In this statistical inference analysis, we delve into the global adolescent fertility rate in 2020, with the objective of determining whether it significantly differs from a hypothesized mean of 50 births per 1000 girls aged 15-19. We employ a two-sided t-test on the reproductive rate (R) to assess the statistical significance of this difference, making informed decisions about the population parameter based on sample data.
Assignment Solution Sample:
Statistical inference is a critical process that enables us to make informed decisions about a population based on the available sample data. In this statistical inference assignment, we explore the concept of statistical inference by focusing on global adolescent fertility rates in 2020. Our aim is to determine if the mean global adolescent fertility rate is significantly different from a hypothesized value of 50 births per 1000 girls aged 15-19.
To address this question, we employ a two-sided t-test on the reproductive rate (R) in our sample. In the following sections, we break down the steps and present our findings:
- P-Values and Hypothesis Testing:
- Results and Conclusion:
P-values are essential tools in hypothesis testing, providing us with information about the likelihood that the observed data could have occurred under the null hypothesis. Typically, we compare the p-value to a predetermined significance level (usually 0.05).
After conducting our t-test, we obtain the following results:
- t statistic = 2.325935
- p-value = 0.1025272
- Critical value = 3.182446
Comparing the p-value (0.1025272) to our significance level (0.05), we observe that the p-value is greater. Consequently, we do not reject the null hypothesis. Based on this analysis, we conclude that the mean global adolescent fertility rate in 2020 is equal to 50 births per 1000 girls aged 15-19.
It's crucial to note that having a statistically significant difference between the sample mean and the null hypothesis mean does not necessarily imply a meaningful finding. There are various factors to consider, including the potential for committing a type I error (false rejection of the null hypothesis). Additionally, the power of the statistical test plays a significant role in the accuracy of our conclusions.
To provide a visual representation of our findings, we present a graph that clearly illustrates the difference between the sample mean and the hypothesized mean. When the p-value is less than the significance level, it leads to the rejection of the null hypothesis in favor of the alternative hypothesis.
In summary, this analysis demonstrates the importance of statistical inference in making informed decisions about population parameters. We've applied a two-sided t-test to assess the global adolescent fertility rate in 2020, ultimately determining that it is not significantly different from the hypothesized value of 50 births per 1000 girls aged 15-19. However, it's essential to remain cautious and consider other factors when interpreting statistical results.