Question

The Striving for Perfection Urgent Care Center feels that its patients wait time is too long.
The staff has noticed that increasing numbers of people are waiting longer in the waiting room.
The national benchmark performance is 90 minutes or less from the time the customer arrives
to the time the customer is treated and discharged.

Part I
The staff decides to examine the time it takes for all patients to move through their service process
on two successive days (columns A & B of the data tab = one sample).

Question 1 (2 points): What type of variable did they choose to examine? Qualitative or quantitative?

Question 2 (2 points): Is the variable categorical, discrete or continuous?

Question 3 (2 points): How many observations did they collect?

Question 4 (2 points): What type of sampling did they use?
Random, systematic, stratified, clustered, or convenience.

Question 5 (20 points): Summarize these data graphically and using data description techlniques.

Question 6 (10 points) Are there any outliers in these data? Justify your answer.

Question 7 (20 points): Is the clinic meeting the national benchmark time?
(Test the hypothesis that the clinic's population mean is less than 90 minutes.
Use a 95% confidence level. Assume the variable is normally distributed.
State whether the assumptions for the test are met or not
Include the six step process described in the Chapter 9 Quiz.)

Part II
The staff thought that the type of service might have an impact on the time it took for the patient
to go through the entire process. So they collected a new set of data on one day showing the
elapsed time and a code for four different types of service (columns D and E of the data tab).

Answer Questions 1 to 5 for these data (number them 8 to 12),
considering that there are two variables this time. (28 points)

Part III
After the staff identified and changed a number of steps in their process to try to improve the times,
they collected another set of elapsed times for patients to pass through the urgent care facility
on one day after all the changes were implemented (column G of the data tab).

Question 13 (2 points): Are the data in Columns E and G dependent or independent?

Question 14 (2 points): Why is it valid to perform the following test?

Question 15 (20 points): Did the staff succeed in reducing the elapsed processing times?
(Test the hypothesis that the clinic's mean elapsed time after the process improvement is less
than the elapsed time was before the changes.
Use a 95% confidence level. Assume the variable is normally distributed.
State whether the assumptions for the test are met.
Include the six step process described in the Chapter 9 Quiz.)


See other side for Bonus Questions.

Bonus Questions :

Question 1 (20 points)
Using a level of significance of α=0.05, test whether the means of the four types of services
are equal. Assume the samples for the four types were independently drawn and that the four
populations are normally distributed.

Question 2 (20 points):
Compare the sample standard deviations of the four types of service.



dataset

Column A Col. B Col. D Col. E Col. G Sample: elapsed Urgent Care facility patient times in minutes, collected on 2 Sample elapsed times before times after Type of process change process improved successive da servic 65 147 190 200 147 190 179 90 200 90 2 2 30 30 95 125 125 143 30 58 143 2 179 97 179 95 125 95 95 143 240 24 270 120 150 166 58 90 240 240 130 270 120 270 4 120 150 30 125 150 166 166 130 143 130 156 3 156 30 57 136 178 136 178 146 245 243 146 4 245 90 243 4. 240 124 124 270 120 59 150 75 166

Answer 1

Part I
Question 1 : Quantitative.

Question 2: Continuous.

Question 3 : 88

Question 4 : Systematic.

Question 5 :

Question 6 :

Boxplot of Times in minutes 300 250 n 200 150 드 100 50

Descriptive Statistics: Times in minutes

Variable Mean StDev Minimum Q1 Median Q3 Maximum IQR
Times in minutes 106.95 66.02 11.00 61.00 95.00 145.25 270.00 84.25

Upper Whisker=Q3+1.5IQR=145.25+1.5*84.25= 271.625>Maximum value

Lower Whisker=Q1-1.5IQR=61.00-1.5*84.25=-65.375<Minimum value.

We know an outlier lies always outside the interval (Lower Whisker, Upper Whisker). But here maximum and minimum both values fall inside (Lower Whisker, Upper Whisker), so there is no outlier present.

Question 7:

One-Sample T: Times in minutes

Test of mu = 90 vs < 90

95% Upper
Variable N Mean StDev SE Mean Bound T P
Times in minutes 88 106.95 66.02 7.04 118.66 2.41 0.991

Since p-value=0.991>0.05 so we conclude that clinic's population mean is not less than 90 minutes.

Probability Plot of Times in minutes Normal-95% CI 99.9 107.0 66.02 AD 95 P-Value 0.005 90 80 C 60 U 50 30 20 10 100 200 300 200 -100 400 Times in minutes

From the above plot we conclude that variable is not normally distributed.