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# Critical Thinking Exercises 1.) Use and apply real data and information to evaluate a problem.) Use proper statistical methods to make decisions.)...

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Critical Thinking Exercises 1.) Use and apply real data and information to evaluate a problem. 2.) Use proper statistical methods to make decisions. 3.) Demonstrates how statistical methods are used in a real application. CTE 7: Designing Aircraft Seating The sitting distance is defined as the distance from the seat back cushion to the seat in front. It accommodates the buttock-to-knee length plus any additional space to provide comfort. Determining this distance is very important. If the distance is too large, space is wasted and rows of seats may be eliminated. It is estimated that eliminating a single row of seats in an aircraft can cost around 8 million dollars over its life. If the distance is too small, passengers will be uncomfortable and may choose a different airline. Use the data in the table to determine the required seating distance. The following choices must be carefully made. 1) Should the entire population be accommodated? If not, what percentage of the population are you willing to exclude? Explain your reasoning. 2) How much extra room are you providing for the passengers comfort? Explain. 3) Use the given information to determine the sitting distance. Identify the choices and decisions that were made in that determination. The following data is a summary from measurements of large numbers of people. Buttock-to-Knee Length Mean Standard Deviation Distribution Males 23.5 in. 1.1 in. Normal/>/> Females 22.7 in. 1.0 in Normal/>/> Source: Elementary Statistics, Triola, 11 th Edition CTE 8: Central Limit Theorem Instead of rolling a die 100 times, use a calculator (TI83/84) or STATDISK to simulate 100 rolls of a die. Select one of the following random generators that produces the whole numbers 1, 2, 3, 4, 5, 6 randomly. For TI84 and STATDISK directions, click on the following link: TI84 and STATDISK directions Now construct and display a histogram of the 50 sample means. Without actually generating a histogram of the original 5000 rolls, what would you expect the shape of the 5000 simulated roll of a die to be? How does that compare to the histogram that you just created of the 50 sample means? Explain, in your own words, how this demonstrates the Central Limit Theorem. Be specific and clear. Find the mean and standard deviation of the 50 sample means How does the mean of the 50 sample means compare to the mean of many rolls of a fair die? How does the standard deviation of the sample means compare to the standard deviation of outcomes when a single die is rolled a large number of times. How do these results demonstrate the Central Limit Theorem? Explain in your own words using you own results. Be specific and clear. (SLOs 9 & 10) Also STATDISK ASSINGMENT In a WORD doc develop the solution to the following problem: STATDISK can also be used to find those values. Assume a distribution with mean = 0 and a standard deviation = 1 First find the following probabilities in Table A-2, and then find the same using STATDISK. Provide the printouts and explain which values are being used. Less than 2.34 Between 1 and 3 Greater than -2.33 Which method did you prefer and why?
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