Question

1. From a recent poll in which respondents were asked if they felt that U.S. nuclear weapons made them feel safer, 550 out of 1000 people said “no.”

a) Find the sample proportion, ?̂, of people who responded “no”. Use the appropriate formula and show your work.

b) Find the margin of error for a 95% confidence interval for the true population proportion of people who feel that U.S. nuclear weapons do not make them feel safer. Round to three decimal places. Use the appropriate formula and show your work.

c) Construct this 95% confidence interval. Round to three decimal places. Use the appropriate formula and show your work.

d) Write a statement interpreting the confidence interval you found in part (c).

Answer 1

Solution :

Given that,

n = 1000

x = 550

a) Point estimate = sample proportion = = x / n = 550 / 1000 = 0.55

1 - = 1 - 0.55 = 0.45

b) At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

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

= 1.96 (((0.55 * 0.45) / 1000)

= 0.031

c) A 95% confidence interval for population proportion p is ,

± E  

= 0.55  ± 0.031

= ( 0.519, 0.581 )

d) We are 95% confident that the true proportion  of people who feel that U.S. nuclear weapons do not make them feel safer between 0.519 and 0.581.