Answered: Students investigated the packaging of…

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

Students investigated the packaging of potato chips. They purchased

randomly selected bags of chips marked with a net weight of

28.3

grams at different randomly selected stores. They carefully weighed the contents of each bag, recording the weights below (in grams).

a) Do these data satisfy the assumptions for inference? Explain.

b) Find the mean and standard deviation of the weights.

c) Test the hypothesis that the net weight is as claimed.

29.2

28.2

29.3

28.7

28.9

28.5

a) The independence condition

▼

is not

is plausibly

satisfied and the Nearly Normal Condition

▼

is not

is plausibly

satisfied. Therefore, using the Student-t model for inference

▼

may not be

should be

reliable.

b) The mean weight is

nothing

grams.

(Round to two decimal places as needed.)

The sample standard deviation is

nothing

grams.

(Round to four decimal places as needed.)

c) Write appropriate hypotheses for the test.

H0:

▼

mu less than 28.3μ<28.3

mu equals 28.3μ=28.3

mu greater than 28.3μ>28.3

mu not equals 28.3μ≠28.3

HA:

▼

mu equals 28.3μ=28.3

mu greater than 28.3μ>28.3

mu less than 28.3μ<28.3

mu not equals 28.3μ≠28.3

The test statistic is

t=nothing.

(Round to two decimal places as needed.)

The P-value is

nothing.

(Round to three decimal places as needed.)

State your conclusion. Use

α=0.1.

▼

Do not reject

Reject

the null hypothesis. There

▼

is not

sufficient evidence to conclude that the mean weight is

▼

different from

less than

greater than

equal to

28.3

grams.

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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