During the 2009 holiday season, 436 randomly sampled American adults were surveyed regarding their average spending on Black Friday. A 95% confidence interval based on this sample is ($80.31,$89.11).(c) Determine the sample mean x and the sample standard deviation s of the sample.(d) Which would be the confidence level corresponding to an interval ($81.27,$88.15) for the data found in (c)?(e) If the values of the sample mean and sample standard deviation found in (c) do not change, find the sample size N for which a 99% confidence interval would have a margin of error smaller than 5.

c) The sample mean is 84.71 and it is calculated below: From the given information, the 95%…

Answered: During the 2009 holiday season, 436…

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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During the 2009 holiday season, 436 randomly sampled American adults were surveyed regarding their average spending on Black Friday. A 95% confidence interval based on this sample is ($80.31,$89.11).

(d) Which would be the confidence level corresponding to an interval ($81.27,$88.15) for the data found in (c)?

(e) If the values of the sample mean and sample standard deviation found in (c) do not change, find the sample size N for which a 99% confidence interval would have a margin of error smaller than 5.

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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