According to a Pew Research Center study, in May 2011, 41% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students. She selects 378 community college students at random and finds that 162 of them have a smart phone. Then in testing the hypotheses:
H0: p = 0.41 versus
Ha: p > 0.41,
what is the test statistic?
Solution :
Given that,
= 0.41
1 -
= 0.59
n = 378
x = 162
Point estimate = sample proportion =
= x / n = 0.429
Test statistic
z = (
-
) /
*(1-
)
/ n
= ( 0.429 - 0.41) /
(0.41*0.59) / 378
= 0.73
The Test statistic is z = 0.73
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