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Answer:
A 95% confidence interval for this population proportion is [0.081, 0.159].
Step-by-step explanation:
We are given that a market research company conducted a survey to find the level of affluence in a city.
Out of 267 persons who replied to their survey, 32 are considered affluent.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = ~ N(0,1)
where, = sample proportion of people who are considered affluent =
= 0.12
n = sample of persons = 267
p = population proportion
<em>Here for constructing a 95% confidence interval we have used One-sample z-test for proportions.</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> = [ ,
]
= [ ,
]
= [0.081, 0.159]
Therefore, a 95% confidence interval for this population proportion is [0.081, 0.159].