The answer of the condition is Fail to Reject.
A chi-squared test (also chi-square or χ2 test) is a statistical hypothesis test that is valid to perform when the test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and variants thereof. Pearson's chi-squared test is used to determine whether there is a statistically significant difference between the expected frequencies and the observed frequencies in one or more categories of a contingency table.
The data is given as follow:
The experimental weight of cashews = 40 % of 20lbs
= 8
The experimental weight of Brazil Nuts = 15 % of 20lbs
= 3
The experimental weight of Almonds = 20 % of 20lbs
= 4
The experimental weight of peanuts = 25 % of 20lbs
= 5
The observed value is :
So, [tex]{\displaystyle \chi }[/tex] =[tex]\frac{(O-E)^{2}}{E}[/tex]
[tex]{\displaystyle \chi }[/tex]= [tex]\frac{(5-8)^{2}}{8} + \frac{(6-3)^{2}}{3} + \frac{(5-4)^{2}}{4} +\frac{(4-5)^{2}}{5}[/tex]
= 4.575
pvalue = p([tex]{\displaystyle \chi }^{2}[/tex] > 4.575) = [tex]{\displaystyle \chi }^{2}[/tex] cdf(4.575, 99999, 3)
= 0.208 >α
Hence, Fail to reject.
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