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Expert-verified Found in: Page 718 ### The Practice of Statistics for AP Examination

Book edition 6th
Author(s) Daren Starnes, Josh Tabor
Pages 837 pages
ISBN 9781319113339 # Skittles® Statistics teacher Jason Mole sky contacted Mars, Inc., to ask about the color distribution for Skittles candies. Here is an excerpt from the response he received: “The original flavor blend for the Skittles Bite Size Candies is lemon, green apple, orange, strawberry and grape. They were chosen as a result of consumer preference tests we conducted. The flavor blend is $20$ percent of each flavor.”a. State appropriate hypotheses for a significance test of the company’s claim.b. Find the expected counts for a random sample of $60$ candies.c. How large a $\chi 2$ test statistic would you need to have significant evidence against the company’s claim at the α=0.05 level? At the $\alpha =0.01$ level?d. Create a set of observed counts for a random sample of $60$ candies that gives a $P-$value between $0.01$ and $0.05$ Show the calculation of your chi-square test statistic.

Part (a) ${H}_{0}:{p}_{lemon}=0.20,{p}_{lime}=0.20,{p}_{orange}=0.20,{p}_{strawberry}=0.20,{p}_{graph}=0.20$

${H}_{a}:Atleastoneofthe{p}_{i}’sisincorrect.$

Part (b) Expected count for each flavor is $12$

Part (c) If chi square statistic is greater than above critical values at specified level of significance then reject ${H}_{0}$

Part (d) See the step by step solution

## Part (a) Step 1: Given information

The flavor blend is $20%$ of each flavor.

Sample size is $60$ candies.

## Part (a) Step 2: Calculation

The null and alternative hypotheses:

${H}_{0}:{p}_{lemon}=0.20,{p}_{lime}=0.20,{p}_{orange}=0.20,{p}_{strawberry}=0.20,{p}_{grape}=0.20$

${H}_{0}:Atleastoneofthe{p}_{i}’sisincorrect.$

## Part (b) Step 1: Calculation

To get the predicted count, multiply each frequency of flavor by $60$ As a result, the projected count is, ## Part (c) Step 1: Calculation

The degrees of freedom $=df=c-1$

The $df=5-1=4$

For each degree of significance, various critical values will be used.

When significance level$=a=0.05$

${\chi }^{2}=9.49\dots U\mathrm{sin}gexcelformula,=CHIINV\left(0.05,4\right)\phantom{\rule{0ex}{0ex}}{\chi }^{2}=13.28\dots U\mathrm{sin}gexcelformula,=CHIINV\left(0.01,4\right)$

Reject ${H}_{0}$ if the chi square statistic is greater than the crucial values at the selected level of significance.

## Part (d) Step 1: Calculation

The frequency of the random sample is shown in the table below: Using excel, Therefore, the$p-$value is between $0.01$ and $0.05$

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