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Identify the statistical population, sample, and variable of interest in each of the following situations: (a) To learn about starting salaries for engineers graduating from a Midwestern university, twenty graduating seniors are asked to report their starting salary. (b) Fifty computer memory chips were selected from the thousand manufactured that day. The computer memory chips were tested, and 5 were found to be defective. (c) Tensile strength was measured on 20 specimens made of a new plastic material. The intent is to learn about the tensile strengths for all specimens that could conceivably be manufactured with the new plastic material.Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. The article "Properties of Waste Silk Shed Fibertcellulose Green Composite Films" 1. of Composite Materials, 2012: 123-12?) reported that for a sample of 10 specimens with 2% ber content, the sample mean tensile strength (MPa) was 51.3 and the sample standard deviation was 1.2. Suppose the true average strength forms bers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WScheiIulose composite exceeds this value? Each of a group of 20 intermediate tennis players is given two rackets, one having nylon strings and the other synthetic gut strings. After several weeks of playing with the two rackets, each player will be asked to state a preference for one of the two types of strings. Let p denote the proportion of all such players who would prefer gut to nylon, and let X be the number of players in the sample who prefer gut. Because gut strings are more expensive, consider the null hypothesis that at most 50% of all such players prefer gut. We simplify this to Ho: p = .5, planning to reject Ho only if sample evidence strongly favors gut strings a. Which of the rejection regions {15, 16, 17, 18, 19, 20}, {0, 1, 2, 3, 4, 5}, or {0, 1, 2, 3, 17, 18, 19, 20} is most appropriate, and why are the other two not appropriate? b. What is the probability of a type I error for the chosen region of part (a)? Does the region specify a level .05 test? Is it the best level .05 test? c. If 60% of all enthusiasts prefer gut, calculate the probability of a type ll error using the appropriate region from part (a). Repeat if 80% of all enthusiasts prefer gut. d. If 13 out of the 20 players prefer gut, should Ho be rejected using a significance level of .10?The article "Orchard Floor Management Utilizing Soil-Applied Coal Dust for Frost Protection" (Agri. and Forest Meteorology, 1988: 71-82) reports the following values for soil heat flux of eight plots covered with coal dust. 34.7 35.4 34.7 37.7 32.5 28.0 18.4 24.9 The mean soil heat flux for plots covered only with grass is 29.0. Assuming that the heat-flux distribution is approximately normal, does the data suggest that the coal dust is effective in increasing the mean heat flux over that for grass? Test the appropriate hypotheses using a = 05.An article in the Nov. 11, 2005, issue of the San Luis Obispo Tribune reported that researchers making random purchases at California Wal-Mart stores found scanners coming up with the wrong price 8.3% of the time. Suppose this was based on 200 purchases. The National Institute for Standards and Technology says that in the long run at most two out of every 100 items should have incorrectly scanned prices. a. Develop a test procedure with a significance level of (approximately) .05, and then carry out the test to decide whether the NIST benchmark is not satisfied. b. For the test procedure you employed in (a), what is the probability of deciding that the NIST benchmark has been satisfied when in fact the mistake rate is 5%