Table of ContentsExecutive Summary.......................................................................................................................................2

Introduction....................................................................................................................................................2

Methodology and Results..............................................................................................................................2

Efficiency...................................................................................................................................................2

Marked Differences...................................................................................................................................5

Customer Satisfaction................................................................................................................................5

Conclusions and Recommendations..............................................................................................................7

Darshil Shah z3331503 ECON1203

Executive SummaryThis report provides analysis on the issues raised about efficiency and customer satisfaction in AllRepairs. The results are:

Efficiency as measured by the average time it takes for a mechanic to complete a job is approximately 33 minutes in length and has a frequency distribution that conforms to the definition of efficiency where most jobs are done in a short period of time

There seems to be evidence of marked differences between staff undertaking the same jobs when difficulty is hard. The difference is approximately 27 minutes between mechanics

The refrigeration service branch has attained the target of 80% customer either being satisfied or very satisfied (81% of customers were in fact satisfied or very satisfied)

There was not enough evidence to infer that all service branches have not attained the level whereby 80% of the customers are either satisfied or very satisfied on the services provided

It is recommended that the efficiency results be interpreted by the CEO and/or management according the organisation’s goals and aims. Furthermore it is recommended that:

A review be performed for jobs that are identified hard in difficulty as there are some mechanics that are performing well while others that are not as seen through the marked difference result

Customer relation policies should be continued as they are producing the established target

IntroductionThe aim of this report is to analyse the data that has been collected from the refrigeration repair branch in order to reach conclusions about the efficiency of the repair staff along with if there are any marked differences between staff undertaking the same tasks. In addition the question of whether the target of 80% of customers being either satisfied or very satisfied has been achieved across all repair branches must be answered.

The data that was used was collected through a random sample of 293 jobs that were completed during last year. Key variables of interest were Time, Difficulty and Satisfaction.

The report has been organised by splitting methods into preliminary and full scale analysis while integrating the results within them.

Methodology and Results

Efficiency Efficiency of the mechanics has been asked to be measured in the time it takes to complete a job. So the variable of interest is the Time variable which contains ratio data on the total time taken to complete a job.

1) Preliminary Analysis and Results To get a general idea of the efficiency of the mechanics as measured by the time it takes a histogram can be constructed using the frequency distribution of time taken to complete a job by any mechanic:

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Darshil Shah z3331503 ECON1203

Table 1: Frequency distribution of Time taken to complete jobs

A histogram is a useful graphical descriptive technique to give a general idea of the skewness, mode, median, mean and symmetry (if any).

The histogram represents time series data of last year and shows that the distribution of time taken is positively skewed meaning that most of the jobs are completed within a short period of time. This matches a good definition of efficiency as it would be expected that most jobs be completed in the shortest amount of time possible. In addition, frequency distribution shows that most of the jobs are completed in between 10 to 40 minutes as their total relative frequencies are equal to 75.77%. Lastly the distribution does not appear to be symmetrical which again matches to efficiency.

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5 15 25 35 45 55 65 75 85 95 1051151250

102030405060708090

4

56

84 82

41

115 5 1 3 0 0 1

Time taken to complete jobs

Total Time (minutes)

Fre

quen

cy

Figure 1: Histogram of time taken to complete jobs

Bin Frequency Relative Frequency

0< time≤ 10 4 1.37%10<time ≤ 20 56 19.11%20<time ≤ 30 84 28.67%30<time ≤ 40 82 27.99%40<time≤ 50 41 13.99%50<time ≤ 60 11 3.75%60<time ≤ 70 5 1.71%70<time ≤ 80 5 1.71%80< time≤ 90 1 0.34%90< time≤ 100 3 1.02%100<time ≤ 110 0 0.00%110< time≤ 120 0 0.00%120<time ≤ 130 1 0.34%

Darshil Shah z3331503 ECON1203

Furthermore the key descriptive statistics can be calculated for the Time variable such as the mean (x),

the sample variance (s2 ¿, sample standard deviation (s) and coefficient of variance (cv).

The findings show that the mean time taken to complete a job is approximately 33 minutes while the variance is quite high as indicated by the coefficient of variance value of 0.48. This is because tasks of all difficulties were included which means that some would have invariably taken a longer time to complete.

2) Full Scale Analysis and Results To get a more detailed idea about efficiency amongst workers as measured by time taken in minutes to complete a job inference on the population mean needs to be made through a 95% confidence interval estimator of μ. The results will show what times taken to complete jobs can be expected for the population which is the refrigerator repair branch. For this to be carried out

the population is assumed to be a normal distribution where X N ( μ , σ2 ) .But the population standard deviation (σ ¿ is unknown so, a t distribution with the sample standard deviation has to be used in order to calculate the confidence interval.

x± t α2

,v

s

√nwhere v=n−1 degreesof freedom¿32.92 ±t 0.5

2, 292

15.68

√293

¿32.92 ±1.96015.68

√293

¿32.92 ±1.80

LCL=31.12∧UCL=34.72(Where xis the sample mean, 1−α is the confidence level, s is the sample standard deviation and n is the sample size)

The result indicates that if we repeatedly draw samples of size 293 from the population, 95% of the values of x will be such that μ will lie somewhere between x−1.80 (which is 31.12) andx+1.80 (which is 34.72).

This lower and upper limit can be used by management and the CEO to make a decision if the times above are efficient or not more accurately as the confidence interval is now known.

Marked DifferencesIt has been asked if there is any evidence of marked differences in time taken by mechanics when they are undertaking the same job. This is determined by comparing the mean value of the Time variable for

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Table 2: Key descriptive statistics for Time

Key features of variable Time x 32.92

s2 245.75

s 15.68cv 0.48

Darshil Shah z3331503 ECON1203

each difficulty from the Difficulty variable. The notion is that same tasks will be performed if Difficulty is controlled.

1) Analysis and Results

A contingency table can be produced that has the mean time taken by each mechanic to complete a job with the condition of the difficulty level. This table will show if there are any large differences in the mean time taken by each mechanic on a similar type of job.

Table 3: The mean time taken by mechanics to complete a job conditional on difficulty

Difficulty=1 Difficulty=2 Difficulty=3Mechanic 1 20.68 36.11 45.67Mechanic 2 19.71 33.51 55.47Mechanic 3 20.10 34.50 61.00Mechanic 4 19.94 33.93 72.50

RANGE 0.97 2.60 26.83

The table above shows that when tasks are easy (difficulty=1) there is little evidence of any large differences between times taken by each mechanic. This is the same when tasks are of a normal difficulty (difficulty=2).

However when tasks undertaken are hard in difficulty (difficulty=3) then it can be seen that there is evidence for large marked differences where the range is 26.83 minutes. That is a relatively large value and is enough to conclude that there is evidence for a marked difference when mechanics take hard in difficulty tasks.

Customer SatisfactionCustomer Satisfaction has been asked to be surveyed in order to see if 80% of customers are at least satisfied or very satisfied. The variable of interest is the Satisfaction variable which contains ordinal data from Very 1=Dissatisfied to 4=Very Satisfied with the exception of 9=No Response. There are a variety of tools that can be employed to answer if 80% of customers are satisfied or very satisfied in all the AllRepairs service branches.

1) Preliminary Analysis and Results Firstly it is necessary to see if the target has been achieved at the sampled refrigeration service branch by producing a pie chart. A pie chart is appropriate here because relative frequencies are what need to be measured amongst satisfaction. It must be noted that the “No Response” (Satisfaction = 9) values were removed as they provided no statistical information.

Table 4: Frequency Distribution of Satisfaction

Bin Frequency Relative Frequency %Very Dissatisfied 7 3%Dissatisfied 47 17%Satisfied 177 63%

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Darshil Shah z3331503 ECON1203

Very Satisfied 49 18%TOTAL 280 100%

Figure 2: Pie chart for Satisfaction excluded Non Responses

Very Dissatisfied3% Dissatisfied

17%

Satisfied63%

Very Satisfied18%

Satisfaction

With the pie chart it can be seen that 81% of the customers are either satisfied or very satisfied in the service they receive thus satisfying the requirement of 80%

2) Full scale Analysis and Results To see if all service branches of AllRepairs attain the target that 80% of customers are either satisfied or very satisfied a hypothesis test is conducted by testing the population proportion. The sample proportion is considered to be normal as the central limit theorem is invoked.

The hypothesis is:

H 0 : p=0.8

H 1: p<0.8 With sample size n=280 (where all non-responses were removed)

Significance level of 5% as α=0.05

Rejection region of z<−zα=−z0.05=−1.645

And sample proportion p̂=xn=226

280=0.807

Where x = the number of successes = number of customers who were satisfied or very satisfied

z= p̂−p

√ p (1−p )n

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Darshil Shah z3331503 ECON1203

z=0.807−0.8

√ 0.8× 0.2280

=0.29

The z score is greater than the rejection region (0.29>−1.645)

p−value=P ( z<0.29 )=.1141

There is not enough evidence at 5% significance level to reject the null hypothesis that the population proportion is 0.8 or in other words that 80% of the population is at least satisfied or very satisfied.

Conclusions and RecommendationsThrough the analysis of data performed by various and extensive statistical methods, conclusions on the previously raised issues efficiency and customer satisfaction can be answered.

Firstly, the histogram and the confidence intervals for the average time taken by mechanics show that the results fall under the expected definition of efficiency which is performing tasks in the shortest time possible. Ultimately it is up to the CEO and/or management of AllRepairs to decide if the results are what they consider efficient.

Secondly, through the contingency table approach it was realised that there is evidence of marked differences between mechanics undertaking the same tasks. The evidence is that when difficulty is hard mechanics complete jobs at very different times. It is recommended that the mechanics not performing well at these tasks be retrained, evaluated or moved.

Lastly, it was found that both the refrigerator repair service branch and in fact all other service branches have at least 80% of customers either satisfied or very satisfied with the services provided. This was initially determined through a pie chart and more extensively determined through a hypothesis test of the population proportion. It is recommended that nothing be changed at the present.

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