Final answer:
To determine if birth rates vary on weekends, the null hypothesis states birth rates are equal across days, while the alternative hypothesis suggests a difference on weekends. A chi-square test for goodness of fit can be used to compare observed birth frequencies against the expected uniform distribution over the days of the week.
Step-by-step explanation:
To determine if birth rates are different on weekends compared to weekdays at a western hospital where there were a total of 932 births in 20 consecutive weeks, and of these, 216 occurred on weekends, we can perform a hypothesis test. The null hypothesis (H0) would be that births are equally likely to occur on any day of the week. The alternative hypothesis (H1) is that births are not equally likely to occur on each day and differ on weekends compared to weekdays.
To test these hypotheses, one possible statistical test to use is the chi-square test for goodness of fit, which can show if the observed frequencies (births on weekends vs. weekdays) significantly diverge from the expected frequencies under the null hypothesis of a uniform distribution of births across all days.
For the given data, we expect 5/7 of births to happen on weekdays and 2/7 on weekends over the 20 weeks. Mathematically, this is approximately 665.7 expected births on weekdays and 266.3 births on weekends. Our observed frequencies are 716 births on weekdays (932-216) and 216 on weekends. With the chi-square test, we can calculate whether the difference between expected and observed frequencies is statistically significant at the chosen level of significance (commonly 0.05).