Question

A recent poll randomly selects 150 thirty-five year old females residing in Essex County. For this sample, 37
reported that they are married. (Round all final answers to FOUR decimals.)
a) What is the population and parameter that is being discussed?
b) Construct a 95% Confidence Interval for the population parameter. USE THE WORDS RELATIVE TO
PARAMETER AND POPULATION.
c) Calculate the margin of error.
d) Using the variable discussed in this problem interpret the meaning of the 95% Confidence Interval for
the population parameter.

Answer 1

a)

Population parameter is population proportion p .

b)

Sample proportion = 37 / 150 = 0.2467

95% confidence interval for p is

- Z * sqrt( ( 1 - ) / n) < p < + Z * sqrt( ( 1 - ) / n)

0.2467 - 1.96 * sqrt( 0.2467 * 0.7533 / 150) < p < 0.2467 + 1.96 * sqrt( 0.2467 * 0.7533 / 150)

0.1778 < p < 0.3157

90% confidence interva lis between (0.1778 , 0.3157)

c)

margin of error = Z * sqrt( ( 1 - ) / n)

= 1.96 * sqrt( 0.2467 * 0.7533 / 150)

= 0.0690

d)

Interpretation -

We are 95% confident that popuation proportion of the females reported that they are married is between

0.1778 and 0.3157