Question

# Even within a particular chain of hotels, lodging during the summer months can vary substantially depending...

Even within a particular chain of hotels, lodging during the summer months can vary substantially depending on the type of room and the amenities offered. Suppose that we randomly select 50 billing statements from each of the computer databases of the Hotel A, the Hotel B, and the Hotel C chains, and record the nightly room rates. The means and standard deviations for 50 billing statements from each of the computer databases of each of the three hotel chains are given in the table.

 Hotel A Hotel B Hotel C Sample average (\$) 135 180 125 Sample standard deviation 17.1 22.9 12.5

(a) Find a 95% confidence interval for the difference in the average room rates for the Hotel A and the Hotel C chains. (Round your answers to two decimal places.)
\$  to \$

(b) Find a 99% confidence interval for the difference in the average room rates for the Hotel B and the Hotel C chains. (Round your answers to two decimal places.)
\$  to \$

(c) Do the intervals in parts (a) and (b) contain the value (μ1μ2) = 0?

Yes, the interval in part (a) contains (μ1μ2) = 0.Yes, the interval in part (b) contains (μ1μ2) = 0.    Yes, both intervals contain (μ1μ2) = 0.No, neither interval contains (μ1μ2) = 0.

Why is this of interest to the researcher?

If (μ1μ2) = 0 is contained in the confidence interval, it is implied that there is no difference in the average room rates for the two hotels.If (μ1μ2) = 0 is contained in the confidence interval, it is implied that there was an error in the database records.    If (μ1μ2) = 0 is contained in the confidence interval, it is implied that the room rate for one of the hotels was \$0.If (μ1μ2) = 0 is contained in the confidence interval, it is implied that the average room rate for the two hotels was \$0.If (μ1μ2) = 0 is contained in the confidence interval, it is implied that there is a difference in the average room rates for the two hotels.

(d) Do the data indicate a difference in the average room rates between the Hotel A and the Hotel C chains?

Yes, the data indicate a difference in the average room rates between the Hotel A and the Hotel C chains.No, the data do not indicate a difference in the average room rates between the Hotel A and the Hotel C chains.

Do the data indicate a difference in the average room rates between the Hotel B and the Hotel C chains?

Yes, the data indicate a difference in the average room rates between the Hotel B and the Hotel C chains.No, the data do not indicate a difference in the average room rates between the Hotel B and the Hotel C chains.

a)

z value at 95% = 1.96

CI = ( x1 -x2)+/- z *sqrt(s1^2/n1 + s2^2/n2)
= ( 135 - 125) +/- 1.96 *sqrt(17.1^2/50 + 12.5^2/50)
= (4.13,15.87)

The 95% CI is 4.13 to 15.87

b)

z value at 99% = 2.576

CI = ( x1 -x2)+/- z *sqrt(s1^2/n1 + s2^2/n2)
= ( 180 - 125) +/- 2.576*sqrt(22.9^2/50 + 12.5^2/50)
= (45.50,64.50)

The 95% CI is 45.50 to 64.50

c)
No, neither interval contains (μ1 − μ2) = 0.

d)
Yes, the data indicate a difference in the average room rates between the Hotel A and the Hotel C chains.

Yes, the data indicate a difference in the average room rates between the Hotel B and the Hotel C chains