Question

The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend

is $600 or less. Amember 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

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≥600Ha:μ<600H0:μ≤600Ha:μ>600H0:μ=600Ha:μ≠600

$

b. What conclusion is appropriate when H0 cannot be rejected?

c. What conclusion is appropriate when H0 can be rejected?

Answer 1

Answer:

a) For this case we are trying to proof that the mean guest bill for a weekend  is $600 or less, so that need to represent the alternative hypothesis, and on the null hypothesis we need to have the complement.

Null hypothesis :$\mu \geq 600$

Alternative hypothesis: $\mu <600$

b) For this case if we fail to reject the null hypothesis we can conclude that at the significance level used $\alpha$ we FAIL to reject the hypothesis that the mean is higher or equal than 600

c) For this case if we to reject the null hypothesis we can conclude that at the significance level used $\alpha$ we can reject the hypothesis and we can conclude that the true mean is significantly lower than 600

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

Solution to the problem

Part a

For this case we are trying to proof that the mean guest bill for a weekend  is $600 or less, so that need to represent the alternative hypothesis, and on the null hypothesis we need to have the complement.

Null hypothesis :$\mu \geq 600$

Alternative hypothesis: $\mu <600$

Part b

For this case if we fail to reject the null hypothesis we can conclude that at the significance level used $\alpha$ we FAIL to reject the hypothesis that the mean is higher or equal than 600

Part c

For this case if we to reject the null hypothesis we can conclude that at the significance level used $\alpha$ we can reject the hypothesis and we can conclude that the true mean is significantly lower than 600