Calculate the test statistic χ2 and state your decision regarding the null hypothesis. 23.It has been rumored that the color distribution of M&amp;M's is 30% brown, 20% yellow, 20% red, 10% orange, 10% blue, and 10% green. You suspect this rumor is incorrect and decide to count how many of each color are contained in a randomly chosen bag in order to perform a Chi-Square goodness-of-fit test at a 5% significance level. Color Brown Yellow Red Orange Blue Green Total Observed 27162112915100Provided the assumptions of the test are satisfied, calculate the test statistic χ2:a. 4.15, Reject H0b. 4.15, Fail to Reject H0c. 16.83, Reject H0d. 16.83, Fail to Reject H0

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Calculate the test statistic χ2 and state your decision regarding the null hypothesis. 23.It has been rumored that the color distribution of M&amp;amp;M&#039;s is 30% brown, 20% yellow, 20% red, 10% orange, 10% blue, and 10% green. You suspect this rumor is incorrect and decide to count how many of each color are contained in a randomly chosen bag in order to perform a Chi-Square goodness-of-fit test at a 5% significance level. Color  Brown  Yellow  Red  Orange  Blue  Green  Total  Observed 27162112915100Provided the assumptions of the test are satisfied, calculate the test statistic χ2:a. 4.15, Reject H0b. 4.15, Fail to Reject H0c. 16.83, Reject H0d. 16.83, Fail to Reject H0

clugiarh0j · Accepted Answer

It is given that the rumor of color distribution of M&amp;amp;M’s is 30% brown, 20% yellow, 20% red, 10% orange, 10% blue, and 10% green.Formula for Test statistic:χ2=∑t=1n(Oi−Ei)Eihere, Oi is observed frequencies and Ei is expected frequencies.Calculations:Observed Frequencies: Color  Brown  Yellow  Red  Orange  Blue  Green  Total  Observed Frequencies 27162112915100Expected Frequencies: Color  Brown  Yellow  Red  Orange  Blue  Green  Total  Expected Frequencies 100×0.30=30100×0.20=20100×0.20=20100×0.10=10100×0.10=10100×0.10=10100Calculate the chi-square test statistic:χ2=(37−30)230+(16−20)220+(21−20)220+(12−10)210+(9−10)210+(15−10)210==930+1620+120+410+110+2510==0.3+0.8+0.005+0.4+0.1+2.5=4.15Therefore, the value of chi-square test statistic is 4.15.Critical Value:Calculate the critical value using Excel:Degrees of freedom:df=n-1=6-1=5Therefore, the chi-square critical value is 11.0705.Decision rule:If Chi-square test statistic &amp;gt; Chi-square critical value, then reject H0.Conclusion:Here, Chi-square test statistic (4.15) &amp;lt; Chi-square critical value (11.070), then Fail to reject H0.Therefore, the correct option is b) 4.15, Fail to reject H0.

Calculate the test statistic \(\displaystyle\chi^{{2}}\) and state

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