By: Kristen Lawlor and Katie Walsh

Egyptians – Used reddish-brown stains derived from henna to color nails and fingertips – Signified social order Chinese – Used colored lacquer: gum arabic, egg whites, gelatin, beeswax – Colors chosen by royalty 1920s and 1930s – French make-up artist, Michelle Menard, invented the modern, glossy nail polish Similar to car paint – Revlon= first modern nail polish brand

Categorical Brand Color Variation of Color Style General Style Extra/Regular Quantitative Cost Number of Swipes Nail Area Test how durable each nail polish was Test how durable each nail polish was Test theory to see if more expensive brands or styles are worth the extra cost Test theory to see if more expensive brands or styles are worth the extra cost Put same clear coat on each nail painted to eliminate nail texture error Put same clear coat on each nail painted to eliminate nail texture error 1 Coat of nail polish 1 Coat of nail polish Stratified and Systematic Sampling Stratified and Systematic Sampling Different variety of age, lined up in groups of color and took every 4 th from line Different variety of age, lined up in groups of color and took every 4 th from line Used cotton balls and nail polish remover to take nail polish off Used cotton balls and nail polish remover to take nail polish off Till nail polish completely removed Till nail polish completely removed

Brands Colors

Histograms and Bar Charts

All costs received from store: A Beautiful Secret Negative Linear Weak Scattered Residual Plot Correlation (r)=0.170 Variance (r 2 )= % of the change in number of swipes is due to the change in cost. Overall, for our population of nail polish, as the cost increases the number of swipes decreases. Thus, the costlier the nail polish is, the less amount of nail polish remover is actually used. However, our data is not sufficient enough to show a strong enough relationship between the two variables.

ASSUMPTIONS 1.SRS 2.Linear Data 3.Independence 4.Normal Residuals 5.Equal Variance CHECKS 1.Sample is randomized, but not by an SRS 2.Data is linear, but weak 3.Assumed 4.Normal Probability Plot of Residuals 5.In Residual plot, change in spread but a very weak change

We reject Ho because the p-value is less than alpha = We have sufficient evidence that the change in number of swipes is equal to the change in cost on the linear regression graph. Thus as the number of swipes changes the cost also changes. Ho: β= 0Ha: β 0 ≠ *

Positive Linear Moderately Strong Scattered Residual Plot Correlation (r)= Variance (r 2 )= % of the change in the number of swipes is due to the change in nail length Overall, for our population of nail polish, as the nail length (amount of nail polished used) increases, the amount of swipes of nail polish remover will also increase. Thus as more nail polish is used on one nail, the more swipes will needed to be used to get the nail polish off.

Calculated Means Average Number of Swipes for each General Style Glitter Long Wearing Maximum Growth Nail Enamel Nail Hardener Nail Lacquer Salon

Calculated Means Average Number of Swipes for each General Style Overall, glitter had the most extreme average mean compared to all other styles Ironically, nail hardeners had lowest mean but large range According to our means: glitter averaged most durable

2-Sample T-Test CONDITIONS

2-Sample T-Test >

Chi Squared Test for Independence ASSUMPTIONS 1.Categorical Data 2.SRS 3.All expected cell counts are ≥ 5 CHECKS 1.Yes, variation of color and number of swipes are in categories 2.Data is randomized but not from an SRS 3.8 out of 12 of cell counts are ≤ 5

Chi Squared Test for Independence Ho: There is no association between the color and amount of swipes Ha: There is an association between the color and amount of swipes = P(χ2>17.15/df=6)= We reject Ho because the p-value is less than α=0.05. There is an association between the color variance and the amount of swipes.

Overall Opinions Cost of nail polish does not affect the durability There is an association between the color variance (light/dark) and the number of swipes of nail polish remover it took to get it off. The glitter nail polish didn’t take longer to come off than the regular nail polish. In the future, if repeating this project, would suggest taking a larger sample size. Overall our tests proved our initial thoughts wrong.

Application to the Population The population at large could use our information, or similar information with larger data in nail salons in order to see which nail products to purchase according to their business strategy. – Some nail salons would preferably have cheaper nail polish that comes off quicker – Others might want customer satisfaction and get the best nail products.

Possible Errors Pressure of cotton ball while removing nail polish Amount of remover on cotton ball Size of nail proved to be positive slope – Could effect entire results – Areas so close, not huge affect Some bias on randomization Not having every brand and color of nail polish Sally Hansen Nail Polish Remover