30 0% Birth Rate 40 42 44 46 48 Date 1. Above is the monthly birthrate (per 1,000 US populations) from 1940-1947. A total of n=96 months are represented. Let p be the correlation between birth rate and time. a. The sample correlation is r=0.6191. Test at the 0.05 significance level the null hypothesis Ho : p =0 versus HA : p # 0. Report the test statistic and p-value. b. Is there an overall linear trend in the data? What does the positive correlation coefficient indicated in terms of the trend in birth rates over time? Describe two non-linear trends in the data and what might be the demographic or historical causes of those nonlinear trends