Question

USA TODAY(USA TODAY, September 7, 2016) reported that based on a survey of a representative sample of 1000 adult Americans, 840 out of 1000 participants claimed that they would prefer adding cheese on their burgers.

a.Use the given information to estimate the proportion of proportion of adult Americans who prefer cheese on their burgers.

b.Verify that the conditions needed in order for the margin of error formula to be appropriate are met.

c.Calculate the margin of error.

d.Interpret the margin of error in the context of this problem.

Answer 1

a) the point estimte for the proportion of adult Americans who prefer cheese on their burgers:

b) the condition needed is

The sample must be reasonably random.

The sample must be less than 10% of the population.

The sample must be large enough so that:

and

for a confidence interval

c) The margin of error =

for 95% confidence interval

d) The margin of error is a measure of the maximum amount by which the sample results are expected to differ from those of the actual population.