Anewspaper editor wants to investigate whether residents of the city support a proposal to build a new high school football stadium. the editor hires a polling firm to conduct a survey and requests that a sample of 500 residents be selected using a stratified sampling design based on voting districts within the city. which of the following methods will achieve the desired sampling design? (a) send a survey to all city residents and use the first 500 returned surveys for the sample. (b) select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained. (c) select one voting district at random, and then select a random sample of 500 from the selected voting district. (d) alphabetize a list of all city residents, and then select the first 500 residents on the list, classifying those selected by voting district. (e) select the first 500 city residents who attend the next high school football game.

Option B

Step-by-step explanation:

Stratified sampling design divides the given population into small sub-groups called strata. The members of each strata share some common features and at any particular time, a sample is randomly selected from each stratum which is then compared to the entire population. During random sampling, a number proportional to the stratum size is selected from all strata. The randomly selected samples from each strata are then combined to form a common random sample.

Considering that the editor wants to adopt stratified sampling, option B fits (Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.)

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

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step-by-step explanation: