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Quantitative Methods - I
Apr 2025 Examination
PLEASE NOTE: This assignment is application based, you
have to apply what you have learnt in this subject into real life scenario. You
will find most of the information through internet search and the remaining
from your common sense. None of the answers appear directly in the textbook
chapters but are based on the content in the chapter
Q1. Propose a method to use Excel
for solving a binomial distribution problem, and discuss the advantages and
limitations of using Excel for such statistical analyses? Solve the below
problem using excel or manual method.
A company manufactures light bulbs,
and it is known that 5% of the light bulbs are defective. If a quality control
inspector randomly selects 20 light bulbs from a production batch, what is the
probability that exactly 2 of them are defective? (10 Marks)
Ans 1.
Introduction
In statistics, probability distributions help in predicting
outcomes in various real-world scenarios. One such crucial distribution is the binomial
distribution, which models the probability of a fixed number of successes
in a given number of trials, provided the trials are independent and have the
same probability of success. Businesses often use binomial distribution to
analyze product defects, success rates in marketing campaigns, and risk
assessment in
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Q2. A cereal company claims that
the average weight of its cereal boxes is 500 grams. A quality control manager
doubts this claim and randomly selects a sample of 50 boxes. The sample has a
mean weight of 495 grams and a standard deviation of 10 grams. Formulate the
null hypothesis (H0) and the alternate hypothesis (H1). - Perform a statistical
to determine if the mean weight of the cereal boxes is significantly different
from 500 grams at a significance level of 0.05 (10 Marks)
Ans 2.
Introduction
Statistical hypothesis testing is a critical tool in quality
control and decision-making, allowing businesses to validate claims about their
products. In this scenario, a cereal company claims that the average weight of
its cereal boxes is 500 grams, but a quality control manager
doubts this and decides to test the claim using a sample of 50 boxes.
The sample has a mean weight of 495 grams and a standard deviation of
10 grams. To determine whether the
Q3(A) Evaluate the importance of
understanding the null and alternate hypotheses in the context of hypothesis
testing and its impact on research outcomes?
State Null and Alternate Hypothesis
for below scenarios
A health organization claims that
the average sodium content in a specific brand of soup is at least 400 mg per
serving. A nutritionist doubts this claim and wants to verify if the average
sodium content is less than 400 mg. State Null and Alternate Hypothesis
A pharmaceutical company claims
that their new drug reduces cholesterol by an average of 50 mg/dL. A medical
researcher wants to verify if the average reduction is not equal to 50 mg/dL.
(5 Marks)
Introduction
Hypothesis testing is a fundamental aspect of statistical
analysis in research. It enables researchers to make data-driven decisions by
assessing whether an observed effect is statistically significant or simply due
to chance. The null hypothesis (
) represents the default assumption that there is no effect
or no significant difference, while the alternative hypothesis (
) suggests that there is an effect or a deviation from the
assumed norm. Understanding these
Q3 (B) Given the following data points for
variables X and Y:
X: 2, 4, 6, 8, 10
Y: 3, 5, 7, 9, 11
Calculate the Pearson correlation
coefficient between X and Y. Given the following data points for variables X
and Y:
X: 1, 2, 3, 4, 5
Y: 2, 4, 5, 4, 5
Determine the equation of the
regression line (Y = a + bX)
Ans 3b.
Introduction
In statistical analysis, correlation and regression are
essential tools for understanding relationships between variables. Pearson’s
correlation coefficient measures the strength and direction of a linear
relationship between two variables, while linear regression provides a
predictive equation that describes this relationship. In this section, we
calculate the Pearson correlation coefficient and derive the regression
equation for given datasets. These analyses help in data-driven
decision-making, forecasting, and pattern recognition in various fields
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