Based on a sample of restaurants in a large city the

Question

1. Referring to the description of the population variance, σ², devise a method of estimating σ² based on the frequencies, f_x.

2. Referring to Exercise 1, and using the data in Exercise 2, estimate σ, the population standard deviation.

Exercise 1

Referring to the description of the population variance, σ², devise a method of estimating σ² based on the frequencies, f_x.

Exercise 2

Suppose health inspectors rate sanitation conditions at restaurants on a five point scale, where a 1 indicates poor conditions and a 5 is excellent. Based on a sample of restaurants in a large city, the frequencies are found to be f₁ = 5, f₂ = 8, f₃ = 20, f₄ = 32, and f₅ = 23. What is the sample size, n? Verify that the sample mean is X‾ = 3.7.