2) We make four independent measurement of the solidity of a certain polymer. We assumethat the measurement errors are normal and have zero expectation. We also assume that allmeasurements have the same standard deviation. The measurement values areX₁ = 20, X₂ = 22, X3 = 19, X4 = 19.a) Estimate the solidity and give a 95% confidence interval assuming that the standard deviationfor one measurement is o = 3.b) Assume now the standard deviation not know. Estimate the standard deviation from thedata..c) Test the hypothesis that the conductivity is 17 on the 90% level assuming the standarddeviation to be known and equal to o = 3.

Hypothesis tests and confidence intervals are used to compare whether the sample is taken from the…

Answered: 2) We make four independent measurement…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x-6.4, y= 6.1, r= - 0.226, P-value = 0.115, and y = 7.81 - 0.269x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x= 6. Use a 0.10 significance level. The best predicted value of y when x= 6 is (Round to one decimal place as needed.)
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 133 to 188 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x=167.80 cm, y=81.36 kg, r=0.286, P-value=0.004, and y=−108+1.19x. Find the best predicted value of y (weight) given an adult male who is 138 cm tall. Use a 0.10 significance level.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 139 to 194 cm and weights of 39 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x= 167.63 cm, y = 81.47 kg, r=0.106, P-value = 0.294, and y = - 108 + 1.04x. Find the best predicted value of y (weight) given an adult male who is 172 cm tall. Use a 0.05 significance level. The best predicted value of y for an adult male who is 172 cm tall is kg. (Round to two decimal places as needed.)
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.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 138 to 194 cm and weights of 39 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x=167.95 cm, y=81.57 kg, r=0.362, P-value=0.000, and y=−103+1.07x. Find the best predicted value of y (weight) given an adult male who is 180 cm tall. Use a 0.01 significance level. The best predicted value of y for an adult male who is 180 cm tall is= kg.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 133 to 188 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.54 cm, y = 81.35 kg, r=0.186, P-value = 0.064, and y = - 109 + 1.12x. Find the best predicted value of ŷ (weight) given an adult male who is 180 cm tall. Use a 0.10 significance level. The best predicted value of y for an adult male who is 180 cm tall is (Round to two decimal places as needed.) kg.
Let X1, . . . , Xn ∼ iid N(0, τ ). Find a pivot V (X, τ ) based on a complete sufficient statistic, andusing V (X, τ ) construct a 100γ% confidence interval for τ .
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 137 to 189 cm and weights of 37 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.50 cm, y =81.41 kg, r=0.232, P-value = 0.020, and y = - 109 + 1.17x. Find the best predicted value of y (weight) given an adult male who is 145 cm tall. Use a 0.01 significance level. The best predicted value of y for an adult male who is 145 cm tall is kg. (Round to two decimal places as needed.)
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Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 137 to 192 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.80 cm, y = 81.45 kg, r=0.211, P-value = 0.035, and y = -103 +1.07x. Find the best predicted value of ŷ (weight) given an adult male who is 145 cm tall. Use a 0.01 significance level. The best predicted value of y for an adult male who is 145 cm tall is (Round to two decimal places as needed.) kg.
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=77.5σ=77.5. You would like to be 99% confident that your esimate is within 0.5 of the true population mean. How large of a sample size is required?n = Do not round mid-calculation. However, use a critical value accurate to three decimal places — this is important for the system to be able to give hints for incorrect answers.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 138 to 190 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.88 cm, y = 81.51 kg, r=0.195, P-value = 0.052, and y= - 105 + 1.05x. Find the best predicted value of y (weight) given an adult male who is 184 cm tall. Use a 0.01 significance level. The best predicted value of y for an adult male who is 184 cm tall is kg. (Round to two decimal places as needed.)

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