Answer:
Since the p value is higher than the significance level so then we can conclude that we have enough evidence to FAIL to reject the null hypothesis and there is no evidence in order to say that the true proportion of teens more than a quarter of Americans age 16 to 17 have sent a text message while driving is higher than 0.25
Step-by-step explanation:
Information provided
n=282 represent the sample selected
X=71 represent the teens indicated that they had sent a text message while driving
estimated proportion of teens indicated that they had sent a text message while driving
is the value that we want to test
represent the significance level
z would represent the statistic
represent the p value
System of hypothesis
We want to check if more than a quarter of Americans age 16 to 17 have sent a text message while driving, and the hypothesis are:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
Replacing we got:
Decision
The p value for this case is:
Since the p value is higher than the significance level so then we can conclude that we have enough evidence to FAIL to reject the null hypothesis and there is no evidence in order to say that the true proportion of teens more than a quarter of Americans age 16 to 17 have sent a text message while driving is higher than 0.25