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ACCOUNTING AND FINANCE
Unit: QUANTATIVE METHODS
NAME: DANIEL KARIUKI NJUGUNA
INSTRUCTIONS: ATTEMPT ALL THE QUESTIONS
QUESTION ONE
(a) Suppose you are an operations manager for a plant that manufactures batteries. Explain
how you can use descriptive and inferential statistics in the industry. (10marks)
For management decision making, it is important to have a wide understanding of the various
factors affecting the industry, market and even the target population. In most cases, managers will
have to rely on research to enhance their decision making. Whether is an investment, marketing,
technology, Human resource or any other decisions, managers might have to rely on various
research works to make proper decisions. Statistical researches are some of the most relied upon
by managers. Such researches are carried out on target population to determine or predict their
behaviors of certain market trends, decisions or changes. Whether it is differential statistics that
focus on the central tendency, frequency, dispersion or variation and position; or inferential
statistics that take the methods to facilitate the estimation of carious characteristics of a population
or decision making on the basis of sample results.
As a manager I would have to take measures that are well thought and guided by outcomes of
reliable research regarding the batteries field. This would have to in consideration to completion,
market changes, new technology on matters energy, expansion, downsizing or any other decision.
Such considerations for various sectorial decision areas would be as detailed below:
Marketing:
Before my company launches a product, along with my team, we would have to make pilot survey
in advance. We would have to make use of various statistical techniques to analyze the data obtain
from the survey on various market factors such as purchasing power, habits of the customers, the
pricing of other products and even the competitors. Such studies would help in knowing things
like the market potential for the batteries. By using such necessary statistical techniques, as a
manger I would be able to make proper advertising strategies, establish good sales territories with
the aim of improving the sales of the batteries.
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Production:
As a manager using proper statistical methods, I would be able to carry out research and various
development programmers to improve the quality of the existing products and even set up quality
control standards that would help maintain good quality for new products. Through research, as a
manger I would be able to understand the market views of a past products, areas or improvements
and qualities that should be maintained in future production. In addition, such data would help my
team in taking decisions regarding quantity and time with regards to internal manufacturing or
Human resource or Manpower planning:
In any organization, and especially when in a manufacturing or production sector, manpower
planning is an integral part of proper management. As a manager, through research targeting the
batteries sector, I can be able to determine and make decisions regarding wages, incentives, labor
turnover, cost of living, proper training, accident rates, employments trends and proper
development programs. Such statistical data can be obtained through internal survey or research
as well as an external study. By understating the above factors, as manager I would be able to
formulate future policies and set up plans for the overall success of the organization.
Finance:
As a manager and when it comes to financial decisions such as investments and others, it is
important to rely on statistics or research. By studying correlation analysis of profits and dividends,
as a manager I would be able to predict and also decide on the probable dividends in future.
Analysis of data obtained that is related to assets and liabilities, sales and purchase or even income
and expenditure would be helpful in ascertaining the financial results of various operations.
As indicated above, statistics and statistical methods can provide mangers with one of the most
valuable tools in proper decision making and hence the success of an organization.
QUESTION TWO
(a) Discuss the various errors in Hypothesis Testing. Also explain the Significance Level
Confidence Level and Degrees of Freedom.(10marks)
Any test is based on probabilities, and no hypothesis is 100% certain, as such, there is always a
chance of making an error. When doing a hypothesis test, two types of errors can occur
Type 1 error and
Type 11 error
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The risks to these two errors are inversely related and are determined by the level of significance
and power of the test. Therefore, it is important to first determine which error has more sever
consequences in the situation you are dealing with before determining the risks.
Type I error
Also known as the false positive, this error refers to rejecting a null hypothesis when it is actually
the correct one. This is the error of accepting an alternative hypothesis when the results can be
attributed to chance. It occurs when we are observing a difference when in truth there none at all
or there can be said to be no statistically significant difference. The probability of making this
error can be depicted as P ( R|H
o
is true), with R being the rejection region for any test.
Type II error
This is also known as the false negative. This is an error that occurs for not rejecting a null
hypothesis when the alternative hypothesis is the true state of nature. This is the error of failing to
accept an alternative hypothesis without adequate power to do so. This error occurs when one fails
to observe the difference when in truth there is one. Statistically, the probability of a type II error
in the test with a rejection region given as R, can be depicted as 1- P(R|H
α
is true). As such, the
power of the test can be said to P(R|H
α
is true).
Significance Level: (Denoted by an alpha (α)
This is a measure of the strength of the evidence that must be preset in any sample before one can
reject the null hypothesis and make a conclusion that the effect is of statistical significance. As
such, a researcher must determine the significance level before conducting an experiment.
The significance level is the probability of rejecting the null hypothesis when it is true. For
example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists
when there is no actual difference. Lower significance levels indicate that you require stronger
evidence before you will reject the null hypothesis.
Confidence Level
In any survey, any different samples can be randomly selected from any sample population and
each of the samples can produce different confidence interval. While some confidence intervals
may include some true population parameter, others do not.
As such, the confidence level refers to the percentage of all the possible samples that can be
expected to include the true population parameters.
This can be further explained by considering an example where all possible samples were selected
from the same population and the confidence interval were computed for each sample. A 95%
confidence level implies that that percentage of the confidence intervals would include the true
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population parameters. Therefore, to confidence level can be said to be high of 95%. Making such
a hypothesis more reliable.
Degrees of Freedom
The Degrees of Freedom refers to the number of values involved in the calculations that have the
freedom to vary. In other words, the degrees of freedom, in general, can be defined as the total
number of observations minus the number of independent constraints imposed on the observations.
The degrees of freedom are calculated for the following statistical tests to check their validity:
t-Distribution
F- Distribution
Chi-Square Distribution
These tests are usually done to compare the observed data with the data that is expected to be
obtained with a specific hypothesis. Degrees of Freedom is usually denoted by a Greek symbol ν
(mu) and is commonly abbreviated as, df. The statistical formula to compute the value of degrees
of freedom is quite simple and is equal to the number of values in the data set minus one.
Symbolically:
df= n-1 Where n is the number of values in the data set or the sample size.

### Unformatted Attachment Preview

SCHOOL: BUSINESS AND ECONOMICS ACCOUNTING AND FINANCE Unit: QUANTATIVE METHODS NAME: DANIEL KARIUKI NJUGUNA INSTRUCTIONS: ATTEMPT ALL THE QUESTIONS QUESTION ONE (a) Suppose you are an operations manager for a plant that manufactures batteries. Explain how you can use descriptive and inferential statistics in the industry. (10marks) For management decision making, it is important to have a wide understanding of the various factors affecting the industry, market and even the target population. In most cases, managers will have to rely on research to enhance their decision making. Whether is an investment, marketing, technology, Human resource or any other decisions, managers might have to rely on various research works to make proper decisions. Statistical researches are some of the most relied upon by managers. Such researches are carried out on target population to determine or predict their behaviors of certain market trends, decisions or changes. Whether it is differential statistics that focus on the central tendency, frequency, dispersion or variation and position; or inferential statistics that take the methods to facilitate the estimation of carious characteristics of a population or decision making on the basis of sample results. As a manager I would have to take measures that are well thought and guided by outcomes of reliable research regarding the batteries field. This would have to in consideration to completion, market changes, new technology on matters energy, expansion, downsizing or any other decision. Such considerations for various sectorial decision areas would be as detailed below: Marketing: Before my company launches a product, along with my team, we would have to make pilot survey in advance. We would have to make use of various statistical techniques to analyze the data obtain from the survey on various market factors such as purchasing power, habits of the customers, the pricing of other products and even the competitors. Such studies would help in knowing things like the market potential for the batteries. By using such necessary statistical techniques, as a manger I would be able to make proper advertising strategies, establish good sales territories with the aim of improving the sales of the batteries. Production: As a manager using proper statistical methods, I would be able to carry out research and various development programmers to improve the quality of the existing products and even set up quality control standards that would help maintain good quality for new products. Through research, as a manger I would be able to understand the market views of a past products, areas or improvements and qualities that should be maintained in future production. In addition, such data would help my team in taking decisions regarding quantity and time with regards to internal manufacturing or outside purchasing. Human resource or Manpower planning: In any organization, and especially when in a manufacturing or production sector, manpower planning is an integral part of proper management. As a manager, through research targeting the batteries sector, I can be able to determine and make decisions regarding wages, incentives, labor turnover, cost of living, proper training, accident rates, employments trends and proper development programs. Such statistical data can be obtained through internal survey or research as well as an external study. By understating the above factors, as manager I would be able to formulate future policies and set up plans for the overall success of the organization. Finance: As a manager and when it comes to financial decisions such as investments and others, it is important to rely on statistics or research. By studying correlation analysis of profits and dividends, as a manager I would be able to predict and also decide on the probable dividends in future. Analysis of data obtained that is related to assets and liabilities, sales and purchase or even income and expenditure would be helpful in ascertaining the financial results of various operations. As indicated above, statistics and statistical methods can provide mangers with one of the most valuable tools in proper decision making and hence the success of an organization. QUESTION TWO (a) Discuss the various errors in Hypothesis Testing. Also explain the Significance Level Confidence Level and Degrees of Freedom.(10marks) Any test is based on probabilities, and no hypothesis is 100% certain, as such, there is always a chance of making an error. When doing a hypothesis test, two types of errors can occur Type 1 error and Type 11 error The risks to these two errors are inversely related and are determined by the level of significance and power of the test. Therefore, it is important to first determine which error has more sever consequences in the situation you are dealing with before determining the risks. Type I error Also known as the false positive, this error refers to rejecting a null hypothesis when it is actually the correct one. This is the error of accepting an alternative hypothesis when the results can be attributed to chance. It occurs when we are observing a difference when in truth there none at all or there can be said to be no statistically significant difference. The probability of making this error can be depicted as P ( R|Ho is true), with R being the rejection region for any test. Type II error This is also known as the false negative. This is an error that occurs for not rejecting a null hypothesis when the alternative hypothesis is the true state of nature. This is the error of failing to accept an alternative hypothesis without adequate power to do so. This error occurs when one fails to observe the difference when in truth there is one. Statistically, the probability of a type II error in the test with a rejection region given as R, can be depicted as 1- P(R|Hα is true). As such, the power of the test can be said to P(R|Hα is true). Significance Level: (Denoted by an alpha (α) This is a measure of the strength of the evidence that must be preset in any sample before one can reject the null hypothesis and make a conclusion that the effect is of statistical significance. As such, a researcher must determine the significance level before conducting an experiment. The significance level is the probability of rejecting the null hypothesis when it is true. For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference. Lower significance levels indicate that you require stronger evidence before you will reject the null hypothesis. Confidence Level In any survey, any different samples can be randomly selected from any sample population and each of the samples can produce different confidence interval. While some confidence intervals may include some true population parameter, others do not. As such, the confidence level refers to the percentage of all the possible samples that can be expected to include the true population parameters. This can be further explained by considering an example where all possible samples were selected from the same population and the confidence interval were computed for each sample. A 95% confidence level implies that that percentage of the confidence intervals would include the true population parameters. Therefore, to confidence level can be said to be high of 95%. Making such a hypothesis more reliable. Degrees of Freedom The Degrees of Freedom refers to the number of values involved in the calculations that have the freedom to vary. In other words, the degrees of freedom, in general, can be defined as the total number of observations minus the number of independent constraints imposed on the observations. The degrees of freedom are calculated for the following statistical tests to check their validity: t-Distribution F- Distribution Chi-Square Distribution These tests are usually done to compare the observed data with the data that is expected to be obtained with a specific hypothesis. Degrees of Freedom is usually denoted by a Greek symbol ν (mu) and is commonly abbreviated as, df. The statistical formula to compute the value of degrees of freedom is quite simple and is equal to the number of values in the data set minus one. Symbolically: df= n-1 Where n is the number of values in the data set or the sample size. Name: Description: ...
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