The UMUC Daily News reported that the color distribution for plain M&M;\'s was:
ID: 3330655 • Letter: T
Question
The UMUC Daily News reported that the color distribution for plain M&M;'s was: 40% brown, 20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a random sample of 100 plain M&M;'s was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the published color distribution is correct. Show all work ana justiy your answer 18- Color Number Brown Ye Tan 18 Green 42 21 127 Identify the null hypothesis and the alternative hypothesis. work, will receive no credit. will recetve no credit Justify your answer. (a) (b) Determine the test statistic. Show all work, writing the correct test statistic, without supporting (c) Determine the P-value. Show all work; writing the correct P- value, without supporting work (d) Is there sufficient evidence to support the claim that the published color distribution is correct?Explanation / Answer
Given table data is as below
set up null vs alternative as
null, Ho:true proportion of all 5 categories equal to their ex— pected value
alternative, H1: atleast one proportion of all 5 categories is diffrent from its ex
pected value.
level of significance, = 0.05
from standard normal table, chi square value at right tailed, ^2 /2 =9.488
since our test is right tailed,reject Ho when ^2 o > 9.488
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table , ^2 o = 10.65
critical value
the value of |^2 | at los 0.05 with d.f n-1 = 4 is 9.488
we got | ^2| =10.65 & | ^2 | =9.488
make decision
hence value of | ^2 o | < | ^2 | and here wereject Ho
^2 p_value =0.0308
there is evidence that atleast one proportion of all 5 categories is diffrent from its ex
pected value.
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