A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.61 hours, with a standard deviation of 2.39 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.43 hours, with a standard deviation of 1.61 hours. Construct and interpret a 90% confidence interval for the mean difference in leisure time between adults with no children and adults with children μ1−μ2. Let μ1 represent the mean leisure hours of adults with no children under the age of 18 and μ2 represent the mean leisure hours of adults with children under the age of 18. -The 90% confidence interval for μ1−μ2 is the range from hours tohours. (Round to two decimal places as needed.) -What is the interpretation of this confidence interval? A. There is 90% confidence that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours. B. There is 90% confidence that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours. C. There is a 90% probability that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours. D. There is a 90% probability that the difference of the means is in t

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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A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.61 hours, with a standard deviation of 2.39 hours. A random sample of

40 adults with children under the age of 18 results in a mean daily leisure time of 4.43 hours, with a standard deviation of 1.61

hours. Construct and interpret a 90%
confidence interval for the mean difference in leisure time between adults with no children and adults with children μ1−μ2.

Let μ1 represent the mean leisure hours of adults with no children under the age of 18 and

μ2 represent the mean leisure hours of adults with children under the age of 18.

-The 90% confidence interval for μ1−μ2
is the range from____ hours to____hours.

(Round to two decimal places as needed.)

-What is the interpretation of this confidence interval?

There is

90%

confidence that the difference of the means is in the interval. Conclude that there is

insufficient evidence of a

significant difference in the number of leisure hours.

There is

90%

confidence that the difference of the means is in the interval. Conclude that there is

significant difference in the number of leisure hours.

There is a

90%

probability that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours.

There is a

90%

probability that the difference of the means is in t

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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