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 0.05 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. Archbishops 15 13 15 12 17 2 18 18 10 14 14 10 15 13 11 14 14 16 7 15 10 5 15 18 Monarchs 12 18 14 14 16 17 15 15 17 16 16 Click the icon to view the table of longevities of archbishops and monarchs. What are the null and alternative hypotheses? Assume that population 1 consists of the longevity of archbishops and population 2 consists of the longevity of monarchs. A. H0: μ1≤μ2 H1: μ1>μ2 B. H0: μ1=μ2 H1: μ1≠μ2 C. H0: μ1≠μ2 H1: μ1>μ2 D. H0: μ1=μ2 H1: μ1<μ2 The test statistic is nothing. (Round to two decimal places as needed.) The P-value is nothing. (Round to three decimal places as needed.) State the conclusion for the test. A. Reject the null hypothesis. There is not sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs. B. Reject the null hypothesis. There is sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs. C. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs. D. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.

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Description: 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 no

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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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

0.05

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.

Archbishops	15	13	15	12	17	2	18	18	10	14	14	10
15	13	11	14	14	16	7	15	10	5	15	18
Monarchs	12	18	14	14	16	17	15	15	17	16	16

Click the icon to view the table of longevities of archbishops and monarchs.

What are the null and alternative hypotheses? Assume that population 1 consists of the longevity of archbishops and population 2 consists of the longevity of monarchs.

H0:

μ1≤μ2

H1:

μ1>μ2

H0:

μ1=μ2

H1:

μ1≠μ2

H0:

μ1≠μ2

H1:

μ1>μ2

H0:

μ1=μ2

H1:

μ1<μ2

The test statistic is

nothing.

(Round to two decimal places as needed.)

The P-value is

nothing.

(Round to three decimal places as needed.)

State the conclusion for the test.

Reject

the null hypothesis. There

is not

sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.

Reject

the null hypothesis. There

sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.

Fail to reject

the null hypothesis. There

is not

sufficient evidence to support the claim that archbishops have lower mean longevity than monarchs.

Fail to reject

the null hypothesis. There

sufficient evidence to support the claim that archbishops have lower mean longevity than 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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