5. Three different distributions Aa Aa There are 431 full-service restaurants in

Question

5. Three different distributions Aa Aa There are 431 full-service restaurants in Alaska. The mean number of seats per restaurant is 77.9. [Source: Data based on the 2002 Economic Census from U.S. Census Bureau.] Suppose that the true population mean = 77.9 and standard deviation = 21 are unknown to the Alaska tourism board. They select a simple random sample of 50 full-service restaurants located within the state to estimate . The mean number of seats per restaurant in the sample is M = 82.1, with a sample standard deviation of s-18.6. (Note: The standard deviation of the distribution of sample means (that is, the standard error, is Although and are unknown to the Alaska tourism board, they are known to you for the purposes of calculating these answers.) The standard or typical average difference between the mean number of seats in the 431 full-service restaurants in Alaska ( 77.9) and one randomly selected full-service restaurant in Alaska is The standard or typical average difference between the mean number of seats in the sample of 50 restaurants (M- 82.1) and one randomly selected restaurant in that sample is The standard or typical average difference between the mean number of seats in the 431 full-service restaurants in Alaska (-77.9) and the sample mean of any sample of size 50 is The z-score that locates the mean number of seats in the Alaska tourism board's sample (M 82.1) in the distribution of sample means is

Explanation / Answer

The standard deviation of the distribution of sample mean (M) = / sqrt(n) = 21/ sqrt(50) = 2.97

The standard or average difference between mean number of seats in the 431 full- service restaurents in Alaska and one randomly selected restaurent in ALaska is = 21 seats

The standard or average difference between mean number of seats in the sample of 50 full- service restaurents in Alaska and one randomly selected restaurent in that sample is = 18 seats

The standard or average difference between mean number of seats in the 431 full- service restaurents in Alaska and seats in the sample of 50 full- service restaurents in Alaska = 21/ sqrt(50) = 2.97 seats

The Z- score that locates the mean number of seats in the Alska Tourism board's sample (M = 82.1) in the distribution of sample means is

Z = (Sample Mean - Population Mean) / (/sqrt(n) = (82.1 - 77.9)/ 2.97 = 1.414

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