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keishlav5183
20.05.2020 •
Mathematics
A survey of 270 young professionals found that one dash eighth of them use their cell phones primarily for e-mail. Can you conclude statistically that the population proportion who use cell phones primarily for e-mail is less than 0.17? Use a 95% confidence interval. The 95% confidence interval is [nothing comma nothing ]. As 0.17 is ▼ within the limits below the lower limit above the upper limit of the confidence interval, we ▼ cannot can conclude that the population proportion is less than 0.17.
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Ответ:
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
Here for constructing 95% confidence interval we have used One-sample z test for proportions.
So, 95% confidence interval for the population proportion, p is ;
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
95% confidence interval for p = [
,
]
= [
,
]
= [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.
Ответ:
-1
Step-by-step explanation: