Question

In a poll of 150 randomly selected U.S. adults, 79 said they favored a new proposition. Based on this poll, compute a 90% confidence interval for the proportion of all U.S. adults in favor of the proposition (at the time of the poll). Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places. What is the lower limit of the 90% confidence interval? What is the upper limit of the 90% confidence interval?

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 79 / 150 = 0.527

1 - = 1 - 0.527 = 0.473

Z/2 = Z0.05 = 1.645

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

= 1.645 (((0.527 * 0.473) / 150)

= 0.067

A 90% confidence interval for population proportion p is ,

± E

= 0.527 ± 0.067

= ( 0.460, 0.594 )

lower limit = 0.460

upper limit = 0.594