Answered: Bonnie and Katie buy some Better Burner…

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

Bonnie and Katie buy some Better Burner brand microwave popcorn in the 25-bag
Extra Value Pack. This brand claims perfect popcorn with a mean popping time of 4
minutes, and cites studies which show that all brands of microwave popcorn have
normally distributed popping times with standard deviation σ = 0.7 minutes. Before
sampling the 25 bags of popcorn themselves, they pop all 25 bags in their sample and
compute a mean popping time = 3.7 minutes.
Is this significant evidence that the true mean popping time really is different
from (not equal to) 4 minutes? Set up appropriate null and alternative hypotheses,
calculate the appropriate test statistic, find the P-value, and state your
conclusion (use α = .05).

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 + ...

Expert Solution

Step 1

Hypotheses to be tested:

$H_{0} : μ = 4 H_{1} : μ \neq 4$

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$Point Estimation, Limit Theorems, Approximations, and Bounds$

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