Chi-square goodness of fit statistic

A random sample of size 40 is drawn from a population having four distinct categories as $i = 1,2,3,4$. The data are given as | Category | 1 | 2 | 3 | 4 | |—|—|—|—|—| | Observed Frequency | 5 | 8 | 12 | 15 | Let $\theta_i$ be the probability that an observation comes from the $i$-th category, $i = 1,2,3,4$. If the chi-square goodness-of-fit test is used to test $H_0: \theta_i = \frac14, i = 1,2,3,4$ against $H_1: \theta_i \ne \frac14$ for some $i = 1,2,3,4$, then which one of the following statements is true?