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Nail Polish Experiment. By: Kristen Lawlor and Katie Walsh. The History of Nail Polish. Egyptians U sed reddish-brown stains derived from henna to color nails and fingertips Signified social order Chinese Used colored lacquer: gum arabic, egg whites, gelatin, beeswax - PowerPoint PPT Presentation

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Predicting Heights Project

Nail Polish ExperimentBy: Kristen Lawlor and Katie WalshThe History of Nail PolishEgyptiansUsed reddish-brown stains derived from henna to color nails and fingertipsSignified social orderChineseUsed colored lacquer: gum arabic, egg whites, gelatin, beeswaxColors chosen by royalty1920s and 1930sFrench make-up artist, Michelle Menard, invented the modern, glossy nail polishSimilar to car paintRevlon= first modern nail polish brand

Durability of Nail PolishTest how durable each nail polish wasTest theory to see if more expensive brands or styles are worth the extra costPut same clear coat on each nail painted to eliminate nail texture error1 Coat of nail polishStratified and Systematic SamplingDifferent variety of age, lined up in groups of color and took every 4th from lineUsed cotton balls and nail polish remover to take nail polish offTill nail polish completely removed

BrandsColors

Histograms and Bar Charts

Linear Regression T-TestNumber of Swipes vs. Cost

All costs received from store: A Beautiful SecretNegativeLinearWeakScattered Residual PlotCorrelation (r)=0.170Variance (r2)=0.02917% 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.

Linear Regression T-TestNumber of Swipes vs. CostCONDITIONSASSUMPTIONSSRSLinear DataIndependenceNormal ResidualsEqual VarianceCHECKSSample is randomized, but not by an SRSData is linear, but weakAssumed Normal Probability Plot of ResidualsIn Residual plot, change in spread but a very weak change

Linear Regression T-TestNumber of Swipes vs. CostWe reject Ho because the p-value is less than alpha = 0.05.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: = 0Ha: 0

-3.343-3.34392.57840.00122 *

Linear Regression T-TestNumber of Swipes vs. Nail Length (Area)

PositiveLinearModerately StrongScattered Residual PlotCorrelation (r)= 0.293Variance (r2)=0.0.08629% of the change in the number of swipes is due to the change in nail lengthOverall, 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 MeansAverage Number of Swipes for each General StyleGlitterLong WearingMaximum GrowthNail EnamelNail HardenerNail LacquerSalon9.57.55.25.555565.857145.083335.85714

Calculated MeansAverage Number of Swipes for each General StyleOverall, glitter had the most extreme average mean compared to all other stylesIronically, nail hardeners had lowest mean but large rangeAccording to our means: glitter averaged most durable

2-Sample T-TestCONDITIONSASSUMPTIONS2 Independent SRSPop1 10*n1 Pop2 10*n23. 2 Normal pop or n1 and n2 30

CHECKSAssumed 510 40 (doesnt check but we go on)n1 and n2 30 (doesnt check but we go on)

2-Sample T-TestHo: 1 = 2 Ha: 1 2

= 2.246

P(t 2.246 df= 3.30016) = 0.051

We fail to reject Ho because our p-value is greater than alpha = 0.05.We have sufficient evidence that the number of swipes of all nails is equal to the number of swipes for the glitter.

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Chi Squared Test for IndependenceASSUMPTIONSCategorical DataSRSAll expected cell counts are 5CHECKSYes, variation of color and number of swipes are in categoriesData is randomized but not from an SRS8 out of 12 of cell counts are 5Chi Squared Test for IndependenceHo: There is no association between the color and amount of swipesHa: There is an association between the color and amount of swipes

= 17.15

P(2>17.15/df=6)= 0.0087

We reject Ho because the p-value is less than =0.05.There is an association between the color variance and the amount of swipes.

Overall OpinionsCost of nail polish does not affect the durabilityThere 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 didnt 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 PopulationThe 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 quickerOthers might want customer satisfaction and get the best nail products.

Possible ErrorsPressure of cotton ball while removing nail polishAmount of remover on cotton ballSize of nail proved to be positive slopeCould effect entire resultsAreas so close, not huge affectSome bias on randomizationNot having every brand and color of nail polishSally Hansen Nail Polish Remover