Question

According to a Pew Research Center study, in May 2011, 32% 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.

Part A She selects 304 community college students at random and finds that 105 of them have a smart phone. Then in testing the hypotheses: H0: p = 0.32 versus Ha: p > 0.32, what is the test statistic? z = . (Please round your answer to two decimal places.)

Part B She selects 351 community college students at random and finds that 130 of them have a smart phone. In testing the hypotheses: H0: p = 0.32 versus Ha: p > 0.32, she calculates the test statistic as z = 2.0230. Then the p‑value = . (Please round your answer to four decimal places.)

Answer 1

Solution :

Given that,

P₀ = 0.32

1 - P₀ = 1 - 0.32 = 0.68

Part A)

n = 3014

x = 105

= x / n = 105 / 304 = 0.3454

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.3454 - 0.32 / [(0.32 * 0.68) / 304]

= 0.949

Test statistic = 0.95

Part B)

Given that,

This is the right tailed test ,

z = 2.0230

Using standard normal table,

P(z > 2.0230) = 1 - P(z < 2.0230) = 1 - 0.9785 = 0.0215

P-value = 0.0215