Answered: A company claims that the mean weight…

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 company claims that the mean weight per apple they ship is 120 grams with a standard deviation of 12 grams. Data generated from a sample of 49 apples randomly selected from a shipment indicated a mean weight of 122.5 grams per apple. Is there sufficient evidence to reject the company’s claim? (use α = 0.05)

(Null and Alternate Hypothesis, Rejection Region)

A. Ho: µ = 120; Ha: µ < 120; Rejection Region: z < -1.64

B. Ho: µ = 120; Ha: µ < 120; Rejection Region: t < -1.80

C. Ho: µ = 120; Ha: µ > 120; Rejection Region: z > 1.64

D. Ho: µ = 120; Ha: µ ≠ 120; Rejection Region: z < -1.96 or z > 1.96

E. Ho: µ = 120; Ha: µ ≠ 120; Rejection Region: t < -2.20 or t > 2.20

: (Test Statistic)

A. t = 0.03

B. z = 1.46

C. z = 0.03

D. z = 0.55

E. t = 1.46

(p-value and conclusion)

A. p = 1.856; FRHo (No sufficient evidence to reject the claim)

B. p = 0.144; RHo (Sufficient evidence exists to reject the claim)

C. p = 0.928; FRHo (No sufficient evidence to reject the claim)

D. p = 1.856; RHo (Sufficient evidence exists to reject the claim)

E. p = 0.144; FRHo (No sufficient evidence to reject the claim)

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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