A restaurant chain needs to decide whether to open a location in a particular to

Question

A restaurant chain needs to decide whether to open a location in a particular town or not. To gauge the town's demand for a new restaurant, a market analyst asks 51 families how many times per year they eat out, obtaining a sample average of 45 times, with a sample variance of 225. If the true variance for demand is too high, the restaurant may find the new market too risky to enter. Assuming that the numbers of times that families in the town eat out actually follow a normal distribution with unknown standard deviation sigma, find a 95% upper confidence limit b such that Pr(sigma

Explanation / Answer

Note that              
              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha = (1 - confidence level) =    0.05          
X = sample mean =    45          
z(alpha) = critical z for the confidence interval =    1.644853627          
s = sample standard deviation =    15          
n = sample size =    51          
              
Thus,              

Upper bound = b =   48.45488366   [ANSWER]      
              

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