Answer:
90% confidence interval for p is [0.4542 , 0.5105] .
Step-by-step explanation:
We are given that a local board of education conducted a survey of residents in the community concerning a property tax levy on the coming local ballot. Of the 850 residents surveyed, 410 supported the property tax levy.
Let p = proportion of residents in the community that support the property tax levy
= proportion of residents in the community that support the property tax levy in a survey of 850 residents = =
The pivotal quantity that will be used here population proportion p is;
P.Q. = ~ N(0,1)
So, 90% confidence interval for p is given by;
P(-1.6449 < N(0,1) < 1.6449) = 0.90 {At 10% significance level the z table give
critical value of 1.6449)
P(-1.6449 < < 1.6449) = 0.90
P( < < ) = 0.90
P( < p < ) = 0.90
90% confidence interval for p = [ , ]
= [ , ]
= [ 0.4542 , 0.5105 ]
Therefore, 90% confidence interval for p is [0.4542 , 0.5105] .