A business survey randomly sampled 20 different hotels and 20 different log cabins in British Columbia and recorded each of their nightly rates. A natural log transformation was needed in order for the data to satisfy the assumptions for the t-tools. The table below gives the summary statistics for the natural logs of nightly rates.

Natural logarithm of nightly rate per type:

Hotel Rates

Mean: 4.6152

N: 20

Std. Deviation: 0.14510

Log Cabin Rates

Mean: 5.6555

N: 20

Std. Deviation: 0.18008

Total

Mean: 5.1353

N: 40

Std. Deviation: 0.55099

(a) Calculate the 90% confidence interval for the difference in mean logged nightly rates between hotels and log cabins. Back transform this confidence interval to the original scale and interpret this interval on the original scale.

(b) (Based on the confidence interval you found in part (a), after back transformation, would you conclude that there is a difference between the median rates for hotels and log cabins (with 90% confidence)? Explain the logic of your answer.