Answered: Listed below are the numbers of years…

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. 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?

The test statistic, t,

The P-value is

State the conclusion for the test.

Fail to reject

the null hypothesis. There

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.

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.

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.

Reject

the null hypothesis. There

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).

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

18
Archbishops
17
18
12
14
1
15
16
10
16
13
10
12
13
14
12
16
15
8
16
9.
4
23
18
Monarchs
15
19
15
11
19
16
14
18
14
13
16
19

Listed below are the numbers of years that archbishops and monarchs in a certain country lived after their election
or coronation. Assume that the two samples are independent simple random samples selected from normally
distributed populations. Do not assume that the population standard deviations are equal. Use a 0.10 significance
level to test the claim that the mean longevity for archbishops is less than the mean for monarchs after coronation.
All measurements are in years.
Click the icon to view the table of longevities of archbishops and monarchs.

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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