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Q 17.

Expert-verifiedFound in: Page 718

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

${H}_{a}:Atleastoneofthe{p}_{i}\u2019sisincorrect.$

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)

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

Sample size is $60$ candies.

The null and alternative hypotheses:

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

${H}_{0}:Atleastoneofthe{p}_{i}\u2019sisincorrect.$

To get the predicted count, multiply each frequency of flavor by $60$ As a result, the projected count is,

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$=a=0.05$

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

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

The frequency of the random sample is shown in the table below:

Using excel,

Therefore, the$p-$value is between $0.01$ and $0.05$

More candy The two-way table shows the results of the experiment

described in Exercise 27.

Red Survey | Blue Survey | Control Survey | Total | |

Red Candy | $13$ | $5$ | $8$ | $26$ |

Blue Candy | $7$ | $15$ | $12$ | $34$ |

Total | $20$ | $20$ | $20$ | $60$ |

a. State the appropriate null and alternative hypotheses.

b. Show the calculation for the expected count in the Red/Red cell. Then provide a

complete table of expected counts.

c. Calculate the value of the chi-square test statistic.

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