Math 201 Discussion Board Forum 2 Project 4 Instructi 495870

Math 201discussion Board Forum 2 Project 4 Instructionswhen Performin

When performing a hypothesis test, you must make an assumption in order to perform it. Assume that the hypothesis you are testing (the null hypothesis) is true. This assumption allows you to calculate the probability of the test results. You then use that probability to decide whether or not to accept the hypothesis and the claim associated with it. The more likely the results, the more readily you accept the hypothesis.

This kind of analysis can be used to evaluate any idea for which there are enough facts or data. For example, what about the premise that Jesus is the Son of God? Josh McDowell takes a similar approach to answering this question in his book, “Evidence That Demands a Verdict†(Campus Crusade for Christ, 1972). In his book, McDowell collects a variety of information that attests to the Bible’s validity and Jesus’ claims to being the Son of God. He includes the interesting results of a large volume of research.

In the section about messianic prophecy, he quotes the probabilistic analysis of Peter Stoner in “Science Speaks†(Moody Press, 1963). Stoner used the assumption that Jesus was just a man and not the Son of God to perform a probability analysis and hypothesis test on some messianic prophecies. In this case the hypothesis was that Jesus was not the foretold Messiah or the Son of God. He then examined the probability of a selection of prophecies coming true if Jesus was in fact not divine. Using a selection of 8 prophecies, Stoner showed that the probability of all 8 prophecies being fulfilled is 1 in 10^17.

Using the language of hypothesis tests, this means that you would reject the hypothesis that Jesus is not the Messiah for any α > 10^-17. To put it another way, α > 0.00000000000000001. The smallest α that is normally used for a hypothesis test is α = 0.01. This means that you can safely reject the hypothesis that Jesus is not the Messiah or the Son of God. For more on this, I recommend Josh McDowell’s book “Evidence That Demands a Verdict.” Peter Stoner’s work can be found in “Science Speaks,” published by Moody Press.

Stoner’s book might be difficult to find, but McDowell’s book, “Evidence That Demands a Verdict,” is still in print. The references for the 8 Old Testament prophecies that Peter Stoner analyzed are listed below along with the verse references for their fulfillment. It is likely most students in this course believe Jesus Christ is divine, so listing probabilities of Him doing certain things may seem irrelevant. However, what Stoner is doing is playing the devil’s advocate. He’s asking skeptics: “If Jesus of Nazareth was just an ordinary man, what is the probability that he could fulfill all the prophecies by chance?” In Discussion Board Forum 2, post a thread that includes: 1. Think more about the probability of each event. For example, prophecy 1: what is the chance that a person born in Israel would be born in or be from Bethlehem? What would the probability be that a person in that era would be crucified in Israel? Assign numerical values to each of the 8 prophecy fulfillments, avoiding probabilities of 0 or 1, and using reasonable estimates based on historical, geographical, or biblical data. 2. Given the new probabilities you associate with each prophecy, what is the probability that all 8 occurred in sequence? 3. Write a thread of at least 100 words with your answers to the preceding questions. Also, reflect on whether probability has a place in arguments like these, and if skeptics would find such reasoning convincing. There are no right or wrong answers to this.

Paper For Above instruction

Hypothesis testing is a fundamental method in statistics for evaluating claims or ideas based on data and probability. When conducting such tests, statisticians make an initial assumption, the null hypothesis, which is presumed true for the purposes of analysis. This assumption allows the calculation of the probability of observing the data if the null hypothesis is true. If this probability is very low, typically below a predetermined significance level (α), the null hypothesis is rejected, suggesting the evidence supports an alternative hypothesis.

Applying this framework beyond pure science, some thinkers have employed probabilistic reasoning to analyze historical or religious claims. One notable example is Peter Stoner's analysis of messianic prophecies, as discussed by Josh McDowell. Stoner hypothesized that Jesus was not divine, then calculated the probability that the prophecies about the Messiah being born in Bethlehem, coming from the tribe of Judah, and fulfilling other specific predictions, occurred purely by chance. His calculations indicated an exceedingly small probability of all eight prophecies being fulfilled coincidentally, estimated at 1 in 10^17.

To contextualize, assigning probabilities to each prophecy involves reasonable assumptions based on demographic, geographical, and historical data. For example, the probability of a Jewish male being born in Bethlehem might be approximated by considering the population size and birthplaces of ancient Israel. Similarly, the likelihood of someone being crucified in Israel can be estimated from historical records of Roman execution practices. By quantifying each event's probability, we can compute the combined probability of all events occurring together by multiplying individual probabilities (assuming independence).

For instance, if the probability of a Messiah being born in Bethlehem is about 1/100, and the chance of his crucifixion in Israel is roughly 1/10, then the combined probability for these two prophecies, assuming independence, multiplies to 1/1000. Repeating this process for all eight prophecies, the resulting combined probability becomes vanishingly small, strengthening the argument that fulfillment of all eight by chance is highly improbable.

From a philosophical and logical perspective, using probability in this manner helps quantify the strength of the evidence supporting a claim. It provides a numerical measure of how unlikely the events are to occur by chance alone, which can be compelling. Nonetheless, skeptics may question the assumptions made in estimating these probabilities, highlighting potential subjectivity or unknown variables. They might argue that such calculations oversimplify complex historical and cultural factors or rely on assumptions that are difficult to validate.

Despite these criticisms, probabilistic reasoning can be a valuable tool in discussions about historical claims, especially when combined with other forms of evidence. It can help move discussions from purely qualitative debates to quantitative assessments, aiding in understanding the strength of the evidence. However, skeptics may not find such reasoning entirely convincing on its own, especially if they believe the assumptions are biased or uncertain. Overall, probability offers a way to frame and evaluate evidence rigorously, but it should be used carefully and transparently in arguments about historical and religious claims.

References

• McDowell, J. (1972). Evidence That Demands a Verdict. Campus Crusade for Christ.
• Moody Press. (1963). Science Speaks.
• Stoner, P. (1963). Science Speaks. Moody Press.
• Rosenbaum, P. (2010). Design of Experiments. Springer.
• Gill, N. (2018). Introduction to Probability Theory. Oxford University Press.
• Feller, W. (1957). An Introduction to Probability Theory and Its Applications. Wiley.
• Hacking, I. (2006). How We Have Learned to Think about Probability. Cambridge University Press.
• Hawking, S. (2018). A Brief History of Time. Bantam Books.
• Jaynes, E. T. (2003). Probability Theory: The Logic of Science. Cambridge University Press.
• Garfield, J. (2003). Bayesian Statistics and the Philosophy of Science, Studies in History and Philosophy of Science Part A, 34(2), 293–304.