Question

In a survey of 865 registered voters in Washington, 408 people are in favor of making Pi Day an official holiday.

1. Which of the following would be the appropriate format for a confidence interval for the proportion of Washington voters who are in favor of making Pi Day an official holiday?

• A. a<σ<b
• B. a<¯x<b
• C. a<μ<b
• D. a<s<b
• E. a<p<b
• F. a<ˆp<
• G. a<x<b
• H. a<n<b

• 
  2. Using the format you selected above, find the 95% confidence interval for Pi Day support. (Round to four decimal places.)
  a=? b=?

• 
  3. What is the margin of error for this confidence interval? (Round to four decimal places.)
  ε=?

Answer 1

Solution :

Given that,

n = 865

x = 408

1) correct option is = E

a < p < b

2) Point estimate = sample proportion = = x / n = 408 / 865 = 0.4717

1 - = 1 - 0.4717 = 0.5283

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 (((0.4717 * 0.5283) / 865)

= 0.0333

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.4717 - 0.0333 < p < 0.4717 + 0.0333

( 0.4384 < p < 0.5050 )

a = 0.4384

b = 0.5050

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

E = 1.96 (((0.4717 * 0.5283) / 865)

E = 0.0333