Question

The manager of a resort hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel's accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of future weekend guest bills to test the manager's claim.

(a)

Which form of the hypotheses should be used to test the manager's claim? Explain.

H₀: μ ≥ 600

H_a: μ < 600

H₀: μ ≤ 600

H_a: μ > 600

H₀: μ = 600

H_a: μ ≠ 600

A) The hypotheses H₀: μ ≥ 600 and H_a: μ < 600 should be used because the accountant wants to test the manager's claim that the mean guest bill μ is greater than or equal to 600 and find evidence to support μ < 600.

B)The hypotheses H₀: μ ≤ 600 and H_a: μ > 600 should be used because the accountant wants to test the manager's claim that the mean guest bill μ is less than or equal to 600 and find evidence to support μ > 600.   

C)The hypotheses H₀: μ = 600 and H_a: μ ≠ 600 should be used because the accountant wants to test the manager's claim that the mean guest bill μ is equal to 600 and find evidence to support μ ≠ 600.

(b)

What conclusion is appropriate when

H₀

cannot be rejected?

A)We are able to conclude that the manager's claim is wrong. We can conclude that μ = 600.

B)We are not able to conclude that the manager's claim is wrong.We cannot conclude that μ > 600.    

C) We are not able to conclude that the manager's claim is wrong. We cannot conclude that μ ≠ 600.

D) We are able to conclude that the manager's claim is wrong. We can conclude that μ ≤ 600.

E) We are not able to conclude that the manager's claim is wrong. We can conclude that μ ≥ 600.

(c)

What conclusion is appropriate when

H₀

can be rejected?

A) We are not able to conclude that the manager's claim is wrong. We can conclude that μ < 600.

B) We are not able to conclude that the manager's claim is wrong. We can conclude that μ > 600.    

C) We are able to conclude that the manager's claim is wrong. We can conclude that μ < 600.

D)We are able to conclude that the manager's claim is wrong. We can conclude that μ ≠ 600.

E) We are able to conclude that the manager's claim is wrong. We can conclude that μ > 600.

Answer 1

a) The manager of a resort hotel stated that the mean guest bill for a weekend is $600 or less.

Hence the hypothesis are :

H₀: μ ≤ 600

H_a: μ > 600

B)The hypotheses H₀: μ ≤ 600 and H_a: μ > 600 should be used because the accountant wants to test the manager's claim that the mean guest bill μ is less than or equal to 600 and find evidence to support μ > 600.   

b)

When H₀ cannot be rejected :

This means there are sufficient evidences to support the claim that the mean guest bill for a weekend is $600 or less.

Hence the correct option is :
B) We are not able to conclude that the manager's claim is wrong. We cannot conclude that μ > 600.   

c)

When H₀ can be rejected :

This means there are no sufficient evidences to support the claim that the mean guest bill for a weekend is $600 or less.

Hence the correct option is:

E) We are able to conclude that the manager's claim is wrong. We can conclude that μ > 600.