Question

1. We wish to estimate what percent of adult residents in a certain county are parents. Out of 600 adult residents sampled, 330 had kids. Based on this, construct a 95% confidence interval for the proportion p of adult residents who are parents in this county.

Express your answer in tri-inequality form. Give your answers as decimals, to three places.

< p < Express the same answer using the point estimate and margin of error. Give your answers as decimals, to three places.

p = ±±

2. We wish to estimate what percent of adult residents in Ventura County like chocolate. Out of 600 adult residents sampled, 454 like chocolate. Based on this, construct a 90% confidence interval for the proportion (p) of adult residents who like chocolate in Ventura County.

1. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.

   Confidence interval =

2. 
   
3. Express the same answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.

   < p <

4. 
   
5. Express the same answer using the point estimate and margin of error. Give your answers as decimals, to three places.

   p = ±±

Answer 1

Solution :

1) Given that,

n = 600

x = 330

Point estimate = sample proportion = = x / n = 330 / 600 = 0.550

1 - = 1 - 0.550 = 0.450

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.960}

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 (((0.550 * 0.450) / 600)

= 0.040

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.550 - 0.040 < p < 0.550 + 0.040

( 0.510 < p < 0.590 )

± E  

= 0.550 ± 0.040

= ( 0.510, 0.590 )

2) Given that,

n = 600

x = 454

Point estimate = sample proportion = = x / n = 454 / 600 = 0.757

1 - = 1 - 0.757 = 0.243

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645 (((0.757 * 0.243) / 600 )

= 0.029

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.757 - 0.029 < p < 0.757 + 0.029

( 0.728 < p < 0.786 )

± E

= 0.757  ± 0.029

= ( 0.728, 0.786 )