A sample of 50 Fortune 500 companies (Fortune, April $14,2003$ showed that 5 were based in New York, 6 in California, 2 in Minnesota, and I in Wisconsin.
a. Develop an estimate of the proportion of Fortune 500 companies based in Minnesota.
b. Develop an estimate of the number of Fortune 500 companies based in Minnesota.
c. Develop an estimate of the proportion of Fortune 500 companies that are not based in these four states.
July 16, 2019
I believe the book answer for (a) is incorrect; it should be .04
all right. This question gives us some information about the locations of 50 Fortune 500 companies, and it wants us to use point estimators to make some claims about the population. So part eh asks for the proportion of companies located in Minnesota, and it wants a point estimator for that. So for a sample, that's gonna be the number in Minnesota all over the total number, and our sample, which is two in Minnesota, divided by 50 in our sample, which simplifies 2.0. For then, Part B wants us to use this estimator to determine the expected amount of companies based in Minnesota in the population. So we can say that the expected value is equal to the total amount of people in the population, or in this case, cos times the proportion we expect to be based in Minnesota, which is equal to 500 times 0.4 which is equal to 20. Then part See wants us to find the proportion of companies not based in Minnesota based on a point estimator, so that's equal to they're 50 total states, minus the number of states we don't want. So number of companies in those five states all over our sample size of 50. So plug in the numbers in get 50 minus looking at our data five plus six plus two plus one. Oh, over 50. And that simplifies to 36 over 50 or as a decimal 0.72