Sample proportion 45 a sample shows n 1000 with x 580 yes

Sample proportion = 45 % a sample shows n = 1000 with x 580 \"yes\" response smaller the 0.55?

Solution

ans) population proportion = 0.55....
sample size = 1000 and sample proportion = 580 / 1000 = 0.58..

to thest: H0: popltn prop = 0.55 ag. popltn prop. < 0.55.....

standard error = sqrt [ 0.55 * (1 - 0.55) / 1000 ] = 0.01573213..
Test statistic = (0.58 - 0.55) / 0.01573213 = 1.906926....
p-value = 0.02826509
at 99% confidence , this p-value is greater than 0.01..so, null hypothesis is true,,,proportion is 0.55...

but at 95% conf. interval, we reject H0 and state that the proportion is indeed smaller than 0.55..