Debi Jones

3/15/04

STATS Project

Summer and Winter Spending on Beauty Rises

Men and women have been spending lots of money to help them look good physically. Beauty shops to gyms have profited a lot from this ongoing trend. In some places, like Los Angeles, the cost of going to the beauty shop has risen. Los Angles has no problem with keeping their cliental year round, no matter what season it is. Now for a place, like Lake Tahoe, I think seasons do affect the amount of time and money that people will spend in beauty shops. I wanted to know if it mattered whether people spend more money in beauty shops getting services done in the summer than in the winter. I have used cluster sampling to help determine this question. I chose to take 30 days in both months, January and July, in the year of 2003. I had access to find out what the daily totals were for the money made in services done.

My null hypothesis is that people will not spend more money in the summer months and will spend more in the winter months. The alternative hypothesis in this experiment is that people will spend more money in the summer months to be ‘beautified’ than they would spend in the winter months. The minor null hypothesis is that knowing how much was made of the first Saturday of the month of July will not be a good determiner of what will be made on the first Saturday of the month of January. My minor alternative hypothesis is that by knowing what was spent on the first Saturday of the month of July will be a proper predictor for knowing how much will be made on the first Saturday of the month of January.

Column Statistics

Summary statistics

This data shows that the mean amount of money spent in the winter is $979.10 with the standard deviation of 741.27 is less compared to the mean amount of money spent in the summer $1782.97 with the standard deviation of 718.17. The data shows that the variance of how much was spent in the winter month compared with the median and the mean is about $200 and considering what the price of a hair cut or artificial nails are, the variance is not very large. The same type of variance shows up with comparing the mean dollars of the summer month to the median number spent it the summer month.

Box plot for project

As the box plot graph shows, more money was spent in the summer than in the winter. In addition, the summer month shows in the graph that it has a wider range of money spent and a higher median compared to the winter month. We can notice that the winter month has the highest outlier compared to the summer outliers.

Histogram

Also noting that both January’s and July’s information is somewhat symmetric (as shown above). The winter month shows that the information is unimodal and skewed to the right. The summer month data shows that it is also unimodal and skewed to the right. These graphs show how much was made during the month. It can be noted that during the winter less money was made compared to the summer. It is shown by the sizes of the columns that in the winter the columns are smaller (in height), compared to the summer month where the majority of the columns are lager in size (in height).

Stem and Leaf for project

Variable: Winter

0 : 02234

0 : 555666667888899

1 : 002

1 : 578

2 : 00

High: 2408, 3412

Variable: Summer

0 : 888

1 : 22233333

1 : 66677888999

2 : 034

2 : 58

High: 3212, 3347, 3367

The same type of situation that happened with the histogram happens here with the stem and leaf thought the numbers show that there are some outliers. The majority of the data shows that within the actual stem and leaf, but there is data that are considered outliers. This data shows that there may be days that more money was spent compared to the rest of the month. This information is shown in the winter $2408 and $3412. For the summer, the outliers are $3212, $3347, and $3367. These outliers in the data were found mainly on Saturdays when majority of people were able to make it to the beauty shop. There are various amounts of reasons, such as they work during the week and Saturday is the best day to go to the beauty shop, or many weddings are held on Saturdays and many bridal parties get their services done at beauty shops on those days.

One Sample T Statistics

95% Confidence interval results:
m - mean of Variable

With 95% confidence, we can conclude that the mean number of dollars spent on beauty in the winter falls between $702 and $1256. The winters a margin of error is $265.122.We can also conclude that the data for the 95% confidence that the mean number of dollars spent on beauty is spent in the summer falls between $1515 and $2051. The summer’s margin of error is $256.86.

Paired T Statistics

Paired T-test results:
m_D - mean of the differences between Summer and Winter
H₀:m_D = 0
H_A:m_D > 0

The paired data shows that there is a very low correlation between the money spent in a beauty shop in the winter than in the summer.

Simple Linear Regression

Simple linear regression results:
Dependent Variable: Winter
Independent Variable: Summer

Sample size: 30
Correlation coefficient: 0.4367
Estimate of sigma: 678.66327

The simple linear regression line shows several important things. The first part is that the P-value is 0.0158 and the correlation coefficient is .04367. According to the r-value, there is a moderate correlation to the regression line. According to the P-value, there is a positive correlation between the summer money spent and the winter money spent on beauty. With 95% confidence of the amount spent on the first Saturday of July, $1752 falls between $726.33 and $1233.95. One can conclude that the summer values are not a determined by the winter values.

In conclusion, one can say that we can reject the alternative hypothesis, and fail to reject the null hypothesis. According to the season, people spend more money making themselves look “beautiful” in the summer compared to the winter. In addition, we can conclude that the summer is not a proper predictor of how much money these people spend on beauty in the winter. So for the minor null hypothesis we fail to reject because there is not enough evidence to support the idea that knowing what happens in the summer can tell you how the winter will be.