Question

A paper reported that in a representative sample of 286 American teens age 16 to 17, there were 79 who indicated that they had sent a text message while driving. For purposes of this exercise, assume that this sample is a random sample of 16- to 17-year-old Americans. Do these data provide convincing evidence that more than a quarter of Americans age 16 to 17 have sent a text message while driving? Test the appropriate hypotheses using a significance level of 0.01. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z	=
P-value	=

z=

p-value=

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.25

H_a : p > 0.25

n = 286

x = 79

= x / n = 79 / 286 = 0.2762

P₀ = 0.25

1 - P₀ = 1 - 0.25 = 0.75

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.2762 - 0.25 / [(0.25 * 0.75) / 286]

= 1.024

Test statistic = z = 1.02

P(z > 1.024) = 1 - P(z < 1.024) = 1 - 0.8471 = 0.1529

P-value = 0.1529