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

Essay

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

i). Compute the expected frequencies.
ii). Compute the value of $\chi ^ { 2 }$ .
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 $\alpha = 0.05$ level of significance.