**Title: Statistical Analysis of Soldier Representation in Historical Battles****Critical Values:**- \( z_{0.005} = 2.575 \)- \( z_{0.01} = 2.335 \)- \( z_{0.025} = 1.96 \)**When Degrees of Freedom (d.f.) = 31:**- \( t_{0.005} = 2.744 \)- \( t_{0.01} = 2.453 \)- \( t_{0.025} = 2.040 \)- \( t_{0.05} = 1.696 \)- \( t_{0.1} = 1.282 \)- \( t_{0.2} = 1.309 \)**Problem Statement:**In a random sample of soldiers who fought in the Battle of Preston, 774 soldiers were from the New Model Army, and 226 were from the Royalist Army. Use a 0.05 significance level to test the claim that fewer than one quarter of the soldiers were Royalists.**Analysis:**This problem involves a hypothesis test. You are tasked to determine whether the proportion of Royalist soldiers is less than 25% of the total sample. Steps to solve this would include:1. Define null and alternative hypotheses.2. Calculate the test statistic.3. Compare the calculated value with the critical value at a 0.05 significance level.4. Make a decision to accept or reject the null hypothesis based on the comparison.Note: If further analysis details, such as the steps of calculation or decision rules, are necessary, consult the corresponding sections on hypothesis testing methodologies.

Name: **Title: Statistical Analysis of Soldier Representation in Historical
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: **Title: Statistical Analysis of Soldier Representation in Historical Battles****Critical Values:**- \( z_{0.005} = 2.575 \)- \( z_{0.01} = 2.335 \)- \( z_{0.025} = 1.96 \)**When Degrees of Freedom (d.f.) = 31:**- \( t_{0.005} = 2.744 \)- \( t_{0.01