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.

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.

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0