A health inspector wants to check compliance with a new city ordinance on meat storage. Since he can only inspect 10 of the 33 stores, he chooses to do a stratified random sample that consists of all 3 of the large chain stores, 4 of the 10 smaller chain stores, and 3 of the 20 locally-owned stores.

Question

A health inspector wants to check compliance with a new city ordinance on meat storage. Since he can only inspect 10 of the 33 stores, he chooses to do a stratified random sample that consists of all 3 of the large chain stores, 4 of the 10 smaller chain stores, and 3 of the 20 locally-owned stores.

From his inspection he finds that 2 of the 3 large chain stores are compliant, 1 of the 4 smaller chain stores is compliant, and 1 of the 3 locally-owned chain stores is compliant.

Using the sample results, estimate the proportion of the entire population of stores that is compliant with the ordinance.

Answer 1

A)

0.121

B)
0.4

C)
0.6

D)
0.879

Answer 2

The answer is D

Answer 3

To estimate the proportion of the entire population of stores that is compliant with the ordinance, we can use the information given about the sample results.

First, let's calculate the proportions of compliant stores within each stratum (large chain, small chain, and locally-owned).

For the large chain stores:
- The sample includes 3 large chain stores, and 2 of them are compliant.
- So, the proportion of compliant large chain stores in the sample is 2/3.

For the small chain stores:
- The sample includes 4 small chain stores, and 1 of them is compliant.
- So, the proportion of compliant small chain stores in the sample is 1/4.

For the locally-owned stores:
- The sample includes 3 locally-owned stores, and 1 of them is compliant.
- So, the proportion of compliant locally-owned stores in the sample is 1/3.

Next, we need to account for the different sizes of each stratum in the population.

The large chain stores represent 3 out of 33 stores in total (3/33).
The small chain stores represent 10 out of 33 stores in total (10/33).
The locally-owned stores represent 20 out of 33 stores in total (20/33).

Now, we can calculate the estimated proportion of compliant stores in the entire population by multiplying the proportions of compliant stores within each stratum by their respective stratum sizes, and then summing them up:

Estimated Proportion of Compliance = (Proportion of Compliance in Large Chains * Proportion of Large Chains) +
(Proportion of Compliance in Small Chains * Proportion of Small Chains) +
(Proportion of Compliance in Locally-owned Chains * Proportion of Locally-owned Chains)

= (2/3) * (3/33) + (1/4) * (10/33) + (1/3) * (20/33)

Simplifying this expression will give us the estimated proportion of compliance with the ordinance in the entire population of stores.