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Following Are Observed Frequencies H0:p1=0.35H _ { 0 } : p _ { 1 } = 0.35

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Following are observed frequencies. The null hypothesis is H0:p1=0.35H _ { 0 } : p _ { 1 } = 0.35 , p2=0.25,p3=0.2,p4=0.05,p5=0.15p _ { 2 } = 0.25 , p _ { 3 } = 0.2 , p _ { 4 } = 0.05 , p _ { 5 } = 0.15 .
 Category 12345 Observed 383124234\begin{array}{l|lllll}\text { Category } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Observed } & 38 & 31 & 24 & 23 & 4\end{array}

i). Compute the expected frequencies.
ii). Compute the value of χ2\chi ^ { 2 } .
iii). How many degrees of freedom are there?
iv). Test the hypothesis that the distribution of the observed frequencies is as giver null hypothesis. Use the α=0.05\alpha = 0.05 level of significance.

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