Question

In a survey of 4,428 people, 49% approved of the way the president is handling COVID- 19. Construct a 90% confidence interval for the population of people who approve of the way that the president is handling COVID-19. Show your work, express your answer as an interval, and (if applicable) round your answer to 3 decimal places.

Answer 1

Solution:

Given:

Sample size = n = 4428

Sample proportion =

confidence level = c = 90%

where

Z_c is z critical value for c = 90% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.90) / 2 = 1.90 / 2 = 0.9500

Look in z table for Area = 0.9500 or its closest area and find corresponding z value.

Area 0.9500 is in between 0.9495 and 0.9505 and both the area are at same distance from 0.9500

Thus we look for both area and find both z values

Thus Area 0.9495 corresponds to 1.64 and 0.9505 corresponds to 1.65

Thus average of both z values is : ( 1.64+1.65) / 2 = 1.645

Thus Z_c = 1.645

Thus

thus

Thus  a 90% confidence interval for the population of people who approve of the way that the president is handling COVID-19 is: