Question

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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 = 6.84	x2 = 6.27
s1 = 0.67	s2 = 0.75

(a)

State the null and alternative hypotheses.

H₀:

μ₁ − μ₂ ≠ 0

H_a:

μ₁ − μ₂ = 0

H₀:

μ₁ − μ₂ = 0

H_a:

μ₁ − μ₂ ≠ 0

    

H₀:

μ₁ − μ₂ > 0

H_a:

μ₁ − μ₂ ≤ 0

H₀:

μ₁ − μ₂ ≤ 0

H_a:

μ₁ − μ₂ = 0

H₀:

μ₁ − μ₂ ≤ 0

H_a:

μ₁ − μ₂ > 0

(b)

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

(c)

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

p-value =

(d)

What is your conclusion?

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

Answer 1

(a)

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:

Ha:

This corresponds to a right-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.

(b)

Test Statistics

(c)

The p-value is p = 0.0275

(d)

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

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