Research Objective Suppose in a certain chemical factory named ‘R&Co’ there was a report published about chemical process viscosity for 3 years. R&Co assured environmental activist by saying that their chemical viscosity is 84.00 in every year, but recently one study indicated that chemical viscosity reading of R&Co may contain more than that amount. Considering that the chemical viscosity reading per year varies from one time period to another, we can formulate this problem as a test of hypothesis about the median (θ) of the distribution of the chemical viscosity reading per year.

Null and alternative hypotheses that are related to the research objective.

Here, we are assuming a significance level of \(\alpha\) = 0.05.

Hypothesis:

Null Hypothesis, \(H_o\), \(\mu\) = 84.00

Alternative Hypothesis, \(H_a\), \(\mu\) > 84.00

As the standard deviation for the population is not given, we will go for the t-test.

Test Statistics:

We can write the test statistics as, \[ t = \frac{\overline{X} - \mu}{S/\sqrt{n}}\]

# load the library
library(readxl)
# Set directory for data file
Chemical_process_Viscosity <- read_excel("C:/Users/md.mominul.islam/OneDrive - South Dakota State University - SDSU/Nonparametric/Nonparametric_Rabid/Projects/Data Set/Chemical process Viscosity.xlsx")
View(Chemical_process_Viscosity)
#only selecting chemical viscosity reading
project1 <- as.data.frame(Chemical_process_Viscosity)
head(project1)
#Statistical summary of Reading
summary(project1$Reading)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   82.25   84.47   85.13   85.28   86.27   88.00

Binomial Test for the Chemical Viscosity

Test Statistic

# One-sample t-test
res <- t.test(project1$Reading, mu = 84, alternative ="greater")
# Printing the results
res 
## 
##  One Sample t-test
## 
## data:  project1$Reading
## t = 5.7708, df = 35, p-value = 7.739e-07
## alternative hypothesis: true mean is greater than 84
## 95 percent confidence interval:
##  84.90238      Inf
## sample estimates:
## mean of x 
##  85.27595

From the test statistic, we got the t-value=23.862 and a p-value is 7.739e-07 which is significantly smaller than the significance level \(\alpha\) = 0.05

p-value

From the test statistic, we got the p-value is 7.739e-07

Decision about the null hypothesis Decision about Null Hypotheses: As the p-value is less than the significance level, we reject null hypotheses. So we can clearly say that distribution of the chemical viscosity reading per year is greater than 84.00.

Conclusion with respect to the research objective

From research objective, we know that R&Co assured environmental activist by saying that their chemical viscosity is 84.00 in every year, but recently one study indicated that chemical viscosity reading of R&Co may contain more than that amount. Considering that the chemical viscosity reading per year varies from one time period to another, we formulated a binomial test where we found that distribution of the chemical viscosity reading per year is greater than 84.00.