There are 505 full-service restaurants in North Dakota. The mean number of seats
ID: 3236461 • Letter: T
Question
There are 505 full-service restaurants in North Dakota. The mean number of seats per restaurant is 74.1. Suppose that the true population mean mu = 74.1 and standard deviation sigma = 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 mu. The mean number of seats per restaurant in the sample is M = 78.3, with a sample standard deviation of s = 17.8. The standard deviation of the distribution of sample means (that is, the standard error, sigma_M) is _____ The standard or typical average difference between the mean number of seats in the 505 full-service restaurants in North Dakota (mu = 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 (M = 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 505 full-service restaurants in North Dakota (mu = 74.1) and the sample mean of any sample of size 45 is _____ The z-score 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 ____ 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.Explanation / Answer
a) SE = Standard deviation/ sqrt(n) = 17.8/sqrt(45)=2.653
b) Difference = 78.3 -74.1=4.2
C) The answer is 0 since the average of one sample observation will be equal to sample mean only.
D) Difference = 78.3-74.1=4.2
e) z score would be 0 for the sample mean.
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