Question

Measurements on the percentage of enrichment of 12 fuel rods used in a nuclear reactor were reported in the data below. Assume the population of interest is normally distributed

A. Test the hypotheses H0 : µ = 2.95 vs. H1 : µ > 2.95 at the 0.01 significance level. provide a copy of your R input and output, state your conclusion in context

B. Find and interpret the lower 99% confidence bound on the true mean percentage of enrichment. use the interval from your R output

DATA:

(%)

3.11

2.88

3.08

3.01

2.84

2.86

3.04

3.09

3.08

2.89

3.12

2.98

Answer 1

a ) input

x<-c(3.11,2.88,3.08,3.01,2.84,2.86,3.04,3.09,3.08,2.89,3.12,2.98)
> install.packages("ggpubr")
> library(ggpubr)
t.test(x, mu = 2.95, alternative = "less")

output

> t.test(x, mu = 2.95, alternative = "less")

   One Sample t-test

data: x
t = 1.5953, df = 11, p-value = 0.9305
alternative hypothesis: true mean is less than 2.95
95 percent confidence interval:
-Inf 3.052744
sample estimates:
mean of x
2.998333

since p value is greater than 0.01 so we accept the H0

b )

> t.test(x, mu = 2.95, alternative = "less" ,conf.level = 0.99)

   One Sample t-test

data: x
t = 1.5953, df = 11, p-value = 0.9305
alternative hypothesis: true mean is less than 2.95
99 percent confidence interval:
-Inf 3.080684
sample estimates:
mean of x
2.998333
lower 99% confidence bound = 3080684

we are 99% confident that the true mean percentage of enrichment is less than 3.080684