Answer:
95% confidence interval for the percentage of all U.S. public high school students who are obese is [0.110 , 0.190].
Step-by-step explanation:
We are given that 15% of a random sample of 300 U.S. public high school students were obese.
Firstly, the pivotal quantity for 95% confidence interval for the population proportion is given by;
P.Q. = ~ N(0,1)
where, = sample % of U.S. public high school students who were obese = 15%
n = sample of U.S. public high school students = 300
p = population percentage of all U.S. public high school students
<em>Here for constructing 95% confidence interval we have used One-sample z proportion statistics.</em>
<u></u>
<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> = [ ,
]
= [ ,
]
= [0.110 , 0.190]
Therefore, 95% confidence interval for the percentage of all U.S. public high school students who are obese is [0.110 , 0.190].