Divine providence? Use the following information to answer Exercises 1.4.141.4.18. Dr. John Arbuthnot (16671735) was physician to England's Queen Anne. He was also one of the rst scientists to publish a use of p- values and to apply the logic of statistical inference:l His goal was to prove the existence of God, and he took as evidence the fact that for 82 years in a row male christenings had outnumbered female chris- tenings. His argument: The p-value is so extremely tiny that the extra male births cannot be due to chance. Therefore the excess males must be due to \"Divine Providence.\" Here is a summary of his data: Number of male christenings: 484,382 Number of female christenings: 453,841 Total number of christenings: 938,223 Proportion of males: 0.516276 1.4.14 Let's take a look at Dr. Arbuthnot's hypotheses. a. What was Dr. Arbuthnot's research hypothesis? b. Let a'be Arbuthnot's parameter. Tell in words what a" refers to. 6. State in words, and then in symbols, what Dr. Arbuthnot's null hypothesis was. d. Was Arbuthnot's alternative hypothesis one-sided or two-sided? Give your reasoning. 1.4.15 Based solely on the observed value of p and the null value for Jr, would you expect the evidence against the null hypothesis to be strong or weak? Explain your reasoning. 1.4.16 Based solely on the sample size n (ignoring the value of dis- tance a"), would you expect the evidence against the null hypothe- sis to be strong or weak? Explain your reasoning. 1.4.17 Suppose (against all historical evidence) Arbuthnot had been an early feminist, equally willing to accept an excess of female births as evidence of \"Divine Providence.\" In that case, his p-value would have been (half/ twice) as large. 1.4.18 Summary. For the analysis based on the data provided, a. The distance between p and x is (tiny/small/large/huge). b. The sample size is (tiny/small/large/huge). c. The alternative hypothesis is -sided (one/two)