Question

mathematical statistics use RStudio program to write a code

# Download the datas et Nile rm(list-1s)) 1ibrary(help "datasets") data("Nile" view (Nile) # Find the mean and sd of the data. It has only one variable. # Problem 1 # Design a one-tailed test with a null hypothesis HO: mu>1000 , assuming that the population sd is known and # is same as the sample sd and probability of error (alpha) 10%, can you reject the null? (50 points) # Problem 2 # Repeat the same exercise assuming that the population sd is not known. (50 points) # show all the necessary steps in each of the questions.

Answer 1

#Download the datset Nile
rm(list=ls())
library(help= "datasets")
data("Nile")
View(Nile)

Mean<-mean(Nile)
Standard_Deviation<-sd(Nile)

# Solution of Problem 1
n<-length(Nile)

mu=1000

Standard_Deviation1<-(n-1)*Standard_Deviation/n
T_KNOWN=(Mean-mu)/sqrt(Standard_Deviation1/n)

##OUTPUT as follows

> T_KNOWN
[1] -62.30908
# conclusion
# calculated |t|= 62.3 > tabulated t=1.29 for 100 df at 10% level of significance and our null hypothesis is rejected

# Solution of Problem 2

# H0: mu >1000
#one sided 90% confidence interval for mu

t.test(Nile, mu=1000, alternative="greater", conf.level=0.90)

#OUTPUT AS follows

One Sample t-test

data: Nile
t = -4.7658, df = 99, p-value = 1
alternative hypothesis: true mean is greater than 1000
90 percent confidence interval:
897.5169 Inf
sample estimates:
mean of x
919.35

# conclusion

# calculated |t|= 4.7 > tabulated t=1.29 for 99 df at 10% level of significance and our null hypothesis is rejected