Question

According to a Pew Research Center study, in May 2011, 43% 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 281 community college students at random and finds that 145 of them have a smart phone. Then in testing the hypotheses:

H 0 : p = 0.43 versus

H a : p > 0.43,

what is the test statistic?

z = ______. (Please round your answer to two decimal places.)

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.43

Ha : p > 0.43

n = 281

= x / n = 145 / 281 = 0.52

P0 = 0.43

1 - P0 = 1 - 0.43 = 0.57

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.52 - 0.43 / [(0.43*0.57) / 281 ]

= 2.91

Test statistic = z = 2.91

P(z > 2.91) = 1 - P(z < 2.91) = 1 - 0.9982

P-value = 0.0018