Question

The mother of a teenager has heard a claim that 25% of teenagers who drive and use a cell phone reported texting while driving. She thinks that this rate is too high. She polls 40 randomly selected teenagers, and 5 of them report having texted while driving. Test the hypothesis that fewer than 25% of these drivers have texted while driving. Use a level of significance of 0.01.

Answer 1

As we are testing here whether less than 25% of teenagers use a cell phone reported texting while driving, therefore the null and the alternative hypothesis here are given as:

The sample proportion here is computed as:
p = x/n = 5/40 = 0.125

The test statistic here is computed as:

As this is a one tailed test, the p-value here is computed from the standard normal tables here as:
P = P(Z < -1.8257) = 0.0339

As the p-value here is 0.0339 > 0.01 which is the level of significance, therefore the test is not significant here and we dont have sufficient evidence here that the rate of teenagers who drive and use a cell phone reported texting while driving is less than 25%.