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 9440 observations, the sample mean interval was x1 = 63.6 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 24,053 observations, the sample mean time interval was x2 = 72.8 minutes. Historical data suggest that ?1 = 8.21 minutes and ?2 = 12.62 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.)lower limit =__upper limit =__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 40 mothers gave a sample mean of x1 = 68.36. Another random sample of 36 fathers gave x2 = 57.34. Assume that ?1 = 11.83 and ?2 = 11.72.(a)Let ?1 be the population mean of x1 and let ?2 be the population mean of x2. Find a 99% confidence interval for ?1 – ?2. (Round your answers to two decimal places.)lower limit=__upper limit=__

Sample size n1= 9440 , n2= 24.053 Sample mean xbar1 = 63.6 ,xbar2 = 72.8 Population standard…

Answered: The U.S. Geological Survey compiled…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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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 9440 observations, the sample mean interval was x₁ = 63.6 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 24,053 observations, the sample mean time interval was x₂ = 72.8 minutes. Historical data suggest that ?₁ = 8.21 minutes and ?₂ = 12.62 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.)

lower limit	=__
upper limit	=__

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 40 mothers gave a sample mean of x₁ = 68.36. Another random sample of 36 fathers gave x₂ = 57.34. Assume that ?₁ = 11.83 and ?₂ = 11.72.

(a)Let ?₁ be the population mean of x₁ and let ?₂ be the population mean of x₂. Find a 99% confidence interval for ?₁ – ?₂. (Round your answers to two decimal places.)

lower limit=__

upper limit=__

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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