Mean, Standard Deviation and Confidence Intervals

The average price charged denoted as  and standard deviation represented as  is 55.5833 and 8.5452 respectively. Also, the convectional significance level is 0.05 symbolized as .

Upper bound =  = 55.5833+1.96*(8.5452/ SQRT (36)) = 58.3747

Lower bound =   = 55.5833-1.96*(8.5452/ SQRT (36)) = 52.7919

Therefore, average price charged lies between 52.7919 and 58.3747

Question 3(b):

Upper bound =  = 52.6774+1.96*(9.9471/SQRT (124)) = 54.4282

Lower bound =   = 52.6774+1.96*(9.9471/SQRT (124)) = 50.9266

Therefore, the average price charged lies between 50.9266 and 54.4282

Question 3(c):

The confidence intervals do not overlap and the average price charged by restaurants with a water view exceeds those without a water view, therefore, I will recommend to Cassie to justify the premium price.

Question 3(d):

If the mean and the standard deviations are the same, therefore, the confidence intervals will overlap even if the sample sizes are different.

Question 3(e):

Repeating procedure from part (a) through part (c):

Upper bound =  = 55.5833+1.96*(8.5452/ SQRT (500)) = 56.3323

Lower bound =   = 55.5833-1.96*(8.5452/ SQRT (500)) = 54.8343

Upper bound =  = 55.5833+1.96*(8.5452/ SQRT (600)) = 56.2671

Lower bound =   = 55.5833-1.96*(8.5452/ SQRT (600)) = 54.8995

The two confidence intervals do overlap and the average price charged is the same, therefore, I will recommend to Cassie not to justify the premium price.

Question 3(e):

Cassie needs to be cautious about mean and standard deviation statistics rather than sample size when constructing and comparing two confidence intervals. This is because if the mean and the standard deviation are the same for the two groups, therefore, the confidence interval will overlap resulting in a different decision.