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 hospital manager wants to know the average blood test turn-around time. To estimate this a sample of blood test turn-around times was taken, the sample data is provided on (Lab1csv). The population standard deviation is known to be 7.5 minutes.

Lab1 File: https://drive.google.com/file/d/1afXk3F_dIvo6LsaWJMKfKxcqvXjxSnf6/view?usp=sharing

USE R STUDIO TO SOLVE PROBLEM

2. As noted earlier, the hospital manager is not sure whether average turn-around time is 40 minutes. In order to test this hypothesis use the sample data (Lab1csv).

a) First calculate a p-value.
b) Test the hypothesis at the 10% significance level and report your finding.
c) Test the hypothesis at the 1% significance level and report your finding.

Explanation / Answer

Null hypothesis:

H0: average turn-around time is 40 minutes

Alternative Hypothesis:

H1: average turn-around time is not around 40 minutes

alpha=0.05

mean(Lab1$Time)

43.53333

Z=x-mean/sd/sqrt(n)

=43.5333-40/7.5/sqrt(30)

=2.5804

p value=0.0098

p<0.05

Reject Null hypothesis

there is sufficient statistical evidence at 5% level of significance that the average turn-around time is 40 minutes.

average turn-around time is not 40 minutes

Solutionb:

z=2.5804

p=0.0098

alpha=10%=0.10

p<alpha

Reject Null Hypothesis

Solutionc:

z=2.5804

p=0.0098

alpha=0.01

p<alpha

Reject Null hypothesis.

Accept alternative Hypothesis.

There is no sufficient evidence at 1% level of significance to conclud that  average turn-around time is 40 minutes.

Code iN R:

t.test(Lab1$Time,mu=40,conf.level = 0.90)

One Sample t-test

data: Lab1$Time
t = 2.0232, df = 29, p-value = 0.05236
alternative hypothesis: true mean is not equal to 40
99 percent confidence interval:
38.71954 48.34712
sample estimates:
mean of x
43.53333

p>alpha

Fail to reject Null Hypothesis.

average turn-around time isdifferent 40 minutes.

Solutionc:

t.test(Lab1$Time,mu=40,conf.level = 0.99)

Output:

One Sample t-test

data: Lab1$Time
t = 2.0232, df = 29, p-value = 0.05236
alternative hypothesis: true mean is not equal to 40
99 percent confidence interval:
38.71954 48.34712
sample estimates:
mean of x
43.53333

p=0.05236

p>alpha

p>0.1

Fail to reject null hypothesis

accept alternative HYpotehsis

average turn-around time is different from 40 minutes.

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