Chapter 12.1, Problem 20E

Following are observed frequencies. The null hypothesis is $H_0:p_1=0.4,p_2=0.25,p_3=0.05,p_4=0.1,p_5=\mathrm{0.2.}$

1. Compute the expected frequencies.
2. Compute the value of ${\chi }^2.$
3. How many degrees of freedom are there?
4. Test the hypothesis that the distribution of the observed frequencies is as given by the null hypothesis. Use the $\alpha =0.05$ level of significance.