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.
A) 0.121
B) 0.4
C) 0.6
D) 0.879

B?

To estimate the proportion of the entire population of stores that is compliant with the ordinance, we need to calculate the weighted average of the compliance rates for each type of store.

The compliance rate for large chain stores is 2 out of 3, or 2/3.
The compliance rate for smaller chain stores is 1 out of 4, or 1/4.
The compliance rate for locally-owned stores is 1 out of 3, or 1/3.

To calculate the weighted average, we multiply each compliance rate by the proportion of that type of store in the population, and then sum up the results.

There are 3 large chain stores out of a total population of 33 stores, so the proportion of large chain stores is 3/33.
There are 10 smaller chain stores out of a total population of 33 stores, so the proportion of smaller chain stores is 10/33.
There are 20 locally-owned stores out of a total population of 33 stores, so the proportion of locally-owned stores is 20/33.

Now we can calculate the weighted average:
(2/3) * (3/33) + (1/4) * (10/33) + (1/3) * (20/33) = 2/33 + 10/132 + 20/99 ≈ 0.121.

Therefore, the estimate of the proportion of the entire population of stores that is compliant with the ordinance is approximately 0.121.

So the correct answer is A) 0.121.

To estimate the proportion of the entire population of stores that is compliant with the ordinance, we need to calculate the proportion of compliant stores in each stratum and then weigh them based on the size of the stratum.

First, let's calculate the proportion of compliant stores in each stratum:

- Large chain stores: Out of the 3 large chain stores inspected, 2 were compliant. The proportion of compliant stores in the large chain stratum is 2/3 = 0.6667.
- Smaller chain stores: Out of the 4 smaller chain stores inspected, 1 was compliant. The proportion of compliant stores in the smaller chain stratum is 1/4 = 0.25.
- Locally-owned stores: Out of the 3 locally-owned stores inspected, 1 was compliant. The proportion of compliant stores in the locally-owned stratum is 1/3 = 0.3333.

Next, we weigh these proportions based on the size of each stratum:

- Large chain stores represent 3/33 ≈ 0.0909 of the total population.
- Smaller chain stores represent 10/33 ≈ 0.3030 of the total population.
- Locally-owned stores represent 20/33 ≈ 0.6061 of the total population.

Finally, we multiply the proportion of compliant stores in each stratum by the proportion of the population represented by that stratum, and sum them up:

(0.6667 * 0.0909) + (0.25 * 0.3030) + (0.3333 * 0.6061) = 0.0606 + 0.0758 + 0.2020 = 0.3384

So, the estimated proportion of the entire population of stores that is compliant with the ordinance is approximately 0.3384. However, none of the given options match this estimate, so the correct answer is not provided.