How to Get a Birth, Death, Marriage, or Divorce Certificate

As indicated on Table 1 below, the analysis conducted on the births, marriages, deaths, and divorces within the USA and the territories established that there were slight variations in the data between 2005 and 2004. The average birth rate was 12,338 babies born in 2005, a difference of 319 babies in 2004, while the death rate had a slight difference of 76 people within the same two years. But in general terms, there were more babies born compared to the people who died between 2005 and 2004. Similarly, the averages had slight variations for marriages and divorces within 2005 and 2004 with 5,281 and 5,438 marriages respectively while the death rates were 2,902 in 2005 and 2,997 in 2004. 

Table 1: Summary Table for the results 

From the standard deviation values obtained, it is clear that the data points are not at a proximity to the mean and thus, are dispersed over an extensive set of values. The analysis of the standard deviation is best supported by the significant variations between the minimum and maximum ranges indicated in the table above. The minimum values are shallow, an indication of how far the values were away from the mean. There was something that might have happened at a national level to provoke such trends in not only the births, deaths, marriages, but also the divorces in certain months. 

To test the null hypothesis: the birth rates in 2005 are equal to the birth rates in 2004, the t-test was used, and the value of the test statistic gotten was -2.85 while the P-value obtained was 0.003. Therefore, as the test stat -2.85 is smaller than 1.66 (which is the one tail critical value) I would reject the null hypothesis as the data at this point is said to be none supportive of the null hypothesis ( Schönbrodt, Wagenmakers, Zehetleitner, & Perugini, 2017) . Hence, the alternative hypothesis is adopted since it is clear that the number of births in 2005 is not equal to the number of births in 2004. 

In the determination of the death rates a similar null hypothesis, which stated; the death rates in 2005 are equal to the death rates in 2004 was adopted. The alternative hypothesis read; the death rates in 2005 do not equal death rates in 2004, and through a t-test, the test statistic value was found to be -3.55 and the P-value 0.0003. Since the test stat value (-3.55) is smaller than one tail critical value (1.29), I would reject the null hypothesis as the data does not support it. Therefore, the alternative hypothesis would be adopted instead. This is because, in the analysis of data using the t-test if the test statistic value is greater than the critical one-tail value, the null hypothesis is rejected. 

The rate of marriages in 2005 was equal to that in 2004 was the model null hypothesis used in the assessment while the alternative hypothesis was that the rate of marriage in 2005 was not equal to the rate of marriage in 2004. The P-value was computed as 6.21E-08 while the test statistic value was -5.69 as the test statistic was smaller than the critical one tail t value, which was found to be 1.66. The null hypothesis would, therefore, be rejected as it is not supported by the data since the number of marriages in 2005 is not equal to several marriages in 2004. 

For the rate of divorces, the null hypothesis was also rejected as it was not supported by the data, which indicated that the rate in 2005 was not equal to the divorce rate in 2004. The p-value in this analysis was 1.99E-10 while the test statistic was -6.92, a value that was much smaller than the one tail critical t value of 1.29. The alternative hypothesis which stated the rates in 2005 were not equal to the divorce rates in 2004 was preferred, and the null hypothesis, which indicated that the rates in 2004 and 2005 were equal, was rejected. 

References 

Schönbrodt, F. D., Wagenmakers, E. J., Zehetleitner, M., & Perugini, M. (2017). Sequential hypothesis testing with Bayes factors: Efficiently testing mean differences. Psychological Methods, 22(2), 322.