Q 8.137. - Elementary Statistics

Question

Big Bucks. In the article "The $\backslash (350,000$ Club" (The Business Journal, Vol. 24, Issue 14, Pp. 80-82), J. Trunelle et al. examined Arizona public-company executives with salaries and bonuses totaling over $\backslash )350,000$ The following data provide the salaries, to the nearest thousand dollars, of a random sample of $20$ such executives.

Step-by-Step Solution

Answer

It is reasonable to apply the $t-$interval procedure to obtain the confidence interval of the population mean based on this sample.

Step 1: Given information

516	574	560	623	600
770	680	672	745	450
450	545	630	650	461
836	404	428	620	604

Step 2: Explanation

Now, draw a probability plot for the given data.  

Now construct a box plot for a given data.  

Step 3: Explanation

Now construct the histogram for the given data.  

The sample size here is moderate $(n=20)$ We can observe from the graphs that there is no outlier in the sample. The plotted points fall closely along a straight line, indicating that the variable under study is approximately regularly distributed. As a result, applying the $t-$interval approach to estimate the confidence interval of the population means based on this sample is appropriate.