please answer the following question on statists

Q #1

In this problem, we explore the effect on the mean, median, and mode of multiplying each data value by the same number. Consider the following data set. 6, 6, 7, 10, 14 LO USE SALT (a) Compute the mode, median, and mean. mode 6 median 7 mean 13.6 X (b) Multiply each data value by 6. Compute the mode, median, and mean. mode 9 X median 10 X mean 6 XThe Grand Canyon and the Colorado River are beautiful, rugged, and sometimes dangerous. Thomas Myers is a physician at the park clinic in Grand Canyon Village. Dr. Myers has recorded (for a 5-year period) the number of visitor injuries at different landing points for commercial boat trips down the Colorado River in both the Upper and Lower Grand Canyon (Source: Fatefuf Journey by Myers, Becker, Stevens). Upper Canyon: Number of Injuries per Landing Point Between North Canyon and Phantom Ranch 2 3 1 1 3 4 6 9 3 1 3 Lower Canyon: Number of Injuries per Landing Point Between Bright Angel and Lava Falls 8110672143011321 USE SALT (a) Compute the mean, median, and mode for injuries per landing point in the Upper Canyon. (Enter your answers to one decimal place.) meanx m..._., 5. [-/1 Points] BBUNDERSTAT12 3.2.010.M|.S. MY NOTES ASK YOUR TEACHER | PRACTICE ANOTHER In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the following data set. 8, 14, 4, 16, 12 USE SALT (a) Use the defining Formula, the computation formula, or a calculator to compute 5. (Enter your answer to four decimal places.) S (b) Add 5 to each data value to get the new data set 13, 19, 9, 21, 17. Compute 9. (Enter your answer to four decimal places.) S (c) Compare the results of parts (a) and (b). In general, how do you think the standard deviation ofa data set changes if the same constant is added to each data value? 0 Adding the same constant c to each data value results in the standard deviation remaining the same. 0 Adding the same constant c to each data value results in the standard deviation increasing by c units. 0 Adding the same constant c to each data value results in the standard deviation decreasing by c units. 0 There is no distinct pattern when the same constant is added to each data value in a set. Need Help? In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 16, 11, 14, 16, 13. USE SA (a) Use the dening formula, the computation formula, or a calculator to compute 5. (Round your answer to four decimal places.) (b) Multiply each data value by 7 to obtain the new data set 112, 77, 98, 112, 91. Compute 5. (Round your answer to four decimal places.) (c) Compare the results of paris (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c? O Multiplying each data value by the same constant c results in the standard deviation being |c| times as large. 0 Multiplying each data value by the same constant 6 results in the standard deviation being |c| times smaller. 0 Multiplying each data value by the same constant 6 results in the standard deviation increasing by c units. 0 Multiplying each data value by the same constant 6 results in the standard deviation remaining the same. (d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be 5 = 2 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calculations? 0 Yes ONo Given 1 mile = 1.6 kilometers, what is the standard deviation in kilometers? (Enter your answer to two decimal places.) Need Help? Do bonds reduce the overall risk of an investment portfolio? Let X be a random variable representing annual percent return For Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data. X: 22 D 34 15 30 19 38 21 14 10 y: 10 2 22 28 25 9 12 9 2 8 la USES (a) Compute EX, 2x2, 2y, 2y2. \":33: WSW: (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation forx and for y. (Round your answers to four decimal places.) (c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Round your answers to two decimal places.) X Y Use the intervals to compare the two funds. 0 75% of the returns for the balanced fund fall within a narrower range than those of the stock fund. 0 75% of the returns for the stock fund fall within a narrower range than those of the balanced fund. 0 25% of the returns for the balanced fund fall within a narrower range than those of the stock fund. 0 25% of the returns for the stock fund fall within a wider range than those of the balanced fund. (d) Compute the coefficient of variation for each fund. (Round your answers to the nearest whole number.) X Y Use the coefficients of variation to compare the two funds. 0 For each unit of return, the stock fund has lower risk. 0 For each unit of return, the balanced fund has lower risk. 0 For each unit of return, the funds have equal risk. If 5 represents risks and } represents expected return, then 5/} can be thought of as a measure of risk per unit of expected return. In this case, why is a smaller CV better? Explain. O A smaller CV is better because it indicates a higher risk per unit of expected return. 0 A smaller CV is better because it indicates a lower risk per unit of expected return. Need Help? Kevlar epoxy is a material used on the NASA space shuttles. Strands of this epoxy were tested at the 90% breaking strength. The following data represent time to failure (in hours) for a random sample of 50 epoxy strands. Let x be a random variable representing time to failure (in hours) at 90% breaking strength. 0.52 1.80 1.52 2.05 1.03 1.18 0.80 1.33 1.29 1.11 3.34 1.54 0.08 0.12 0.60 0.72 0.92 1.05 1.43 3.03 1.81 2.17 0.63 0.56 0.03 0.09 0.18 0.34 1.51 1.45 1.52 0.19 1.55 0.02 0.07 0.65 0.40 0.24 1.51 1.45 1.60 1.80 4.69 0.08 7.89 1.58 1.62 0.03 0.23 0.72 la uses (a) Find the range. S (b) Use a calculator to calculate 2x and 2X2. (c) Use the results of part (b) to compute the sample mean, variance, and standard deviation for the time to failure. (Round your answers to four decimal places.) E = :l s = :l (d) Use the results of part (c) to compute the coefcient of variation. (Round your answer to the nearest whole number.) m 32 Hka 7 Measures 0f Variatic X 6 9 O Q Q https://www.webassign.net/web/Studant/AssignmentResponses... {3 (! 0i 6'" 5:: g . {3 I {'5 . \"h \\_l A (b) Use a calculator to calculate Ex and 2x2. 2x= :l (c) Use the results of part (b) to compute the sample mean, variance, and standard deviation for the time to failure. (Round your answers to four decimal places.) (d) Use the results of part (c) to compute the coefcient of variation. (Round your answer to the nearest whole number.) What does this number say about time to failure? O The standard deviation of the time to failure is just slightly smaller than the average time. 0 The coefcient of variation says nothing about time to failure. O The standard deviation of the time to failure is just slightly larger than the average time. I O The standard deviation is equal to the average. Why does a small CV indicate more consistent data, whereas a larger CV indicates less consistent data? Explain. O A small CV indicates more consistent data because the value of s in the numerator is smaller. 0 A small CV indicates more consistent data because the value of s in the numerator is larger. Need Help? i i v ,0 Type here to search e For mallard ducks and Canada geese, what percentage of nests are successful (at least one offspring survives)? Studies in Montana, Illinois, Wyoming, Utah, and California give the following percentages of successful nests (Reference: The Wildlife Society Press, Washington, D.C.). X.' Percentage success for mallard duck nests 74 47 17 32 23 y: Percentage success for Canada goose nests 42 57 3O 42 66 USE SALT (a) Use a calculator to verify that 2x = 193; 2X2 = 9,527; 2y = 237; and 2y2 = 12,033. 2x _ 2x2 :I 2y _ 2,2 :l (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for X, the percent of successful mallard nests. (Round your answers to four decimal places.) X 52 S (c) Use the results of part (a) to compute the sample mean, variance, and standard deviation for y, the percent of successful Canada goose nests. (Round your answers to four decimal places.) y 52 S 5% (d) Use the results of parts (b) and (c) to compute the coefcient of variation for successful mallard nests and Canada goose nests. (Round your answers to one decimal place.) X 5' Write a brief explanation of the meaning of these numbers. What do these results say about the nesting success rates for mallards compared to Canada geese? 0 "he CV is the ratio of the standard deviation to the mean; the CV for Canada goose nests is higher. 0 The CV is the ratio of the standard deviation to the mean; the CV for Canada goose nests is equal to the CV for mallard nests. 0 "he CV is the ratio of the standard deviation to the mean; the CV for mallard nests is higher. 0 "he CV is the ratio of the standard deviation to the variance; the CV for Canada goose nests is higher. 0 "he CV is the ratio of the standard deviation to the variance; the CV for Canada goose nests is equal to the CV for mallard nests. 0 "he CV is the ratio of the standard deviation to the variance; the CV for mallard nests is higher. Would you say one group of data is more or less consistent than the other? Explain. O The X data group is more consistent because the standard deviation is smaller: O The two groups are equally consistent because the standard deviations are equal. O The y data group is more consistent because the standard deviation is smaller: Need Help? 11. [-I1 Points] DETAILS BBUNDERSTAT12 3.2.022. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER What was the age distribution of prehistoric Native Americans? Extensive anthropological studies in the southwestern United States gave the following information about a prehistoric extended family group of 86 members on what is now a Native American reservation. For this community, estimate the mean age expressed in years, the sample variance, and the sample standard deviation. For the class 31 and over, use 35.5 as the class midpoint. (Round your answers to one decimal place.) 1-10 1120 21-30 31 and over Age range (years) 34 15 23 14 Number of individuals 3 S Z Need Help? N Xl || II in II Alexander Borbely is a professor at the University of Zurich Medical School, where he is director of the sleep laboratory. The histogram in the figure below is based on information from his book Secrets of Sleep. The histogram displays hours of sleep per day for a random sample of 200 subjects. Estimate the mean hours of sleep, standard deviation of hours of sleep and coefficient of variation. (Enter x to 1 decimal place, s and CV to 2 decimal places.) 90 90 Frequency 80 70 64 60 50 40 30 22 20 14 10_ 4 2 2 2 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 Hours of sleep CV Need Help? Read It