With rising health care costs and patients demanding improved levels of service,

Question

With rising health care costs and patients demanding improved levels of service, many hospitals are using statistical methods to assist in process improvement. Here we consider a hospital that has a target of 40 minutes turn-around time on blood tests (i.e. from test request to receipt of results).

The manager has implemented some process improvements and believes the average turn-around time is now less than 40 minutes. Some new (post-improvement) turn-around time data has been collected and is provided in csv format (Lab2csv). The population standard deviation remains 7.5 minutes.

Lab2 File: https://drive.google.com/file/d/1sMcE47y24q7OAObIcXGODCz1LdYNGjFG/view?usp=sharing

USE R STUDIO TO SOLVE PROBLEM

d) Calculate a point estimate of the average (post-improvement) turn-around time.
e) Test the hypothesis at the 10% significance level and report your finding.
f) Test the hypothesis at the 1% significance level and report your finding.

Explanation / Answer

The complete R nippet is as follows

# read the data into R dataframe
data.df<- read.csv("C:\Users\586645\Downloads\Chegg\time.csv",header=TRUE)
str(data.df)

## average
mean(data.df)

## 10% signficance level

t.test(data.df$Time,mu=40,alternative = "less",conf.level = 0.90)

## 1% signficance level

t.test(data.df$Time,mu=40,alternative = "less",conf.level = 0.99)

The results are

> mean(data.df$Time)
[1] 38.03333
> ## 10% signficance level
> t.test(data.df$Time,mu=40,alternative = "less",conf.level = 0.90)

   One Sample t-test

data: data.df$Time
t = -1.2916, df = 29, p-value = 0.1033, as the p value is not less than 0.1 , hence we fail to reject the null hypothesis and concldue that average turn-around time is not less than 40 minutes
alternative hypothesis: true mean is less than 40
90 percent confidence interval:
-Inf 40.03014
sample estimates:
mean of x
38.03333

> ## 1% signficance level
> t.test(data.df$Time,mu=40,alternative = "less",conf.level = 0.99)

   One Sample t-test

data: data.df$Time
t = -1.2916, df = 29, p-value = 0.1033

as the p value is not less than 0.01 , hence we fail to reject the null hypothesis and concldue that average turn-around time is not less than 40 minutes

alternative hypothesis: true mean is less than 40
99 percent confidence interval:
-Inf 41.78204
sample estimates:
mean of x
38.03333

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