Question: You are to imagine that you are part of a select marketing group. This select group has been asked to consider the Colorado City Convention and Visitors Bureau survey of 25 hotels in the local area. The survey is concerned with the current availability of rooms. The availability of the rooms was as follows:

90, 72, 75, 60, 75, 72, 84, 72, 88, 74, 105, 115, 68, 74, 80, 64, 414, 82, 48, 58, 60, 80, 48, 58,108.

Each person in the marketing group must select a sample of 10 hotels from the list. In a report prepared and submitted by yourself only, describe the methods your imaginary group chose to select the 10 hotels. Discuss the pros and cons of each sampling method. Calculate the average number of available rooms in one sample. Calculate the standard deviation of the number of available rooms in that sample. Construct a frequency distribution of the sample mean, and plot a histogram of this distribution. Use the central limit theorem to calculate and identify the sampling distribution of the sample mean.

Consider the average available for all hotel rooms. Identify the point estimate of the average number of available hotel rooms in this lesson from each sample. Construct and Interpret a 95% confidence level for the true mean number of available hotel rooms, based on the point estimate of each sample. Describe how the confidence intervals will change depending on whether the population standard deviation is known or unknown