In March 2000, the New York Times conducted “a telephone poll of a random sample

Question

In March 2000, the New York Times conducted “a telephone poll of a random sample of 1003 adults in all 50 states, giving all phone numbers, listed and unlisted, a proportionate chance of being included.” We can treat this as a simple random sample. One question asked was, “Do you think what is shown on television today is less moral than American society, more moral than American society, or accurately reflects morality in American society?” Of the answers, 46% said “Less,” 37% said “Accurate,” 9% said “More,” and the others had no opinion. We might use these data to answer the question, “Do less than half of all adults think TV is less moral than society?” In order to test this, define the null and the alternative hypotheses, define the sampling distribution, use your data to calculate a standard score, and calculate a p-value. If your significance level is 0.05, what is your conclusion?

Explanation / Answer

null hypothesis: p=0.5

alternate hypothesis:p<0.5

sampling distribution will be approximately normal as np>10 and n(1-p)>10 here n=1003

for std error=(p(1-p)/n)1/2 =0.0158

hence test stat z=(phat-p)/std error =(0.46-0.50)/0.0158=-2.534

for above test stat; p value =0.0056

as p value is less then 0.05; we reject null hypothesis and conclude that ess than half of all adults think TV is less moral than society

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