Questions:

A large hotel chain is trying to decide whether to convert more of its rooms to non-smoking rooms. In a random sample of 400 guests last year, 166 had requested non-smoking rooms. This year, 205 guests in a sample of 380 preferred the non-smoking rooms.

1. Construct a 95% confidence interval for the difference between the population proportion of guests who requested non-smoking rooms in these two years.

2. Would you recommend that the hotel chain convert more rooms to non-smoking? Support your recommendation by testing the appropriate hypotheses at 0.01 level of significance.

3. Find the p-value of the test and briefly explain what the value means.