A paper reported that in a representative sample of 292 American teens age 16 to

Question

A paper reported that in a representative sample of 292 American teens age 16 to 17, there were 75 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.)

State your conclusion.

Reject H0. We have convincing evidence that more than a quarter of Americans age 16 to 17 have sent a text message while driving.Reject H0. We do not have convincing evidence that more than a quarter of Americans age 16 to 17 have sent a text message while driving.    Do not reject H0. We have convincing evidence that more than a quarter of Americans age 16 to 17 have sent a text message while driving.Do not reject H0. We do not have convincing evidence that more than a quarter of Americans age 16 to 17 have sent a text message while driving.

Explanation / Answer

here null hypothesis: p=0.25

alternate hypothesis: p>0.25

for n=292 ; std errror =(p(1-p)/n)1/2 =0.0253

sample proportion phat=75/292=0.2568

therfore test statistic z=(phat-p)/std error =(0.2568-0.25)/0.0253=0.27

for above test statistic p value =0.3935 (please try 0.3936 if this does not work for rounding error)

as p value is higher then 0.01 level

Do not reject H0. We do not have convincing evidence that more than a quarter of Americans age 16 to 17 have sent a text message while driving.

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