Pay attention to text in bold letters Be sure you understand

Pay attention to text in bold letters. Be sure you understand if the question pertains to a distribution of X values (scores) or a distribution of sample means (M values) 6. Three different distributions There are 559 full-service restaurants in Delaware. The mean number of seats per restaurant is 99.2. [Source: Data based on the 2002 Economic Census from U.S. Census Bureau.] Suppose that the true population mean = 99.2 and standard deviation = 20 are unknown to the Delaware 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 = 103.4, with a sample standard deviation of s = 18.2 The standard deviation of the distribution of sample means (that is, the standard error, aM) is Although and are unknown to the Delaware tourism board, they are known to you for the purposes of calculating these answers.) (Note: The standard or typical average difference between the mean number of seats in the 559 full-service restaurants in Delaware ( = 99.2) and one randomly selected full-service restaurant in Delaware is The standard or typical average difference between the mean number of seats in the sample of 50 restaurants (M = 103.4) and one randomly selected restaurant in that sample is The standard or typical average difference between the mean number of seats in the 559 full-service restaurants in Delaware ( = 99.2) and the sample mean of any sample of size 50 is The z-score that locates the mean number of seats in the Delaware tourism board\'s sample (M distribution of sample means is 103.4) in the Use the unit normal tables and accompanying figures to answer the question that follows. To use the tables, click on the Unit Normal Tables tab below the figures, and use the dropdown box to select the desired range of z-score values. A table of the proportions of the normal distribution corresponding to that range of z-scores will appear. If you need a different range of z-scores, simply click on the box again and select a new range. Suggestion: Make a sketch of the area under the normal distribution you are seeking. This sketch will help you determine which column(s) of the normal table to use in determining the appropriate probability.

Solution

The standard error is: sigma m=sigma/root over n

=20/root over (50)

=2.82

The standard or typical average difference between the mean number of seats in the 559 full service restaurant is M-mu=103.4-99.2=4.2

The z score is:

M-mu/(sigma/root over n)

=(4.2)/2.82=1.48