Question-2 a. A dynamic cone penetrometer DCP is used for measuring material resistance to penetration (mm/blow) as a cone is driven into pavement. A sample of size 52 for DCP values in pavement structure evaluation has a mean of 28.7615 and a standard deviation of 12.2647. Test that the true = average DCP value, μ 30 against that the true average DCP value, μ< 30 using level of significance of 0.02.
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- A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with mean 75.5 psi and standard deviation 3.5 psi. How is the standard deviation of the sample mean changed when the sample size is increased from n = 4 ton = 48 Round all intermediate calculations to four decimal places (e.g. 12.3456) and round the final answer to three decimal places (e.g. 98.768). The standard deviation is reduced ✓by i 1.25 psi. Statistical Tables and ChartsThe blood pressure (average of systolic and diastolic measurements) of each of 25 randomly selected persons was measured. The average was 97.5 mm Hg, and the standard deviation was 8.05 mm Hg. What is the critical t value? What is the margin of error?Assume that ui and µ2 are the averages of maximum speeds of new high-tech electric scooter types. Use the t test at significance level 0.01 to test Ho: µi - µ2 = -18 versus H.: μι - μ2<18 for the following data: ni = 6, x1=117.8, si=5.06, n2 = 6, xz= 128.2, and s2 = 5.28. (where n, , and s denote the sample size, sample mean and sample standard deviation respectively.) %3D
- 1. Model 1: OLS, using observations 1-706 Dependent variable: RST Coefficient Std. Error t-ratio p-value const 3586.38 38.9124 92.17 <0.0001 *** TOTWRK −0.150746 0.0167403 −9.005 <0.0001 *** Mean dependent var 3266.356 S.D. dependent var 444.4134 Sum squared resid 1.25e+08 S.E. of regression 421.1357 R-squared 0.103287 Adjusted R-squared 0.102014 F(1, 704) 81.08987 P-value(F) 1.99e-1810538.19 Log-likelihood −5267.096 Akaike criterion 10538.19 Schwarz criterion 10547.31 Hannan-Quinn 10541.71 RSTi =3586.38−0.150746 x TOTWRKi , R2=0.103287,SER=421.1357 (38.9124) (0.0167403) Question? could you please help with this question below. 3) By observing the GRETL output in Part (1) above, provide a detailed explanation of the coefficient of determination. Based on your analysis, is this a good model? Why or why not?To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 46 feet. Assume the population standard deviation is 4.5 feet. At α=0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. The critical value(s) is/are Find the standardized test statistic z for μ1−μ2.A researcher claims that the average wind speed in a certain city is 8 miles per hour. A sample of 32 days has an average wind speed of 8.2 miles per hour. The standard deviation of the population is 0.6 mile per hour. At 0.05, is there enough evidence to reject the claim? STEP 2. The critical value (s) is/are: z1 = z2 =
- Pulse rates of adult men are approximately normal with a mean of 70 and a standard deviation of 8. Which choice correctly describes how to find the proportion of men that have a pulse rate greater than 78? (a) Find the area to the right of z = -1 under a standard normal curve. (b) Find the area to the right of z=1 under a standard normal curve. (c) Find the area to the left of z = 1 under a standard normal curve. (d) Find the area between z=-1 and z=1 under a standard normal curve. (e) None of the aboveThe finished inside diameter of a piston ring is normally distributed with a mean of 10 centimeters and a standard deviation of 0.03 centimeter. If in a couple of years, the mean and the standard deviation of the nished inside diameter of a piston ring change both to dierent values μ and σ, what proportion of rings will have inside diameters exceeding μ + 2.5σ?A series of measurements in the lab led to an experimental result of 32.9 mL, with a calculated standard deviation of 0.3 mL. What is the standard way to report this result? Select one: 32.6-33.2 mL 32.9 ± 0.3 mL 32.9 ± 0.30 mL = 32.9 mL
- A random sample of 16 adult male wolves from the Canadian Northwest Territories gave an average weight x₁ = 97 lb with estimated sample standard deviation s₁ = 6.7 lb. Another sample of 26 adult male 14 wolves from Alaska gave an average weight x2 = 88 lb with estimated sample standard deviation $₂ = 7.5 lb. USE SALT (a) Let u represent the population mean weight of adult male wolves from the Northwest Territories, and let μ2 represent the population mean weight of adult male wolves from Alaska. Find a 75% confidence interval for μ1-2. (Round your answers to one decimal place.) lower limit upper limit (b) Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 75% level of confidence, does it appear that the average weight of adult male wolves from the Northwest Territories is greater than that of the Alaska wolves? Because the interval contains only…A random sample of 17 adult male wolves from the Canadian Northwest Territories gave an average weight x1 = 98.6 pounds with estimated sample standard deviation s1 = 5.6 pounds. Another sample of 26 adult male wolves from Alaska gave an average weight x2 = 88.2 pounds with estimated sample standard deviation s2 = 6.0 pounds. (a) Categorize the problem below according to parameter being estimated, proportion p, mean μ, difference of means μ1 – μ2, or difference of proportions p1 – p2. Then solve the problem. μp μ1 – μ2p1 – p2 (b) Let μ1 represent the population mean weight of adult male wolves from the Northwest Territories, and let μ2 represent the population mean weight of adult male wolves from Alaska. Find a 99% confidence interval for μ1 – μ2. (Use 1 decimal place.) lower limit upper limit (c) Examine the confidence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of…