A poll done for Newsweek found that 13% of Americans have seen or sensed the pre

Question

A poll done for Newsweek found that 13% of Americans have seen or sensed the presence of an angel. A contingent doubts that the percent is really that high. It conducts its own survey. Out of 100 Americans surveyed, only 3 had seen or sensed the presence of an angel. As a result of the contingent’s survey, at a 5% level of significance, would you agree with the Newsweek poll? In your answer, show your hypothesis (2 points), your calculated z or t score (2 points), and your decision to accept or not accept the null hypothesis (1 point).

Explanation / Answer

We have to test the null hypothesis H0: p=0.13 against the alternative Ha: p<0.13

Sample proportion phat=3/100=0.03

Sample size n=100

We have np=100*0.13=13>5 and n(1-p)=100*(1-0.13)=87>5, so we use z-score.

Test statistic Z= (phat-0.13)/sqrt(p*(1-p)/n) =(0.03-0.13)/sqrt(0.13*(1-0.13)/100) = -2.97

Left tailed z at 5% level is z=-1.645

As calculated z<-1.645, we reject the null hypothesis and conclude that we do not agree with newsweek poll and proportion is significantly lower than 13%.

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