Answered: A survey conducted by the American…

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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Question

A survey conducted by the American Automobile Association showed that a family of four spends an average of $215.60 per day while on vacation. Suppose a sample of 64 families of four vacationing at Niagara Falls resulted in a sample mean of $256.45 per day and a sample standard deviation of $78.50.

(a)

Develop a 95% confidence interval estimate of the mean amount spent per day in dollars by a family of four visiting Niagara Falls. (Round your answers to the nearest cent.)

$ to $

(b)

Based on the confidence interval from part (a), does it appear that the population mean amount spent per day by families visiting Niagara Falls differs from the mean reported by the American Automobile Association? Explain.

No. The overall average daily vacation expenditure of $215.60 per day is between the upper and lower limits of the confidence interval for the population mean at Niagara Falls. This suggests we cannot determine if the population mean at Niagara Falls is greater than the overall average daily vacation expenditure.Yes. The overall average daily vacation expenditure of $215.60 per day is between the upper and lower limits of the confidence interval for the population mean at Niagara Falls. This suggests the population mean at Niagara Falls is less than the overall average. Yes. The lower limit for the confidence interval for the population mean at Niagara Falls is greater than overall average daily vacation expenditure of $215.60 per day. This suggests the population mean at Niagara Falls is greater than the overall average.Yes. The upper limit for the confidence interval for the population mean at Niagara Falls is less than overall average daily vacation expenditure of $215.60 per day. This suggests the population mean at Niagara Falls is less than the overall average.No. The lower limit for the confidence interval for the population mean at Niagara Falls is greater than overall average daily vacation expenditure of $215.60 per day. This suggests we cannot determine if the population mean at Niagara Falls is greater than the overall average daily vacation expenditure.

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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