Reference no: EM132459307

Nonparametric Hypothesis Tests, Categorical Data, Trans MSA

Part 1. General

Where appropriate copy Excel Data to Minitab to determine or check answers.
Assume alpha = 0.05 for all Problems.

Problem 1

Clarkman Appliance is receiving complaints from their field service technicians of delays waiting for replacement parts. For some repair jobs, they get replacement parts from their warehouse (internal) while for other jobs they get them directly from their vendors. To compare their internal warehouse process with their vendor process, they obtain a sample of part replacement times from recent repair jobs. Historically, the time to receive replacement parts is skewed right. Using an appropriate hypothesis test, which of the following would you most likely conclude?

Ho: Median Internal Warehouse = Median Vendor
Ha: Medians are not equal

a. Cannot make a determination because data are not Normal
b. There is no significant difference between the internal warehouse and vendor
c. Internal process has significant lower part replacement time (lower median)
d. Vendor process has significantly lower part replacement time (lower median)

Problem 2

Suppose you conduct a customer satisfaction study on passive lock systems for new vehicles. One variable of interest is the delay time preference and whether it is affected by Gender. Based on a chi-square test (Minitab >> Tables >> Cross Tabulation and Chi Square), which of the following would you most likely conclude?

Row Factor: Gender (Male vs. Female)
Column Factor:
Delay Time Preference to Activate: No Delay, 10 Seconds, or 20 Seconds

Ho: Two Variables are independent; Ha: Not independent

a. The two variables are not independent (Chi-Square p-value = 0.000), delay time preference differs between male and female drivers
b. The two variables are independent (Chi-Square p-value = 0.705) with both preferring No Delay over the others
c. The two variables are independent (Chi-Square p-value = 0.705) with both preferring 10 second delay over the others
d. The two variables are independent (Chi-Square p-value = 0.705) with both preferring 20 second delay over the others

Part 2. Wait Room Time Analysis

A small medical office wants to better understand office wait time. They conduct a study where they track patient wait times for 3 process steps (wait room, wait for clinician 1, wait for clinician 2). They also record the time of day and the group that patients visit (3 Groups noted as A, B, and C). They are unsure about the underlying distribution of office wait time and thus are concerned with simply using conventional parametric hypothesis tests. (Note: Assume alpha = 0.05)

Problem 3

They wish to determine if there is a difference in wait times for the three steps (wait room time, wait for clinician 1, and wait for clinician 2. Use an appropriate nonparametric hypothesis test(s) to test for a difference in the populations (medians). Which of the following would you conclude? (Note: Use worksheet labeled ‘wait time stacked data')

a. All groups are identical
b. Groups are not identical; Wait for clinician 1 has the shortest wait time
c. Groups are not identical; Wait for clinician 2 has the shortest wait time
d. Groups are not identical; Wait for time in wait room has the shortest wait time among the steps

Problem 4

Next, they wish to determine if there is a difference in wait room timesby Team (A, B, vs. C). Use an appropriate nonparametric hypothesis test(s) to test for a difference in the populations (medians). Which of the following would you conclude? (Note: Use ‘un-stacked data')

a. All groups are identical
b. Groups are not identical; Team A has the longest wait room time
c. Groups are not identical; Team B has the longest wait room time
d. Groups are not identical; Team C has the longest wait room time

Part 3. Transactional MSA - Journal Entries

A Black Belt working with an accounting department has noticed an increasing trend in the average number of days to accurately close a journal entry. Currently, a computer keeps track of the time between when a transaction is recorded in a journal and when the entry is closed (in number of days). Before launching into a full-scale project to decrease the average number of days until journal entry close, the Black Belt decides to run a quick study to determine the validity of the data that is being measured by the computer. To test the system, she picks 20 journal entries at random and manually tracks the amount of time between when an entry is made to when it is closed. She also obtains the computer generated result for the same 20 items.

Method A: Computer Automated Data Collection
(Note: currently main source for data collection)

Method B: Manual Data Collection (special study used as Standard Reference)

Compare the manual result (reference values) and the automatically recorded time (measurements from normal business process) using a Paired t-test in Minitab.

Problem 5

Based on a paired t-test, which of the following conclusions may be reasonably concluded?

a. Two methods are not different (automated system appears no different than the manual validation check) based on p-value =0.001
b. Two methods are different where the automated system has significantly higher repeatability error with p-value = 0.001
c. Two methods are different where automated system has significant bias of 1.25 from standard (manual), with p-value =0.001
d. The automated system is consistently resulting in lower times than those obtained manually

Problem 6
Based on your above analysis, which follow-up action would you most likely recommend doing next?

a. Recommend a study on ways to improve the automated computer measurement system more accurate
b. Launch a full-scale BB project to decrease the average number of days to close a journal entry.
c. Switch to measuring the average number of days to close a journal entry using the manual system
d. Recommend adjustments to the computer system to only address issues with entries taking more than 15 days as all discrepancies between manual and automated occur when the manual reading is greater than or equal to 16

Part 4. Deposit Processing Time

Checking account closing rates have steadily increased over the past few years for a large regional bank. From conducting a customer survey, the company finds a strong correlation between deposit processing time and customer satisfaction.The first step in their continuous improvement effort is to ensure that the reporting of the deposit processing time is valid. For ease of analysis, a Black Belt randomly selects a common group of 50 deposits' and assigns to both a Branch and Headquarters. Analyze the data using a repeated measurement study.

Problem 7

Using a repeated measurements scatter plot (use STAT >> Regression >> fitted line plot in Minitab), what is the R-squared between the measurements obtained at the branch (X) versus those at headquarters (Y)?

a. 0.992
b. 98.3%
c. 47.4%
d. 92.1%

Problem 8

What percent of total study variation may be attributed to measurement system variation (i.e., Find Total Gage R&R - % Study Variation using Gage R&R Crossed Tool - ANOVA Method in Minitab)? (Hint: Use the data in stacked format from the Excel file).

a. 9.3%
b. 32.92%
c. 99.57%
d. 0.86%

Attachment:- Nonparametric Hypothesis Test.rar