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- Which of the following is the Lagrangian interpolation polynomial for the following points?Percentages of public school students in fourth and eighth grades who were above the proficiency level were given for 8 western states 4th Grade Proficiency 8th Grade Proficiency Arizona 15 21 California 11 18 Hawaii 16 16 Montana 22 37 New Mexico 13 13 Oregon 21 32 Utah 23 26 Wyoming 19 25 Construct a scatterplot and comment on any interesting characteristics Find the least squares equation. If Nevada had a 4th grade proficiency of 14%, what would you expect the 8th grade proficiency to be?The Greer Tire company manufactures a new steel-belted radial tire to be sold through a national chain of discount stores. Because the tire is a new product, Greer’s managers believe that the mileage guarantee offered with the tire will be an important factor in the acceptance of the product. Let X = miles that the tires last: X~N(60,000 2,500) Find the mileage guarantee that ensures this company will repair no more than 15% of its product for free. Assume the distribution of tire mileage is normal.
- Find the curve of best-fit y = axb to the following data by using the method of least square.According to scientists, the cockroach has had 300 million years to develop a resistance to destruction. In a study conducted by researchers, 6 comma 0006,000 roaches (the expected number in a roach-infested house) were released in the test kitchen. One week later, the kitchen was fumigated and 18 comma 10718,107 dead roaches were counted, a gain of 12 comma 10712,107 roaches for the 1-week period. Assume that none of the original roaches died during the 1-week period and that the standard deviation of x, the number of roaches produced per roach in a 1-week period, is 1.61.6. Use the number of roaches produced by the sample of 6 comma 0006,000 roaches to find a 9595% confidence interval for the mean number of roaches produced per week for each roach in a typical roach-infested house. Find a 95% confidence interval for the mean number of roaches produced per week for each roach in a typical roach-infested house.Given a set of points, the least-squares line formed by letting xbe the independent variable will not necessarily be the sameas the least-squares line formed by letting y be the independentvariable. Give an example to show why this is true.
- The hourly wages of a sample of 130 system analysts are given belowmean=60mode=73median=74range=20variance=324The coefficient of variation equals...?Suppose a doctor measures the height, x, and head circumference, y, of 8 children and obtains the data below. Thecorrelation coefficient is 0.944 and the least squares regression line is y = 0.199x + 11.982. Complete parts (a) and (b)below.Height, x27.5 25.5 26.25 25.25 27.5 26.25 26 27.25 27.25 27 27.25 ФHead Circumference, # 17.5 17.0 17.2 17.0 17.5 17.3 17.2 17.4 17.3 17.3 17.4(a) Compute the coefficient of determination, R?R?.% (Round to one decimal place as needed.)(b) Interpret the coefficient of determination and comment on the adequacy of the linear model.Approximately % of the variation inis explained by the least-squares regression model.According to the residual plot, the linear model appears to be (Round to one decimal place as needed.)If f1x2 = 2x3 + Ax2 + 4x - 5 and f122 = 5, what is thevalue of A?
- Are the signs of the coefficients on the variables "Frequency of Flights" and "Destination is a Big City" corresponding to the utility of the "Air" mode meaningful? Utility for Car Utility for Air param. t stat Param. t stat Constant 4.77 6.995 0 fixed Travel Time (mins) -0.03 -16.926 -0.03 -16.926 Travel Cost / Income ($/$) -726.35 -4.28 -726.35 -4.28 Frequency of Flights (per week) 0 fixed 0.12 13.414 Is Destination a Large City 0 fixed 1.5 5.576 Travel Party Size > =2^2 1.75 5.873 0 FixedA certain company produces fidget spinners with ball bearings made of either plastic or metal. Under standard testing conditions, fidget spinners from this company with plastic bearings spin for an average of 2.7 minutes, while those from this company with metal bearings spin for an average of 4.2 minutes. A random sample of three fidget spinners with plastic bearings is selected from company stock, and each is spun one time under the same standard conditions; let x¯1x¯1 represent the average spinning time for these three spinners. A random sample of seven fidget spinners with metal bearings is selected from company stock, and each is likewise spun one time under standard conditions; let x¯2x¯2 represent the average spinning time for these seven spinners. What is the mean μ(x¯1−x¯2)μ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2x¯1−x¯2 ? 3(2.7)−7(4.2)=−21.33(2.7)−7(4.2)=−21.3 A 3−7=−43−7=−4 B 2.7−4.2=−1.52.7−4.2=−1.5 C…A researcher wants to examine the relationship between time spend on social media (variable X) and loneliness (variable Y) in young adults. A randomly sample of n = 52 young adults was asked how much time in average they spend on social media each day and how lonely day feel on a typical day. The partial computations of collected data produced the following results: SP = -14 MX = 10 SSx = 36 MY = 16 SSY = 49 A. Based on these results, is there a significant correlation between time spend on social media and loneliness among young adults? Use a Pearson correlation test with p < .05, 2-tails to answer this research question. Follow the steps of hypothesis testing and insert your answers below. In your calculations,round all numbers to two decimal places to avoid rounding errors. ANSWER H0: H1: Computed Pearson r = df for decision about H0: Critical r-value used for decision about H0: Decision about H0 (i.e., reject or fail to…
