7:40 PM Points: 10 Question 6 of 6 Suppose that 20% of the residents in a certai

Question

7:40 PM Points: 10 Question 6 of 6 Suppose that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly sample 400 state residents and will then compute the proportion in the sample that support a property tax increase. How likely is the resulting sample proportion to be within.04 of the true proportion (i.e., between.16 and .24)? (Hint: Use the sampling distribution of the sample proportion in this case.) It is certain that the resulting sample proportion will be within .04 of the There is roughly a 99.7% chance that the resulting sample proportion will There is roughly a 95% chance that the resulting sample proportion will There is roughly a 68% chance that the resulting sample proportion will true proportion. be within.04 of the true proportion. be within.04 of the true proportion. be within.04 of the true proportion.

Explanation / Answer

here std error of mean =(p(1-p)/n)1/2 =(0.2*0.8/400)1/2 =0.02

as 0.04 margin of error is equaivelent to 2 std deviation therfore from empirical rule:

there is roughly 95% chance that the resulting sample proportion will b within 0.04 of the true proportion

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