In a random sample of 8 people, the mean commute time to work was 33.5 minutes and the standard deviation was 7.3 minutes. A 98% confidence interval using the t-distribution was calculated to be (25.8,41.2). After researching commute times to work, it was found that the population standard deviation is 8.6 minutes. Find the margin of error and construct a 98% confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results.The margin of error of μ is _____(Round to two decimal places as needed.) ←In a random sample of 8 people, the mean commute time to work was 33.5 minutes and the standard deviationwas 7.3 minutes. A 98% confidence interval using the t-distribution was calculated to be (25.8,41.2). Afterresearching commute times to work, it was found that the population standard deviation is 8.6 minutes. Find themargin of error and construct a 98% confidence interval using the standard normal distribution with the appropriatecalculations for a standard deviation that is known. Compare the results.The margin of error of μ is.(Round to two decimal places as needed.)...Clear allCheck answer

Given,sample size, sample mean, standard deviation, 98% confidence interval using t-distribution is…

Answered: In a random sample of 8 people, the…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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In a random sample of 8 people, the mean commute time to work was 33.5 minutes and the standard deviation was 7.3 minutes. A 98% confidence interval using the t-distribution was calculated to be (25.8,41.2). After researching commute times to work, it was found that the population standard deviation is 8.6 minutes. Find the margin of error and construct a 98% confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results. The margin of error of μ is _____ (Round to two decimal places as needed.)

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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