A business survey randomly sampled 20 different hotels and 20 different log cabins in British Columbia and recorded each of their nightly rates. The survey provided the following summary statistics regarding nightly rates in Canadian dollars. Summary statistic Average Standard deviation Type Hotel rates 102.05 15.50 Note: Please note that the third column summarizes the differences between the original observations. By choosing a test, you will be using certain columns of the above table, but not all of them. (a) (1 mark) Are the two samples independent of each other or paired? Why? (b) (2 marks) Would a pooled t-test be appropriate to analyze this research problem using the summary statistics presented in the table above? Explain why or why not. What options could be considered in analyzing this question? Hotel rates (c) (5 marks) Suppose that it was decided that a natural log transformation was needed in order for the data to satisfy the assumptions for the t-tools. The table below is the summary statistics for the natural logs of nightly rates. Calculate the 90% confidence interval for the difference in mean logged nightly rates between hotels and log cabins (SHOW ALL STEPS). Back transform this confidence interval to the original scale and interpret this interval on the original scale. LnNightlyRate Log cabin rates Total Mean 4.6152 5.6555 Log cabin rates 290.28 52.05 5.1353 N 20 20 Differences -188.23 48.96 40 Std. Deviation .14510 .18008 .55099 (d) (2 mark) Based on the confidence interval you found in part (c), 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.