Question

In a recent​ year, a poll asked 2184 random adult citizens of a large country how they rated economic conditions. In the​ poll, 28​% rated the economy as​ Excellent/Good. A recent media outlet claimed that the percentage of citizens who felt the economy was in​ Excellent/Good shape was 26​%. Does the poll support this​ claim? ​a) Test the appropriate hypothesis. Find a 90​% confidence interval for the proportion of adults who rated the economy as​ Excellent/Good.

a.) ( , )

Answer 1

90% confidence interval for p is

- Z/2 * sqrt [ ( 1 - ) / n ] < p < + Z/2 * sqrt [ ( 1 - ​​​​​​​) / n ]

0.28 - 1.645 * sqrt [ 0.28 ( 1 - 0.28) / 2184] < p < 0.28 + 1.645 * sqrt [ 0.28 ( 1 - 0.28) / 2184]

0.264 < p < 0.296

90% CI is ( 0.264 , 0.296 )

Since claimed proportion 0.26 not contained in confidence interval, reject H0.