Introduction
In this assignment we will discuss and describe applications of statistics and probability theory to a real-world problem. Our goal is to provide descriptive statistics and statistical inference for Beltway Shoe Company that sells leather shoes in Western and Eastern regions of the United States of America. We are given with the data set that represents sales in 50 shoe stores in Western Region and 50 shoe stores in Eastern Region. For each shop, the information about original price, sale price and the number of days to sell was recorded. These factors are the three variables given.
We begin with descriptive statistics. For both regions we calculate sample mean, median, range and sample standard deviation for each of the three given variables for both regions. The results are presented in the table below:
For Western Region:
For Eastern Region:
Develop a 90% confidence interval for population mean values for the number of days to sell and sell price in both regions. The 90% CIs are given in the table below (Stattrek.com, 2016):
In order to determine possible outliers, construct boxplots:
Western Region:
Eastern Region:
Boxplots determine outliers in the number of days to sell in eastern region. There are two extra high values: 189 days and 166 days (Stattrek.com, 2016).
Calculate the sample size that is required for a margin of error of the mean selling price in Western region of $5 (with 90% level of confidence):
The sample should contain at least 85 observations.
Repeat the same procedure for Eastern Region and margin of error of $4.
The sample should contain at least 279 observations.
Calculate the estimated selling price and the number of days to sell for a pair of shoes with an original price of $120 in Western region and a pair of shoes with an original price of $125 in Eastern region:
Conclusion
As a conclusion, we have obtained the following results
We are 90% confident that the true population mean of sales price in Western region is between $74.05 and $86.83.
We are 90% confident that the true population mean of sales price in Eastern region is between $61.52 and $108.96.
We are 90% confident that the true population mean of the number of days to sell in Western region is between 52.06 and 73.3 days.
We are 90% confident that the true population mean of the number of days to sell in Eastern region is between 52.74 and 71.98 days.
The sample size that is required for a margin of error of the mean selling price in Western region of $5 (with 90% level of confidence) is 85 observations
The sample size that is required for a margin of error of the mean selling price in Eastern region of $4 (with 90% level of confidence) is 279 observations
A pair of shoes in Western region, which was put on sale for $120, will be sold for approximately $87.93 on the 63th day of sales.
A pair of shoes in Eastern region, which was put on sale for $125, will be sold for approximately $98.09 on the 63th day of sales.
References
Stattrek.com,. (2016). Boxplots. Retrieved 18 January 2016, from http://stattrek.com/statistics/charts/boxplot.aspx?Tutorial=AP
Stattrek.com,. (2016). Confidence Interval. Retrieved 18 January 2016, from http://stattrek.com/estimation/confidence-interval.aspx
