Question

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 the US Census Bureau.]

Suppose that the true population mean µ = 99.2 and standard deviation σ = 21 are unknown to the Delaware tourism board. They select a simple random sample of 50 full-service restaurants located within the state to estimate µ. 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, σ M) is ___

Answer 1

The standard error (σM), for the full-service restaurants sample in Delaware, is calculated to be approximately 2.57 seats. It is found by dividing the sample standard deviation of 18.2 by the square root of the sample size, which is 50.

Step-by-step explanation:

The standard deviation of the distribution of sample means, also known as the standard error (σM), can be calculated using the formula σM = s / √ n, where s is the sample standard deviation, and n is the sample size. In Delaware, for a sample size of 50 full-service restaurants with a sample standard deviation of 18.2, the standard error is calculated as follows:

1. First, identify the sample standard deviation (s) as 18.2.
2. Next, find the square root of the sample size (n) which is √50.
3. Divide the sample standard deviation by the square root of the sample size to get the standard error (σM).

Calculating this gives us σM = 18.2 / √50 = 18.2 / 7.07 ≈ 2.57. Therefore, the standard error (standard deviation of the distribution of sample means) is approximately 2.57 seats.