test on pupulation mean of a normal distribution when the population variance is known:
Ztest(mu0,H1,alpha,sigma,sample) # if sample available
Ztest(mu0,h1,alpha,sigma,n,barx) # if statistics are provided
# Power calculation
Ztest.power(H1,alpha,sigma,n,delta)
# Sample size calculation
sample.size.Ztest(H1,sigma,alpha,beta,delta)

#Test on pupulation mean of a normal distribution when the population variance is unknown:
Ttest(mu0=?,H1=?,alpha=?,sample=?) #If data are available
Ttest(mu0=?,H1=?,alpha=?,n=?,barx=?,s=?) #If statistics are provided s=sd(data)
# Power calculation
Ttest.power(H1=?,est.sigma=sn,alpha=?,n=?,delta=?)
# Sample size calculation
sample.size.Ttest(H1=?,est.sigma=sn, beta=?,delta=?,alpha=?

#One-Sample Proportion Z-tests on a population proportion:
Proptest(p0=?,H1=?,alpha=?,n=?,X=?)
# Power calculation
Proptest.power(H1=?,alpha=?,p0=?,p1=?,n=?)
# Sample size calculation
sample.size.Proptest(H1=?,beta=?,alpha=?,p0=?,p1=?)

`mu0`	the hypothesized value of the population mean in Z-tests and T-tests
`H1`	type of alternative hypothesis: "two", "left", or "right"
`alpha`	the significance level
`sample`	a vector of the observed sample
`sigma`	the known population standard deviation
`n`	the sample size
`barx`	the observed sample mean
`delta`	the delta value in power/sample size calculation of Z-test/T-test
`beta`	the desired power for sample size calculation
`s`	the observed sample standard deviation
`est.sigma`	an estimate of the population standard deviation in power/sample size calculation of T-test
`sigma0`	the hypothesized value of the population standard deviation in Chi-square-tests
`lambda`	the lambda value in power/sample size calculation of Chi-square-tests
`p0`	the hypothesized value of the population proportion
`X`	number of observations belongs to a class of interest
`p1`	the p1 value in power/sample size calculation of One-sample Prportion Z-tests

Conduct hypothesis testing on population mean, population variance, and population proportion. Compute power of a test, and calculate the required sample size for a desired power.

`test`	As long as the function has "test", it produces the test results of using three approaches.
`power`	As long as the function has "test", it computes the power of the test.
`sample.size`	As long as the function has "sample.size", the outcome is the minimum sample size required to reach the given power.

deweiwang@stat.sc.edu

Dewei Wang

Chapter 9 of the textbook "Applied Statistics and Probability for Engineers" 7th edition

#Ztest
#must include the = sign
Ztest(mu0=3,H1="two",alpha=0.05,sigma=0.9,n=15,barx=2.78)
Ztest.power(H1="two",alpha=0.05,sigma=0.9,n=15,delta=3.25-3)
sample.size.Ztest(H1="two",sigma=0.9,alpha=0.05,beta=1-0.9,delta=3.75-3)

#Ttest
#must include the = sign
x=c(131.15, 130.69, 130.91, 129.54, 129.64, 128.77, 130.72, 128.33,
128.24, 129.65, 130.14, 129.29, 128.71, 129.00, 129.39, 130.42,
129.53, 130.12, 129.78, 130.92)
data.summary(x)
Ttest(mu0=130,H1="two",alpha=0.05,sample=x)
Ttest.power(H1="two",est.sigma=sd(x),alpha=0.05, n=length(x),delta=0.5)
sample.size.Ttest(H1="two",est.sigma =sd(x),beta=0.25,delta=0.1,alpha=0.05)

#Chi-square test
#must include the = sign
Chi2test(sigma0=sqrt(0.01),H1="right",alpha=0.05,n=20,s=sqrt(0.0153))
Chi2test.power(H1="right",alpha=0.05,n=20,lambda=1.25)
sample.size.Chi2test(H1="right",beta=0.2,lambda=1.25,alpha=0.05)

Chi2test(sigma0=0.01,H1="right",alpha=0.01,n=15,s=0.008)
Chi2test.power(H1="right",alpha=0.01,n=15,lambda=1.5)
sample.size.Chi2test(H1="right",beta=0.2,lambda=1.25,alpha=0.01)

#One-sample proportion Z-test
#must include the = sign
Proptest(p0=0.05, H1="left",alpha=0.05,n=300,X=7)
Proptest.power(H1="left",alpha=0.05,p0=0.05,p1=0.03,n=300)
sample.size.Proptest(H1="left",beta=0.1,alpha=0.05,p0=0.05,p1=0.03)