Question

In: Statistics and Probability

A researcher believes that 8% of males smoke cigarettes.

A researcher believes that 8% of males smoke cigarettes. If the researcher is correct, what is the probability that the proportion of smokers in a sample of 512 males would differ from the population proportion by greater than 3%? Round your answer to four decimal places.

Solutions

Expert Solution

 

n = 512

= 8% =0.08

1 - = 1 - 0.08 = 0.92

=   = 0.08

= √ ( 1 - ) / n

=  √ 0.08 * 0.92 / 512

= 0.0120

= 0.0120

P(   > 0.03 )

1 - P ( 0.05 < < 0.11 )

1 -P ( 0.05 - 0.08 / 0.0120 ) < ( -    / ) < ( 0.11 - 0.08 / 0.0120)

1 -P ( - 0.03 / 0.0120 < z < 0.03 / 0.0120 )

1 - P (-2.5 < z < 2.5 )

1 - P ( z < 2.5) - p ( z < -2.5)

Using z table

= 1 - ( 0.9938 - 0.0062)

= 1 - 0.9876

= 0.0124

Probability = 0.0124.

orchestra answered 2 years ago
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