Quantitative Methods I (PAD 503) Assignment: Statistical Solutions

This assignment solution addresses several statistical problems from a Quantitative Methods course (PAD 503). It includes calculations and interpretations for problems related to meter butler productivity, marriage license processing times, and faculty member age analysis. The solution covers measures of central tendency (mean, median, and mode), measures of dispersion (range, variance, and standard deviation), and hypothesis testing. The document also provides a memorandum summarizing the analysis of marriage license waiting times and offers insights into the appropriate use of statistical measures for different scenarios. Detailed calculations and tables are provided to support the analysis and conclusions drawn for each question, referencing relevant chapters in statistical textbooks.

Running head: QUANTITATIVE METHODS
Quantitative Methods
Name of the Student
Name of the University
Course ID

1QUANTITATIVE METHODS
Table of Contents
Question 4.2.....................................................................................................................................2
Question 4.6.....................................................................................................................................3
Memorandum...............................................................................................................................3
Question 5.2.....................................................................................................................................4
Question 5.4.....................................................................................................................................5
Question 5.8.....................................................................................................................................6
Question 6.2.....................................................................................................................................8
Question 6.8...................................................................................................................................11
Measures of central tendency....................................................................................................11
Measures of dispersion..............................................................................................................12
Bibliography..................................................................................................................................15

2QUANTITATIVE METHODS
Question 4.2
Table 1: Comparison of productivity of meters’ butlers
Figure 1: Productivity of meter butlers
Total number of parking tickets issued has increased from 29 tickets in May 10 to a total
of 35 tickets in May 11. In percentage term productivity in all categories except ticket range
between 61 and 70 has more or less increased or remain almost same. The percentage of tickets
of meter butlers with number of tickets between 61 and 70 was 10.34 percent. This has declined

3QUANTITATIVE METHODS
to 2.86 percent in May 11. From the comparison it can therefore be said that overall productivity
of meter butlers has increased.
Question 4.6
Table 2: Percentage distribution for marriage license
Figure 2: Percentage distribution of marriage license
Memorandum

4QUANTITATIVE METHODS
To: The city clerk
From:
Date: 2/3/2020
Subject: Analysis of marriage license time
The purpose of this memo is to inform you the about the analysis report obtained from
analysis of time required for obtaining marriage license. As per your consideration the service
quality is good is required time for marriage license is less than 10 minutes. The acceptable time
is 15 minutes. As obtained from the only 22.15 percent cases the time for marriage license is less
than 22.15. In 42.91 percent cases applicants receive license in less than 15 minutes. There are
52.07 percent of sample applicants have to wait for more than 15 minutes to obtain marriage
license. The complaints of couple that they have to wait too long to receive marriage license is
therefore correct and actions should be taken to reduce the waiting time.
Regards,
Question 5.2
The mean age of the faculty members is computed as
Mean age= ∑ of age of all faculty members
Number of faculty member
¿ 64+31+65+27 +35+40+33
7
¿ 295
7
¿ 42.14 year

5QUANTITATIVE METHODS
Arranging the data in ascending order gives the data of the following form
Median age corresponds to 4th observation of the data set which is 35 years.
From the computation of mean and median age of faculty members in the sociology department
of the university, the mean age is obtained as 42.14 years while the median age is obtained as 35
years. The sociology department head though not wish to lie with statistics, however he would
like to make the department appear youthful. Since, median age comes to be lower than mean
age the department should send dean the median age. As median is a useful measure determining
center of the distribution sending median age would accomplish both purpose of the department
head.
Question 5.4
Number of feet by which the missiles missed the target are recorded as 26, 147, 35, 63
and 51.
From the data, mean feet by which the missiles missed the target can be computed as
Mean feet= ∑ of feet the missiles missed the target
Number of ×target is missed
¿ 26+147+35+63+ 51
5

6QUANTITATIVE METHODS
¿ 322
5
¿ 64.4
Arranging the data in ascending order,
26, 35, 51, 63, 147
Median is the 3rd observation of the data set that is 51.
The army should report median number of feet that is 51 feet. Median is preferable over
mean the data set contains extreme values. These extreme values are considered as outlier and
with these outlier mean is pulled or distorted towards the extreme values. The information
regarding number of feet contains one extreme value of 147 feet which is outlier in the data set
and therefore inflates the mean value. Hence, reporting median would give a better
understanding regarding middle value of the data set to the army.
Question 5.8
Hypotheses
Null hypothesis (H0): The average case load for case workers is less than or equal to 45
μ ≤ 45
Alternative hypothesis (HA): The average case load for case workers exceeds 45.
μ> 45
Level of significance
The level of significance chosen for the test is 5% or 0.05.

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Test statistic
The computed test statistic for the test is
t= x−μ
σ
√ n
t1−α ,n−1
¿ 52.5−45
20.77
√10
¿ 7.5
6.5697
¿ 1.141603
Decision rule
The decision rule for upper tail test for mean states rejection of null hypothesis when
compute t value is greater than critical t. The critical t value at 5% significance level and 9
degrees of freedom is 1.8331. Since, the computed t is smaller than the critical t, the null
hypothesis is accepted that is average case load for caseworkers is less than or equal to 45.
The result of hypothesis test based on the accompanying sample data suggests that the
average case load for case workers does not exceed 45. This in turn indicates compliance with
the specification of collective bargaining. The agency therefore is correct in claiming
compliance.

8QUANTITATIVE METHODS
Question 6.2
Table 2: Number of daily visits to food banks in Chickasaw
Mean=Total number of visits∈past two weeks
Number of days
¿ 99
14
¿ 7.07

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Table 4: Number of visits arranged in ascending order
Median= 7+8
2
¿ 15
2
¿ 7.5

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Table 4: Calculation for Standard deviation
Standard deviation= √ ∑
i=1
14
( Xi−μ )2
N
¿ √ 178.9286
14
¿ √12.7806
¿ 3.5750

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Question 6.8
Table 5: Number of days for delivery
Measures of central tendency
Mean
Table 6: Calculation for mean
Mean=∑ Xf
∑ f
¿ 71
20
¿ 3.55