What\'s the news? The Pew Research Center reported in 2012 that 23% of 18- to 29

Question

What's the news? The Pew Research Center reported in 2012 that 23% of 18- to 29-year-olds watch cable news channel regularly. The director of the media relations at a large university wants to know whether the population proportion of the cable news viewers among students at her university is greater than the proportion among 18- to 29-year-olds in general. She surveys a simple random sample of 200 students at the university and finds that 66 of the watch cable news regularly. Can she conclude that the proportion of the students at her university who watch cable news regularly os greater than 0.23?

a. State the null and alternate hypotheses.

b. Compute the value of the test statistic.

c. Do you reject H0? Use the a=0.01 level.

d. State a conclusion.

Explanation / Answer

a) here null hypothesis:Ho: p<=0.23

alternate hypothesis: Ha: p>0.23

b) for p=0.23 and n=200 ; std error =(p*(1-p)/n)1/2 =0.0290

sample proportion phat =(66/200)=0.33

therfore test statistic z=(phat-p)/std error =(0.33-0.23)/0.0290 =3.45

c) for 0.01 level and right tailed test critical value =2.33

as test statistic is higher than critical value ; we reject null hypothesis

d) we have sufficient evidence to conclude that proportion of the students at her university who watch cable news regularly os greater than 0.23

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