A random sample of n = 81 observations has a mean x = 26.3 and a standard deviation s = 3.9. (a) Give the point estimate of the population mean ?. Find the 95% margin of error for your estimate. (Round your answer to four decimal places.) (b) Find a 90% confidence interval for ?. (Round your answers to three decimal places.) to What does "90% confident" mean? There is a 90% chance that an individual sample mean will fall within the interval. There is a 10% chance that an individual sample mean will fall within the interval limits. In repeated sampling, 10% of all intervals constructed in this manner will enclose the population mean. 90% of all values will fall within the interval limits. In repeated sampling, 90% of all intervals constructed in this manner will enclose the population mean. (c) Find a 90% lower confidence bound for the population mean ?. (Round your answer to two decimal places.) Why is this bound different from the lower confidence limit in part (b)? This bound is calculated using n, while the lower confidence limit in part (b) is calculated using n . This bound is calculated using n , while the lower confidence limit in part (b) is calculated using n. This bound is calculated using z?, while the lower confidence limit in part (b) is calculated using z?/2. The lower bounds are based on different values of x. This bound is calculated using z?/2, while the lower confidence limit in part (b) is calculated using z?.

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 n = 81 observations has a mean x = 26.3 and a standard deviation s = 3.9. (a) Give the point estimate of the population mean ?. Find the 95% margin of error for your estimate. (Round your answer to four decimal places.) (b) Find a 90% confidence interval for ?. (Round your answers to three decimal places.) to What does "90% confident" mean? There is a 90% chance that an individual sample mean will fall within the interval. There is a 10% chance that an individual sample mean will fall within the interval limits. In repeated sampling, 10% of all intervals constructed in this manner will enclose the population mean. 90% of all values will fall within the interval limits. In repeated sampling, 90% of all intervals constructed in this manner will enclose the population mean. (c) Find a 90% lower confidence bound for the population mean ?. (Round your answer to two decimal places.) Why is this bound different from the lower confidence limit in part (b)? This bound is calculated using n, while the lower confidence limit in part (b) is calculated using n . This bound is calculated using n , while the lower confidence limit in part (b) is calculated using n. This bound is calculated using z?, while the lower confidence limit in part (b) is calculated using z?/2. The lower bounds are based on different values of x. This bound is calculated using z?/2, while the lower confidence limit in part (b) is calculated using z?. (d) How many observations do you need to estimate ? to within 0.5, with probability equal to 0.95? (Round your answer up to the nearest whole number.) observations

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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