Double Pack Tic TacsDouble Pack Tic Tacs

Kamyia MasonKamyia Mason

Mariah RosadoMariah Rosado

IntroductionIntroduction

Question: Is there an equal amount Question: Is there an equal amount of yellow and red tic tacs in a 1 oz. of yellow and red tic tacs in a 1 oz. Cherry Passion Big Pack tic tac box?Cherry Passion Big Pack tic tac box?

Population of interest:Population of interest: 1 oz. big pack 1 oz. big pack Cherry Passion tic tac box Cherry Passion tic tac box

Introduction (cont.)Introduction (cont.)

We collected our data and recorded it in a We collected our data and recorded it in a table.table.

We conduct a Chi-squared goodness-of-fit We conduct a Chi-squared goodness-of-fit test.test.

Strengths: The amount of tic tacs in each Strengths: The amount of tic tacs in each sample were equal.sample were equal.

Weaknesses: Our sample might be too Weaknesses: Our sample might be too small.small.

Data CollectionData Collection

We gathered five 1 oz. big pack Cherry We gathered five 1 oz. big pack Cherry Passion tic tacs and labeled them letter A Passion tic tacs and labeled them letter A to E.to E.

For each pack of tic tacs, we separated the For each pack of tic tacs, we separated the red from the yellow tic tacs and counted red from the yellow tic tacs and counted the total amount of reds and yellows.the total amount of reds and yellows.

This process was done one by one for This process was done one by one for packs letter A to E. And the amount of red packs letter A to E. And the amount of red and yellow tic tacs in every pack was and yellow tic tacs in every pack was recorded in a chart.recorded in a chart.

Exploratory Data AnalysisExploratory Data Analysis

LetterLetter ObserveObserved of Redd of Red

ObserveObserved of d of YellowYellow

AA 2929 3131

BB 2525 3535

CC 3838 2222

DD 3333 2727

EE 2929 3131

Exploratory Data AnalysisExploratory Data Analysis

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10

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30

40

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60

A B C D E

RED

YELLOW

Explanatory Data AnalysisExplanatory Data Analysis

ColorColor ObservedObserved ExpectedExpected (O-E)²/E(O-E)²/E

RedRed 154154 150150 .107.107

YellowYellow 146146 150150 .107.107

TotalTotal 300300 300300 .214.214

Explanatory Data AnalysisExplanatory Data Analysis

0

20

40

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80

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120

140

160

Obs (O-E)^2/ E

RedYellow

Red DataRed Data: Mean – : Mean – 30.8 SD – 4.4 Min – 30.8 SD – 4.4 Min – 25 Q1 – 27 Median 25 Q1 – 27 Median – 29 Q3- 35.5 Max – 29 Q3- 35.5 Max – 38– 38

Yellow DataYellow Data: Mean : Mean – 29.2 SD – 4.4 Min – 29.2 SD – 4.4 Min – 22 Q1 – 24.5 – 22 Q1 – 24.5 Median – 31 Q3 – Median – 31 Q3 – 33 Max - 3533 Max - 35

Inference ProcedureInference Procedure Null Hypothesis: There is an equal amount Null Hypothesis: There is an equal amount

of red and yellow tic tacs in a 1 oz. Cherry of red and yellow tic tacs in a 1 oz. Cherry Passion Big Pack tic tac box.Passion Big Pack tic tac box.

Alternate Hypothesis: There are more Alternate Hypothesis: There are more yellow than red tic tacs in a 1 oz. Cherry yellow than red tic tacs in a 1 oz. Cherry Passion Big Pack tic tac box.Passion Big Pack tic tac box.

Significance Level: Significance Level: αα=.05=.05 Sample Size: 5Sample Size: 5 Significance Test: Chi-squared Goodness Significance Test: Chi-squared Goodness

of Fit testof Fit test

Inference ProcedureInference Procedure

²²ַאַא = ∑ = ∑ (Observed-Expected)²/Expected (Observed-Expected)²/Expected = .214= .214

P-value = .995P-value = .995 We will fail to reject the null We will fail to reject the null

hypothesis since our p-value (.995) is hypothesis since our p-value (.995) is greater than greater than αα (.05). (.05).

ConclusionConclusion

We will fail to reject the null We will fail to reject the null hypothesis that there is an equal hypothesis that there is an equal amount of red and yellow tic tacs in a amount of red and yellow tic tacs in a 1 oz. Cherry Passion Big Pack tic tac 1 oz. Cherry Passion Big Pack tic tac box since our p-value of .995 is box since our p-value of .995 is greater than the greater than the αα=.05 level =.05 level meaning we do not have sufficient meaning we do not have sufficient evidence to reject the null evidence to reject the null hypothesis.hypothesis.

ReflectionReflection Question: Is there an equal amount of Question: Is there an equal amount of

yellow and red tic tacs in a 1 oz. Cherry yellow and red tic tacs in a 1 oz. Cherry Passion Big Pack tic tac box?Passion Big Pack tic tac box?

We collected a sample of 5 Big Pack tic tac We collected a sample of 5 Big Pack tic tac boxes and counted the amount of red and boxes and counted the amount of red and yellow in each then recorded the data in a yellow in each then recorded the data in a table.table.

Our main strength was that the sample Our main strength was that the sample boxes all had the same amount of tic tacs boxes all had the same amount of tic tacs so there was little variation.so there was little variation.

The only weakness that could have effected The only weakness that could have effected the result of the project is the small sample the result of the project is the small sample size.size.

The EndThe End

Thank You!Thank You!