Question

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.

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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