Answer:
95% confidence interval for the percent of all the hospital's admitted patients that year who had an error on their medical bill is [84% , 87%].
Step-by-step explanation:
We are given that a simple random sample of 2200 hospital patients admitted in a given year shows that 85.5% had an error on their medical bill.
Firstly, the pivotal quantity for 95% confidence interval for the population proportion is given by;
P.Q. = ~ N(0,1)
where, = sample % of patients who had an error on their medical bill = 85.5%
n = sample of hospital patients = 2200
p = population percentage of all the hospital's admitted patients that year who had an error on their medical bill
<em>Here for constructing 95% confidence interval we have used One-sample z proportion statistics.</em>
<u>So, 95% confidence interval for the population proportion, p is ;</u>
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < < 1.96) = 0.95
P( <
<
) = 0.95
P( < p <
) = 0.95
<u>95% confidence interval for p</u> = [ ,
]
= [ ,
]
= [0.84 , 0.87]
= [84% , 87%]
Therefore, 95% confidence interval for the percent of all the hospital's admitted patients that year who had an error on their medical bill is [84% , 87%].