Answer:
The total number of interviews will be about 9552, give or take 37.4 or so.
Step-by-step explanation:
Data given
Total of 50000 households
represent the average number of people in household
represent the sample standard deviation of the number of people in household
n= 400 represent the sample size.
Solution to the problem
We can assume that the sample of 400 households are selected using random sampling from a grand box of 50000, and we select 400.
The expected value for the average number of people in a household is 2.38 and the standard deviation is 1.87.
We ar einterested on this case on the expected value for the sum and is defined as:
Expected value sum = Number selected * Expected value= 400*2.38=952
The reason of this is this one: From the definition of sample mean we have:
Where T represent the sum or the total, if we solve for T we got:
Assuming that and if we find the expected value for the total and the variance we got:
And the deviation would be:
And now the standard error for the sum is defined as the product of the square root of n and the single deviation of a box like this:
So then the correct answer would be:
The total number of interviews will be about 9552, give or take 37.4 or so.