Periodically, customers of a financial services company are asked to evaluate the company's financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use α = 0.05 and test to see whether the consultant with more experience has the higher population mean service rating. Consultant A Consultant B n1 = 16 n2 = 10 x1 = 6.81 x2 = 6.26 s1 = 0.68 s2 = 0.75 (a) State the null and alternative hypotheses. 1. H0: μ1 − μ2 = 0 Ha: μ1 − μ2 ≠ 0 2. H0: μ1 − μ2 ≤ 0 Ha: μ1 − μ2 > 0 3. H0: μ1 − μ2 ≠ 0 Ha:μ1 − μ2 = 0 4. H0: μ1 − μ2 ≤ 0 Ha:μ1 − μ2 = 0 5. H0:μ1 − μ2 > 0 Ha: μ1 − μ2 ≤ 0 (b) Compute the value of the test statistic. (Round your answer to three decimal places.) What is the p-value? (Round your answer to four decimal places.) p-value = (c) What is your conclusion? 1. Reject H0. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating. 2. Reject H0. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating. 3. Do not reject H0. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating. 4. Do not Reject H0. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.

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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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Periodically, customers of a financial services company are asked to evaluate the company's financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use

α = 0.05

and test to see whether the consultant with more experience has the higher population mean service rating.

Consultant A	Consultant B
n₁ = 16	n₂ = 10
x₁ = 6.81	x₂ = 6.26
s₁ = 0.68	s₂ = 0.75

(a)

State the null and alternative hypotheses.

1. H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

2. H₀: μ₁ − μ₂ ≤ 0

H_a: μ₁ − μ₂ > 0

3. H₀: μ₁ − μ₂ ≠ 0

H_a:μ₁ − μ₂ = 0

4. H₀: μ₁ − μ₂ ≤ 0

H_a:μ₁ − μ₂ = 0

5. H₀:μ₁ − μ₂ > 0

H_a: μ₁ − μ₂ ≤ 0

(b)

Compute the value of the test statistic. (Round your answer to three decimal places.)

What is the p-value? (Round your answer to four decimal places.)

p-value =

(c)

What is your conclusion?

1. Reject H₀. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating.

2. Reject H₀. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.

3. Do not reject H₀. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating.

4. Do not Reject H₀. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.

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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