Statistical Analysis of Service Time at Gourmet Delight Restaurant

This report analyzes the service time at Gourmet Delight restaurant, focusing on the impact of staff training. The study employs statistical methods, including measures of central tendency and variability, box-whisker plots, histograms, and a t-test, to assess service delivery before and after the training program. The analysis reveals a significant reduction in average service time post-training. However, a follow-up analysis six months later indicates a slight increase in service time, though not statistically significant. The report provides detailed summaries of the statistical findings, including comparisons of serving times, and utilizes visual aids like box-whisker plots and histograms to illustrate the data distributions. The conclusion suggests that while the initial training was effective, management should continue to monitor service times and consider other factors influencing customer satisfaction, such as the restaurant's ability to attract clientele. The report emphasizes the importance of data-driven decision-making in optimizing restaurant operations.

Running head: IMPROVING RESTAURANT SERVICE TIME: GOURMET DELIGHT 1
Improving Restaurant Service Time: Gourmet Delight Paper
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IMPROVING RESTAURANT SERVICE TIME: GOURMET DELIGHT
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Improving Restaurant Service Time: Gourmet Delight
Introduction
The ability of a restaurant to secure and sustain customer royalty is dependent on their
level of service delivery. Service delivery is influenced by several factors such as quality of food
and drinks offered, and service time. In most instances, poor service time will create a negative
perception of the restaurant in the minds of customers (McClellan, Jimenez, & Koutitas, 2017).
Therefore, there is need for management to ensure that service time is not too long such that
clients have to wait for their orders for more than 30 minutes. Most restaurant enforce service
time policies that are guarantee the client delivery of food items within a given period; failure to
which, the client is not expected to pay for his/her meal. By putting in place such policies,
management tries to ensure time optimization and enforce staff competence. If a restaurant is not
operating at maximum efficiency, the service time will be critically handicapped meaning meals
will take considerably long before they are presented on clients' tables.
For a restaurant like Gourmet Delight, the manager needs to run statistical assessments
to discern whether or not the service time is significantly long. Through the use of measures of
central tendency and variability, the restaurant manager can be able to tell whether or not service
time has increased over the last six month beyond 20 minutes. If the service time has indeed
increased, then a plan of action needs to be formulated to ensure that time management by staff
is bettered. (Bajpai, 2009) Such a plan could entail the provision of staff training programs and a
reward & punishment system. The training program will be aimed at improving the competence
of the restaurant staff; while, the reward and punishment system will provide benefits to staff

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members who deliver quality services within a timely fashion, and place penalties on relaxed
staff performance.
Statistical Assessment
Summary Statistics
Summary statistics are a paradigm of descriptive statistics that encompass measures of
central tendency and variability; as well as minimum and maximum values. Measures of central
tendency are used to assess the central point of a given distribution; examples of these measures
are mean, mode, and median. On the other hand, Measures of dispersion or variability are
employed to assess the spread of data in a given distribution. The most well known measures of
dispersion are variance, standard deviation, range, and inter-quartile range (Debra, 2011). Using
the data retrieved from Gourmet Delight's records we can be able to assess for any change in
service delivery over the past six month using these measures. In this assessment will investigate
the aforementioned measures with regard to service time before and after training. The results
are presented as follows.
Summary
Statistics
Serving Times
prior to training
(minutes)
Serving Times
after Training
(minutes)
Central
Tendency
Mean 40.53 20.00
Mode 35 18
Median 39.5 19
Dispersion Variance 92.05 44.28
Standard 9.59 6.65

IMPROVING RESTAURANT SERVICE TIME: GOURMET DELIGHT
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Deviation
Range 40 24
Interquartile
Range
9.50 10.75
Maximum 65 34
Minimum 25 10
According to the results, the average time it took for a client to be served was around
40.53 minutes before the training and 20 minutes after the training. As such, the training
critically improved service delivery by cutting the serving time by more than half. The mode
gives use the most frequent service time at the restaurant. As such, before the training the most
frequent serving time was 35 minutes; but after the training, this time was reduced by almost half
to 18 minutes. The median specifies the central most value in a dataset given they are arranged in
terms of magnitude. In our cause the central most service time before the training was 39.5
minutes, and after the training this figure was mitigated to 19 minutes. Moving on to the
measures of dispersion, the variance of the data gives the spread of the data from the mean.
Therefore, the data from service before training was conducted is more spread out from the mean
given it has a variance of 92.05 minutes and that of service after training is only 44.28 minutes.
The standard deviation gives the spread of individual data points from the mean.
Therefore, a small standard deviation indicates the points are close to the mean of the data. From
the results above it is evident that data values collected after the training are closer to the mean
(6.65 minutes) compare to those collected before staff training was performed (9.59 minutes).
The maximum time it took to be served before the training was 65 minutes; which is

IMPROVING RESTAURANT SERVICE TIME: GOURMET DELIGHT
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considerably highly compared to that of after training which is only 34 minutes. Similarly, the
least time it took to get served before training was higher (25 minutes) than the duration
observed after training was conducted (10 minutes). The difference between the longest and
shortest serving time was also higher before training. Lastly, the inter-quartile range (IQR)
shows the spread of the middle values in the distribution. The serving time after training is more
spread out from the middle values compared to before training; hence, the serving time before
training is more clustered together.
Box-Whisker Plots
A box-whisker plot employs a five number system to provide information on whether a given
distribution is skewed and has outliners. They are especially useful when analyzing large datasets
and comparing two or more sets of data (Maciejewski, 2011). The appropriateness of a box-
whisker plot in the comparison of datasets stems from the fact that the range, spread, and centre
of the data is clearly demonstrated. Below are the box-whisker plots for the serving time before
and after training.
Serving Times prior to training (minutes)
0
10
20
30
40
50
60
70
Maximun
Third Quartile
Median
First Quartile
Minimum

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Box-whisker plot for before training
Serving Times after Training (minutes)
0
5
10
15
20
25
30
35
40
Maximun
Third Quartile
Median
First Quartile
Minimum
Box-whisker plot for after training
From the two box plots it is very clear that the training has increases efficiency in serving time
and reduced erratic. The training has allowed staff to create a more predicable service period that
is within 25 and 15 minutes.
Histogram
A histogram is the most commonly used graphical tool in the discernment of frequency
distribution. It is utilized to provide crucial information on the shape of the distribution
(assessing skewness) (Alagar, 2009). A histogram informs the research whether or not the data is
normally distributed. It is commercially used to inform management where a given process or
service change has taken place. Lastly, a histogram helps use assess whether two services are
significantly different e.g. whether there was change in the serving time before and after the staff
training. Histograms for the two serving time datasets are presented below.

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The histogram below for serving time prior to training indicates that the data is a little bit skewed
to the right. In addition, it demonstrates that majority of the serving time is between 30 and 40
minutes. The dataset has a single outliner for serving time between 60 and 70 minutes. On the
other hand, the histogram for serving after training is uniformly distributed with majority of the
serving time taking place between 15 and 20 minutes. And a single outliner was noted for
serving time between 30 and 35 minutes.
Class Frequency
10 0
20 0
30 5
40 12
50 9
60 3
70 1
More 0

IMPROVING RESTAURANT SERVICE TIME: GOURMET DELIGHT
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10 20 30 40 50 60 70
0
2
4
6
8
10
12
14
Serving Time Prior to Training
Serving Time
Frequency
Class Frequency
5 0
10 3
15 6
20 9
25 5
30 6
35 1
More 0

IMPROVING RESTAURANT SERVICE TIME: GOURMET DELIGHT
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5 10 15 20 25 30 35
0
1
2
3
4
5
6
7
8
9
10
Serving Time After Training
Serving time
Frequency
Six-months After Training
Improvement in serving time can be assessed with summary statistics, box-whisker plot,
histogram, and a hypothesis analysis. The hypothesis analysis will focus on assessing whether or
not there was any difference in the means for serving time after training and six-months after
training (Shi & Tao, 2008). The hypothesis can be presented as follows:
Null Hypothesis (H0): There was no significant difference in the mean for serving time after
training and six-months after training i.e. μ 1=μ 2
Alternative Hypothesis (H1): There was significant difference in the mean for serving time after
training and six-months after training i.e. μ 1≠ μ 2
The hypothesis will be analyzed in Microsoft Excel using "t-test for two samples assuming
unequal variance" test in data analysis. The results will be presented and interpreted. A student
t-test is being used because the data points collect six-months after training were less than 30.

IMPROVING RESTAURANT SERVICE TIME: GOURMET DELIGHT
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95% significance level will be employed; therefore, p-value will be assessed with regards to
alpha=0.05
Results
The results of the summary statistics for six-months later are present below and compared
to those of serving time after training. From the figures below it is clear that average serving time
has increased from 20 minutes to 22.50 minutes; so too has the minimum serving time, median
time, and modal time. On the other hand, the maximum serving time has reduced by 3 minutes
and other measures of variability have also decreased.
Summary
Statistics
Serving Times
after Training
(minutes)
Serving Time
(6 months Late
Central
Tendency
Mean 20.00 22.50
Mode 18 20
Median 19 23
Dispersion Variance 44.28 27.63
Standard
Deviation
6.65 5.26
Range 24 17
Inter-quartile
Range
10.75 7.00
Maximum 34 31
Minimum 10 14

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From the hypothesis results below it is clear that we do not reject the null hypothesis because the
t-stat is within the critical range i.e. -2.01174<1.4789<2.01174. We therefore, conclude there
isn't enough evidence for us to state that the means for serving time after training and six-months
later are significantly different.
t-Test: Two-Sample Assuming Unequal Variances
Serving Time (6
months Late
Serving Times after
Training (minutes)
Mean 22.5 20
Variance 27.63157895 44.27586207
Observations 20 30
Hypothesized Mean
Difference
0
df 47
t Stat 1.47894278
P(T<=t) one-tail 0.072913539
t Critical one-tail 1.677926722
P(T<=t) two-tail 0.145827079
t Critical two-tail 2.01174048

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The Box and whisker plot below indicates that serving time has changed, but not to a large
extent. The customers can expect the serving time to take between 27 and 19 minutes; which is a
drop in service delivery compare to performance immediately after training.
Serving Time (6 months Late
0
5
10
15
20
25
30
35
Maximun
Third Quartile
Median
First Quartile
Minimum
The histogram below indicates that the data is considerably skewed to the right. Moreover, it
demonstrates that majority of the serving time is 15 and 20 minutes. The dataset has a single
outliner for serving time between 30 and 35 minutes.
Class Frequency
5 0
10 0
15 3
20 6
25 5
30 5
35 1