Answer:
As 0.17 is below the upper limit of the confidence interval, so we can conclude that the population proportion is less than 0.17.
Step-by-step explanation:
We are given that a survey of 270 young professionals found that one dash eighth of them use their cell phones primarily for e-mail.
Firstly, the Pivotal quantity for 95% confidence interval for the population proportion is given by;
P.Q. = ~ N(0,1)
where, = sample proportion of people who use their cell phones primarily for e-mail =
= 0.125
n = sample of young professionals = 270
p = population proportion
<em>Here for constructing 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> = [ ,
]
= [ ,
]
= [0.08 , 0.16]
Therefore, 95% confidence interval for the population proportion who use cell phones primarily for e-mail is [0.08 , 0.16].
Since, the above confidence interval have values which is less than 0.17; so we conclude that the population proportion is less than 0.17.