Question

According to a report published by Gallup Institute on February 20, 2020, based on the interview that took place between February 3 and February 16, 77% of 1,028 randomly selected American adults felt they were generally confident in the federal government’s ability to handle a potential corona-virus outbreak. Find the 98% confidence interval.2.

Answer 1

Answer)

N = 1028

P = 0.77

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 791.56

N*(1-p) = 236.44

Both the conditions are met so we can use standard normal z table to estimate the interval

Critical value z from z table for 98% confidence level is 2.33

Margin of error (MOE) = Z*√{P*(1-P)}/√N

Z = 2.33

P = 0.77

N = 1028

After substitution

MOE = 0.03058219437

Interval is given by

(P-MOE, P+MOE)

(0.73941780562, 0.80058219437)