Question

The Pew Research Centers Internet and American Life project surgery of 2,252 American Adults, ages 18...

The Pew Research Centers Internet and American Life project surgery of 2,252 American Adults, ages 18 years and older, conducted January 20, 2012 - February 19, 2011, revealed that 46% of American adults own a smartphone of some kind

A) Perform the two (2) checks necessary for determining the confidence interval for the proportion go American adults who own a smartphone. For each check, clearly state the conclusion using 1 sentence. You must use appropriate notation.

B) Determine and state the 98% confidence interval for the proportion of American adults who own a smartphone.

C) Using one sentence, interpret the 98% confidence interval in the context of this scenario.

Homework Answers

Answer #1

a)

conditions for normality
n p
2252 0.46
np 1035.92
nq 1216.08
np(1-p) 559.3968

both np and nq > 5

hence normal approximation is appropriate

b)

X 1035.92
n 2252
p 0.460
q 0.540
alpha 0.02
z 2.326348
E 0.0244
lower 0.436
upper 0.484

98% confidence interval is (0.436,0.484)

c)

we are 98% confident that true proportion of American adults who own a smartphone lies in this confidence interval

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