Nail Saloon Customer Analysis: A Statistical Maths Assignment Report

This assignment presents a statistical analysis of customer data from a nail saloon, conducted to evaluate customer flow and inform service delivery improvements. The analysis uses a dataset of daily customer counts over 52 days, from which random samples of 30 days and 5 days are drawn for detailed examination. The 30-day sample reveals an average of 62 customers per day, with a 95% confidence interval between 57 and 63. The 5-day sample shows an average of 50 customers, with a wider confidence interval between 31 and 69. Hypothesis tests are performed to compare the overall average to the average number of customers in January (48). The analysis based on the 30-day sample rejects the null hypothesis, suggesting a significant difference, while the 5-day sample fails to reject it. The assignment concludes that larger sample sizes provide more accurate representations of the population data, and Desklib offers additional resources for students.

Running Head: MATHS ASSIGNMENT
Maths Assignment
Name of the Student
Name of the University
Author Note

1MATHS ASSIGNMENT
Introduction
The analysis has been done on request of the owner of a nail saloon to evaluate the
rush of the saloon and this analysis will in turn help the owner to figure out the way in which
services can be provided further to meet the demand of the customers. To do the analysis,
data has been collected on the total number of customers coming to the store each day for 52
days from 2nd January 2018 to 22nd February 2018.
Discussion
Sample of 30 Days
For the purpose of the study, 30 days out of the 52 days have been selected randomly
from the total data. It can be seen from the selected sample that, the average number of
customers that visit each day to the store is 62. The analysis also shows that the number of
customers visiting the store each day is quite close to the average number of clients.
Confidence Interval
It can also be said with 95 percent confidence that the average number of customers
coming for the services each day varies between 57 and 63.
Sample of 5 Days
Again, a random sample of 5 days have been collected from the total data and it can
be seen from the selected sample that, the average number of customers that visit each day to
the store is 50. The analysis also shows that the number of customers visiting the store each
day is quite close to the average number of clients.
Confidence Interval
It can also be said with 95 percent confidence that the average number of customers
coming for the services each day varies between 31 and 69.

2MATHS ASSIGNMENT
Comparing the two different samples, it can be said that the sampling of 5 days shows
that the number of customers visiting the store each day has a larger range than that obtained
from the sample of 30 days and the limit is representing the population much more accurately
when 30 sample days have been considered.
Hypothesis Tests
The average number of customers that visited the store in in the month of January has
been found to be 48. It is to be tested whether the average number of customers visiting the
store is equal to the average number of customers visiting the store in January. Thus, the null
and the alternate hypothesis can be stated as follows:
Null Hypothesis ( H 0 ) : μ=48
Alternate Hypothesis ( H1 ) :μ ≠ 48
From the analysis conducted on 30 collected samples, it can be seen that there is not
enough evidence to accept the null hypothesis. Thus, it can be concluded that there is
significant difference in the average number of clients coming to the store from that of
January.
From the analysis conducted on 5 collected samples, it can be seen that there is not
enough evidence to reject the null hypothesis. Thus, it can be concluded that there is no
significant difference in the average number of clients coming to the store from that of
January. Hence, there is a contradiction in the two types of results obtained.
Conclusion
From the analysis, it can be seen that the sample of 30 days gives a result which is
quite compact and more accurate than the sample of 5 days. This indicates that a larger
sample size represents the population much more accurately than a smaller sample size.