Over half of all American teens (ages 12 to 17 years) have an online profile, ma

Question

Over half of all American teens (ages 12 to 17 years) have an online profile, mainly on Facebook. A random sample of 550 teens with profiles found that 387 included photos of themselves. (a) Give the 90% large-sample confidence interval for the proportion p of all teens with profiles who include photos of themselves. Large-sample Interval: to (b) Give the plus four 90% confidence interval for p . (The plus-four interval always pulls the results away from 0% or 100%, whichever is closer. Even though the condition for using the large-sample interval is met, the plus four interval is more trustworthy.) Plus four Interval: to

Explanation / Answer

a)

90% Large-sample Interval: =0.672 ; 0.736

b) for plus 4 interval we add 2 to success and 4 to total sample size

hence

  90% Large-sample Interval: =0.670 ;0.734

                                                                                           x                    =   387 sample size n                    = 550 sample proportion     p x/n= 0.7036 std error       =Se            =(p*(1-p)/n) = 0.0195 for 90 % CI value of z= 1.6449 margin of error E=z*std error                            = 0.032 lower confidence bound=sample proportion-margin of error 0.672 Upper confidence bound=sample proportion+margin of error 0.736

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