Big salary for the boss: Following is the total compensation, in millions of dollars, for Chief Executive Officers at 17 large U.S. corporations, along with aboxplot of the data.9.15 2.32 23.84 13.12 9.91 6.39 2.194.28 3.18 2.754.646.05 6.596.5911.318.20 25.84 2.85Part 1 of 2ontinueIt is notPart: 1/2Part 2 of 21520Is it reasonable to assume that the conditions for constructing a confidence interval for the mean compensation are satisfied? Explain.▾ reasonable to assume the conditions are satisfied.2530XSIt is not reasonable to assume the conditions are satisfied because the sample (Choose one) contain an outlier.XS0.00Submi

Let X denote the total compensation, in millions of dollars, for Chief Executive Officers at 17 large US corporations.The data on X is given by,X=9.15,2.32,3.18,23.84,13.12,9.91,4.05,6.39,2.19,4.28,2.75,4.64,6.30,11.31,8.20,2.85,25.84It is required to explain whether it is reasonable to assume that the conditions for constructing a confidence interval for the mean compensation are satisfied or not.A confidence interval for a mean is a range of values within which one can reasonably estimate that the population mean falls with a specified level of confidence. It provides a way to quantify the uncertainty associated with estimating the population mean from a sample of data.Inorder to construct the confidence interval , the normality assumption on the data should be satisfied or the sample size should be large enough so that use of Central limit theorem is justified. For the given case the sample size is 17 which is significantly smaller to employ the central limit theorem.The distribution of X can be verified using the Box plotObatin the Boxplot from the EXCEL by going to Insert--->Charts --->Box and Whiskers chartFrom the box plot it is evident that there are two outliers in the data and the median (middle line in the box) is not equal to the mean (cross inside the data). The presence of outliers can lead to skewness in the data, making it non-normally distributed. Non-normally distributed data can violate the assumption required for constructing confidence intervals using methods like the t-test or Z-test.Therefore, It is not reasonable to assume the conditions are satisfied, because there are two outliers. From the box plot it is evident that the normality assumption is not satisfied.Hence, It is not reasonable to assume the conditions are satisfied, because there are two outliers.