Answered: Data on the weights (lb) of the…

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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Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts.			Diet	Regular
μ	μ1	μ2
n	39	39
x	0.79763 lb	0.81843 lb
s	0.00446 lb	0.00751 lb

a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda.

What are the null and alternative hypotheses?

A.H0: μ1≠μ2

H1: μ1<μ2

B. H0: μ1=μ2

H1: μ1<μ2

C.H0:μ1=μ2

H1: μ1>μ2

H0: μ1=μ2

H1: μ1≠μ2

The test statistic, t, is

(Round to two decimal places as needed.)

The P-value is

(Round to three decimal places as needed.)

State the conclusion for the test.

A.Fail to reject the null hypothesis. There

is not sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

B. Reject the null hypothesis. There is not sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

C. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

D. Reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

b. Construct a confidence interval appropriate for the hypothesis test in part (a).

________lb<μ1−μ2<________lb

(Round to three decimal places as needed.)

Does the confidence interval support the conclusion found with the hypothesis test?

No, or Yes,

because the confidence interval contains

only positive values or only negative values or zero.

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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