2 Recall from Lesson 10.1.1 that the desired color distribution for the cereal i

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2 Recall from Lesson 10.1.1 that the desired color distribution for the cereal is: 20% red. 35% white. 45% blue. · · strong evidence against the claim that the population proportions are 20% red, 35% white, and 45% blue could mean that something may be wrong with the production process The Day 3 sample yielded the following results: Red White Bhie 180 360 460 Conduct a chi-square goodness-of-fit test to examine the claim that the population proportions of cereal pieces differ from the desired 20% red, 35% white, and 45% blue distribution, use a 5% significance level for the test. Note: A chi-square test statistic value of 5.99 or more corresponds to p-value of 5% or less. Complete all of the steps for the chi-square goodness-of-fit test. Be sure to begin the test by stating the null and alternative hypotheses. When you state your final conclusion, remember to interpret your conclusion in the context of the cereal piece color distribution case. Refer back to Lesson 10.1.1 for the steps involved in the chl-square goodness-of fit test. Do your results imply that something may be wrong with the production process? Explain your reasoning

Explanation / Answer

here null hypothesis:Ho: population proportion are same as desired 20% red, 35% white and 45% blue distribution.

Alternate hypothesis:Ha:: population proportion differs from desired 20% red, 35% white and 45% blue distribution.

for degree of freedom =categories-1= 3-1=2

for 2 degree of freedom and 0.05 level critical value 2 =5.991

Decision rule:reject Ho if test statistic 2 >5.991

applying chi square goodness of fit test:

from above test statistic =2.51 which is less than crtiical value ;therefore we can not reject null hypothesis

we do not have sufficient evidence to conclude that  population proportion differs from desired 20% red, 35% white and 45% blue distribution.

observed Expected Chi square category Probability O E=total*p =(O-E)^2/E red 0.200 180.000 200.00 2.00 white 0.350 360.000 350.00 0.29 blue 0.450 460.000 450.00 0.22 1 1000 1000 2.51

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