STA101 Statistics for Business Assignment 1 - SML Company Analysis

This assignment solution addresses key statistical concepts relevant to business applications, as outlined in the STA101 Statistics for Business course. Question 1 analyzes covariance and correlation between years of experience and salary, providing interpretations and potential reasons for negative correlation. Question 2 focuses on hypothesis testing, evaluating a company's claim about the proportion of sinus drug users experiencing drowsiness, including null hypothesis, p-value, and confidence interval calculations. Question 3 covers measures of central tendency (mean, median, mode), standard deviation, outlier detection, and the empirical rule for determining data distribution. Finally, Question 4 explores probability calculations related to service schedules and on-time delivery rates. The solution provides detailed calculations, interpretations, and conclusions for each question, demonstrating a comprehensive understanding of statistical methods and their practical applications within a business context. The solution utilizes the provided data and adheres to the assignment's requirements, including appropriate referencing where needed. This document is designed to assist students with their statistics coursework, offering a clear and concise approach to solving complex statistical problems.

[Date]
STATISTICS
Assignment
SML
[company name]

Question 1
(a) Covariance between years of experience (x) and salary (y)
(b) No interpretation would be feasible for the covariance magnitude and hence, only the
direction (Sign) can be described. The negative direction is indicative of the fact that salary
would decrease as the year of experience increases. Thus, it can be said that negative
correlation is present between the variables.
(c) Computation of correlation coefficient or R
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The correlation coefficient is near by the perfect theoretical negative value which is -1. It
represents that the variables year of experience and corresponding salary is reversely
associated.
(d) Salaries are compressible in nature and therefore, the salary of individuals reduce as their
year of experiences increases. The main reason behind this reasoning is high competition in
the market and dynamic market structure.
Question 2
(a) Hypotheses
Claim of the company is that proportion of users of sinus drug experienced drowsiness is not
0.10.
(b) Hypothesis testing for the claim
Number of observation (n) = 900
Number of sample subjects which would be experienced drowsiness =81
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Significance level (alpha) = 0.05
Null hypothesis will not be rejected because the p value is not lower than the significance
level. Thus, alternative hypothesis will not be accepted. Therefore, “it can be concluded
that the proportion of users of sinus drug experienced drowsiness is 0.10”.
(c) Computation of 95% confidence interval
For 95% confidence interval, the z value = 1.960
(d) It is apparent that the hypothesized proportion value is 0.10 which does fall in the
calculated 95% confidence interval range. This implies that null hypothesis will not be
rejected and thus, the decision made in the hypothesis test is correct. Therefore, “it can be
concluded that the proportion of users of sinus drug experienced drowsiness is 0.10”.
Question 3
(a) Mean, median and mode
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Data needs to be arranged in ascending order (Decrease to increase)
Mean
Total of the data points = 21,740
Sample size = 30
Median
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Mode
Maximum frequency reported for the data value = 730
Mode = 730
(b) No, the measures of central tendency are not agreed because mean, median, mode are not
same.
(c) Computation of standard deviation
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(d) Presence of outliers
The lower and upper value of the range would be computed which would be used to
determine the presence of outliers in the data. The data values which are beyond this range
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will be termed as outliers.
Data values 500, 930, 930 and 1030 are beyond the range and therefore, these four values
would be termed as outliers.
(e)Empirical rule for determine whether the sample has drawn from normally distributed
population or not.
It can be seen from the above that sample data of the rent is extracted from the population
which is normally distributed.
Question 4
Computation of probabilities
Schedules:
P ( A )=0.60 , P ( B )=0.30 , P (C )=0.10
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On time service rate
P ( O| A ¿=0.80 , P (O|B ¿=0.60 , P ( O|C )=0.40
( (a) P ( A∧O )
(a) (b) Respective package will deliver on the right time
(c) Delivered package on time is for service A
(d) Delivered package is late by 40 minutes and it is for service B
(e) Delivered package is late by 40 minutes and it is for service C
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