Answered: population mean of x1 and let ?2 be the…

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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1.The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x₁ be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 8880 observations, the sample mean interval was x₁ = 63.0 minutes. Let x₂ be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 25,691 observations, the sample mean time interval was x₂ = 70.2 minutes. Historical data suggest that ?₁ = 8.70 minutes and ?₂ = 12.48 minutes. Let ?₁ be the population mean of x₁ and let ?₂ be the population mean of x₂.

(a) Compute a 95% confidence interval for ?₁ – ?₂. (Use 2 decimal places.)

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(b) Comment on the meaning of the confidence interval in the context of this problem. Does the interval consist of positive numbers only? negative numbers only? a mix of positive and negative numbers? Does it appear (at the 95% confidence level) that a change in the interval length between eruptions has occurred? Many geologic experts believe that the distribution of eruption times of Old Faithful changed after the major earthquake that occurred in 1959.

Because the interval contains only positive numbers, we can say that the interval length between eruptions has gotten shorter.Because the interval contains both positive and negative numbers, we can not say that the interval length between eruptions has gotten longer. We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that the interval length between eruptions has gotten longer.

2.A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x₁ be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x₂ be the empathy score of a father. A random sample of 37 mothers gave a sample mean of x₁ = 67.68. Another random sample of 30 fathers gave x₂ = 59.85. Assume that ?₁ = 11.90 and ?₂ = 10.78.

(a) Let ?₁ be the population mean of x₁ and let ?₂ be the population mean of x₂. Find a 90% confidence interval for ?₁ – ?₂. (Use 2 decimal places.)

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