There are 572 full service restaurants in Vermont The mean n

There are 572 full service restaurants in Vermont. The mean number of seats is 65.7.

Three different distributions There are 572 ful-service restaurants in Vermont. The mean number of seats per restaurant is 65.7. (Source: Data based on the 2002 Economic Census from U.S. Census Bureau.) Suppose that the true population mean mu - 65.7 and standard deviation sigma - 21 are unknown to the Vermont tourism board. They select a simple random sample of 55 ful-service restaurants located within the state to estimate mu.

Solution

5.

a)

sigma(X) = sigma/sqrt(n) = 21/sqrt(55) = 2.831639422 [ANSWER]

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b)

It is the population standard deviation,

sigma = 21. [ANSWER]

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c)

It is the sample standard deviation.

s = 19.1 [ANSWER]

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d)

It is the standard error in part a,

sigma(X) = 2.831639422 [ANSWER]

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e)

z = (M - u)*sqrt(n)/sigma = (69.9-65.7)*sqrt(55)/21 = 1.483239697 [ANSWER]

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f)

Using a table/technology, the right tailed area for the z score in e is

P(z>1.483239697) = 0.069005369 [ANSWER]