1.

A sample of 34 offshore oil workers took part in a simulated escape exercise, resulting in the following data on time [sec] to complete the escape. A stemplot of the data is shown below, where 32|2 = 322 32 | 25 33 | 39 34 | 35 | 0246 36 | 23567 37 | 126 38 | 12359 39 | 0013355578 40 | 01 41 | 42 | 6 a. Determine the value of the fourth spread. b. A data value needs to be lower than or higher than to be considered an outlier. o. Construct a box plot and note any features demonstrated by the box plot (note: this part is not graded.) d. By how much could the largest observation, currently 426, be decreased without affecting the value of the fourth spread? Zinfandel is a popular red wine varietal produced almost exclusively in California. It is rather controversial among wine connoisseurs because its alcohol content varies quite substantially from one producer to another. In May 2013, the author went to the website klwines.com, randomly selected 10 zinfandels from among the 325 available, and obtained the following values of alcohol content. (%] 14.9 14.2 16.5 15.8 14.4 16.2 14.5 14.4 13.9 14.9 a. Calculate and interpret several measure of center. The sample mean is :E = 98 alcohol content and the median is :E : 1LT J 0\" 96 alcohol content. This means that approximately 50% of the sample wines are less than x , and that the sample average alcohol content is x . b. Calculate the sample variance using the defining formula. Elms-)2= 2.128. x .32 = . [round to 3 decimal places). c. Subtracting 13 from each data value [193- = $3- 13} we obtain the following set. Calculate the sample variance using the shortcut formula. Explain '3' The variances of these two sets are not equal to each other because subtracting the same number from each value changes every data value. '13:} The variances are not equal to each other because the means are not equal to each other. '3' The variances of these two sets are equal because subtracting the same number from each value merely shifts every number the same amount. It does not change the spread. C' The variances of these two sets are equal because the data sets are the same size. {3,1 The variances of these two sets are equal because the means are the same. A local real estate brokerage listed the following asking prices for a sample of homes in Redding, CA (10005 of 5]. 191, 244, 314, 254, 302, 1270, 337, 279, 322, 298 Give all your answers below in 10005 of S rounded to 1 decimal place. a. Calculate the mean and median Mean home price :7: = 30? X Median home price :7? = 279 x b. Suppose the 6th observation had been 716 rather than 1270. How would the mean and median change? Revised mean home price it = I Revised median home price if: = c. Calculate a 20% trimmed mean by first trimming the two smallest and two largest observations. Sigma) = 275.8 X d. Calculate a 15% trimmed mean. {round to 1 decimal place} jfr(15) = 283.3 X