Question

] The average cost per night of a hotel room in San Francisco is $550 with a standard deviation is $150 based on a sample of 50 hotel room rates. a) Clearly state what the random variable in this problem is? b) What is an appropriate distribution to be used for finding the confidence intervals for this problem and why? c) Construct a 99% confidence interval estimate on the mean of all hotel room rates. d) What is the 90% confidence interval estimate? e) What is the 95% confidence interval estimate?

Answer 1

a) In this context, the random variable is the " average cost per night of a hotel room in San Francisco".

b) The appropriate distribution will be the Normal distribution, this assumption turns out to be relatively uncontroversial, at least when each of the samples is large, such as N ≥ 30

Central Limit Theorem which says that: given random and independent samples of N observations each, the distribution of sample means approaches normality as the size of N increases, regardless of the shape of the population distribution.

c)   The 99% confidence interval for the population mean expressed as:

Here we have

   and  

95% confidence interval :

99% confidence interval is (495.2699 , 604.7301)

d)   The 90% confidence interval for the population mean expressed as:

Here we have

   and  

95% confidence interval :

90% confidence interval is (514.9982 , 585.0018)

e)   The 95% confidence interval for the population mean expressed as:

Here we have

   and  

95% confidence interval :

95% confidence interval is (508.4221 , 591.5779 )