Question

In February 2019, Gallup asked 1,015 randomly selected U.S. adults how prepared they felt teachers were to handle discipline issues in the classroom. 57% of respondents (a total of 579 respondents) indicated they felt teachers were unprepared or very unprepared. What is the correct 90% confidence interval for p in this scenario?

Answer 1

Solution :

n = 1015

= 0.570

1 - = 1 - 0.570 = 0.430

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 * (((0.570 * 0.430) /1,015)

= 0.026

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.570 - 0.026 < p < 0.570 + 0.026

0.544 < p < 0.596