Statistical Methods II Assignment 2: Hypothesis Testing and Regression

This document presents a comprehensive solution to Assignment 2 for the UU-MTH-3000 Statistical Methods II course. Part A addresses ANOVA, performing hypothesis testing to compare the means of three branches' sales performance. Part B focuses on regression analysis, exploring linear, quadratic, exponential, logarithmic, and power models to determine the best fit for predicting the number of employees based on mail weight, concluding the exponential model is the best fit. Part C delves into time series analysis, comparing 3-day and 4-day moving averages, weighted moving averages, and exponential smoothing to forecast fishing rod sales, concluding that the exponential smoothing model provides the best fit. The assignment also includes a review of a research article analyzing risk-taking by advertising agencies, examining the statistical technique of chi-square test of independence and comparing the findings to a potential study on political affiliation and tax reform. The solution demonstrates the application of various statistical techniques to real-world data and problems.

UU-MTH-3000 Statistical Methods II Assignment 2
Question 1
Assignment 2: Part A
Given the following Data
Branch Managed
by Harrison
Branch Managed
by Dale
Branch Managed
by Stevenson
7.2 8.8 6.9
6.4 10.7 8.7
10.1 11.1 10.5
11 9.8 11.4
9.9
10.6
Using an α=0.01 level of significance, the foolowing test are carried out.
Hypothesis test:
H0 μ1=μ2=μ3 H1 Not all the means are equal
Calculation to test the hypothesis

Branch Managed
by Harrison
Branch Managed
by Dale
Branch Managed
by Stevenson G^2
7.2 8.8 6.9 51.84 77.44 47.61
6.4 10.7 8.7 40.96 114.49 75.69
10.1 11.1 10.5 102.01 123.21 110.25
11 9.8 11.4 121 96.04 129.96
9.9 98.01
10.6 112.36
Total 55.2 40.4 37.5
G_total 133.1
G_total sq 1300.87
SS_T 35.46928571
SS_between 2.041785714
SS_within 33.4275
df_between 3
df_within 11
df_total 14
MS_between 0.680595238
MS_within 3.038863636
F_statistic 0.223963731
p_value 0.877802
The P value is 0.877802
Since, the P value is greater than the level of significant α =0.01, we do hot reject H0
At 1% level of significant there is insufficient evidence to conclude that the mean are not all
equal.
Assignment 2: Part B
Given the following data

Weight of Mail
(pounds)
Number of
employees
11 6
20 10
16 9
6 5
12 8
18 14
23 13
25 16
a) The scatter plot is shown in figure 1 below.
b) The regression modules
i) Linear

ii) Quadratic
iii) Exponential

iv) Logarithmic
v) Power

c) The best model exponential model because the variation is less as indicated by R-square
d) The percentage of the variation in the number of employees explained by the exponential
regression model is 87.53%
e) Using the regression model chosen, the predicted number of employees are given as:
From the equation given, where y is the number of employees and x is the weight in pounds,
then when x=15
y=3.5531 e0.0597 x y=3.5531 e0.0597 ( 15 )=8.7 ≅ 8 employees
Assignment 2: Part C
Given the following Data

Day Rods Sold
1 60
2 70
3 110
4 80
5 70
6 85
7 115
8 105
9 65
10 75
The following analyses of the time series in determining the best model to be used for
forecasting, which is done in excel.
a) 3 day moving average analysis
b) 4 day moving average analysis
c) 3 day weighted moving average analysis with weights w1=0.2, w2=0.3 and w3=0.5 with
w1 on the oldest data
d) Exponential smoothing analysis with a = 0.3.

Day Rods Sold
Three day
moving average
Four day
Moving Average
Three day weighted
moving average
Exponential
smoothing analysis
1 60 #N/A
2 70 60
3 110 63
4 80 80.0000 88.0000 77.1
5 70 86.6667 80.0000 87.0000 77.97
6 85 86.6667 82.5000 81.0000 75.579
7 115 78.3333 86.2500 79.5000 78.4053
8 105 90.0000 87.5000 97.0000 89.38371
9 65 101.6667 93.7500 104.0000 94.068597
10 75 95.0000 92.5000 87.0000 85.3480179
11 95 81.6667 90.0000 78.0000 82.24361253
12 85 78.3333 85.0000 78.0000 86.07052877
85.0000 80.0000 83.0000 85.74937014
e) Exponential smoothing analysis with a = 0.3 provides a better fit of the data
f) The forecast day 13 sales of fishing rods using the exponential smoothing model is
approximately 86
Question 2
Process and findings used in the article is given in the table below.
The primary statistical technique used to analyze the data (if any, advertising agencies take more
risk) in the study was the chi-square test of independence.
No Process Findings
1 Involving 64 account directors and/or heads
of creative departments of advertising
agencies selected from a standard directory.
The respondents were presented with two
advertising options under a plan to launch a
new product. Plan A was a standard one with
an average rate of return (risk averse), and
Plan B was an uncertain one in which there
is a 50% chance of getting a lower rate of
The proportions of agency respondents
that were risk averse/risk seeking were
not significantly different from the
proportions of advertisers that were risk
averse/risk seeking (x2= 3.165, p = .076).

return than the client’s worst forecast and a
50% chance of getting a better rate of return
than the client’s highest forecast (risk
seeking). By use of a chi-square test of
independence, the percentages of
respondents selecting each plan were
compared to percentages produced in a
similar study with advertisers
2 Agencies and advertisers were also
compared on four degrees of risk in light of
the risk taken with their most recent client.
There was no significant difference
between agencies and advertisers on the
amount of risk taken with their most
recent client (x2= 3.165, p = .076, a
= .05)
3 Respondents were asked to what degree they
were willing to take risks if the client is their
smallest client versus if the client is their
largest client. A 4 2 contingency table was
constructed with four degrees of risk and the
two client sizes.
Agencies tended to be more risk taking
with smaller clients than with large
clients: chi-square of 9.819 (p = .021)
4 The effect of agency age on participant
selection of Plan A versus Plan B was
analyzed using a 2 2 contingency table.
Agencies were separated into two age
categories (3–19 years versus 20–135 years)
with Plan A and Plan B as the risk options.
higher proportion of the younger
agencies were more risk seeking than
older agencies ( 2 = 6.75, p = .01)
A a possible study that could be done at my current or past job that could use a similar
methodology and analysis is political affiliation and opinion and tax reform