Refer to the following list of numbers of years that U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. (As of this writing the last president is Gerald Ford, the last pope is John Paul II, and the last British monarch is George VI.) Assume that the data are samples randomly selected from larger populations. Comparing Two Means? Treating the data as samples from larger populations, test the claim that there is a difference between the mean for presidents and the mean for British monarchs.

Solution 2CRE Step 1: Here we have to test that there is a difference between the mean for presidents and the mean for British monarchs, two samples of 38 presidents and 14 monarchs are considered. The data of numbers of years that U.S. presidents and British monarchs lived after their inauguration or coronation respectively are taken into account. Null hypothesis (H ): 0 The null hypothesis states that there is no significant difference between two variables. This can be written as H 0 1 = 02 Where, = T he mean longevity time of presidents after their inauguration. 1 2 T he mean longevity time of monarchs after the coronation. Step 2: Alternative hypothesis (H ): 1 The alternative hypothesis states that there is a significant difference between two variables. It can be written as H : = / 0 1 1 2 Step 3: If the above information is used to infer about the average numbers of years that U.S. presidents and British monarchs lived after their coronation, the following conditions should met. Randomization Condition: In this case, the sample of 38 presidents and a sample 14 monarchs were chosen independently and randomly. Nearly normal Condition: In this case, the original data are given, so existence of outliers can be checked by using box plots. The boxplots of numbers of years that U.S. presidents and British monarchs lived after their coronation respectively are given below: Step 4: Now, the normality condition for both the groups can be checked using Histograms. The histograms of data of numbers of years that U.S. presidents and British monarchs lived after their coronation are given below. Step 5: The following histogram is based on the number of years that British monarchs lived after their coronation. After checking the above histograms, it can be said that, both the histograms are unimodal. Similarly, the histogram of data of the numbers of years that U.S. presidents lived after their coronation is approximately symmetric. On the other hand, the histogram of data of the numbers of years that British monarchs lived after their coronation is positively skewed.