Question
7.6
Attempts: Average: /6 6. Three different distributions There are 50s full-service restaurants in North Dakota. The mean number of seats per restaurant is 74.1. [Source: Data based on the 2002 Economic Census from U.S. Census Bureau.] Suppose that the true population mean 74.1 and standard deviation 20.2 are unknown to the North Dakota tourism board. They select a simple random sample of 45 full-service restaurants located within the state to estimate . The mean number of seats per restaurant in the sample is M = 78.3, with a sample standard deviation of s 178. The standard deviation of the distribution of sample means (that is, the standard error, ) is-- -.(Note: Although and are unknown to the North Dakota 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 505 full-service restaurants in North Dakota ( = 74.1) and one randomly selected full-service restaurant in North Dakota is The standard or typical average difference between the mean number of seats in the sample of 45 restaurants 78.3) and one randomly selected restaurant in that sample is The standard or typical average difference between the mean number of seats in the 50s fuil service restaurants in North Dakota ( = 74.1) and the sample mean of any sample of size 45 is e that locates the mean number of seats in the North Dakota tourism board's sample (M = 78.3) in the distribution of sample means is nying figures to answer the question that follows. To use the tables, click on Use the unit normal tables and accompa the Unit Normal Tables tab below the figures, and use the dropdown box to select the des values. A table of the proportions of the normal distribution corresponding to that range of you need a different range of z-scores, simply click on the box again and select a new Fscores il appear. suggestion: Make a sketeh of the area under the morma distribution you are seeking. this determine which column(s) of the normal table to use in determining the appropriate probabilit is sketch will help you
Explanation / Answer
Answer to the question)
The formula of standard error = population standard deviation divided by square root of sample size
Standard error = 20.2 / sqrt(45)
Standard error = 3.011238
.
Typical average difference from populatio mean is given by the population standard deviation = 20.2
.
Typical average difference from sample mean is given by sample standard deviation = 17.8
For the sample of size 45, the average difference between means will be = 3.011238 ..(that is it is equal to the standard error)
.
Z score = (78.3-74.1)/(3.011238) = 1.3948
