Final answer:
The hypothesis test to use in this scenario is a chi-square test for goodness of fit, with the null hypothesis being that police call frequencies are the same for each day of the week, and the alternative hypothesis being that frequencies differ by day.
Step-by-step explanation:
To address the question regarding the frequencies of police calls on different days of the week, the appropriate hypothesis test to use here is a chi-square test for goodness of fit. The goal in this scenario is to determine if the observed frequencies of calls for each day fit a hypothesized frequency distribution, which in this case would be uniform since the claim is that each day has the same frequency of calls.
The null hypothesis (H0) for this test would be that the frequency of police calls is the same across all days of the week. Formally, we can state this as: "The different days of the week have the same frequencies of police calls." The alternative hypothesis (Ha) is that "The different days of the week have different frequencies of police calls." Essentially, we're testing the claim of uniform distribution (equal frequencies) against the possibility of a non-uniform distribution (unequal frequencies).
However, the fundamental error in this analysis could stem from several issues. Without additional context, potential errors could include assuming that calls are independent of each day, not accounting for variability in call volume due to special events or holidays, or other external factors influencing police calls that are not uniformly distributed across the days of the week.