According to a Gallup poll conducted April 3–6, 2014, 21% of Americans aged 18 t

Question

According to a Gallup poll conducted April 3–6, 2014, 21% of Americans aged 18 to 29 said that college loans and/or expenses were the top financial problem facing their families. Suppose that this poll was based on a random sample of 1450 Americans aged 18 to 29.

a. What is the point estimate of the corresponding population proportion?

b. Construct a 95% confidence interval for the proportion of all Americans aged 18 to 29 who will say that college loans and/or expenses were the top financial problem facing their families. What is the margin of error for this estimate?

Please show ALL work and explain the steps!!! I will rate:)

Explanation / Answer

a) the sample proportion p is a point estimate of the population proportion P.

Point estimate = 21%

b) for 95% confidence interval z value = 1.96

CI = p + / -z * sqrt( p( 1-p)/n)

= 0.21 + /- 1.96 * sqrt ( .21 * .79/ 1450)

= (0.189 , 0.231)

Margin of error = z * sqrt( p( 1-p)/n)

=  1.96 * sqrt ( .21 * .79/ 1450)

= 0.021

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