A recent survey conducted by ZOOM and Applied Research &Consulting LLC reported

Question

A recent survey conducted by ZOOM and Applied Research &Consulting LLC reported that the events of September 11 havemotivated kids to volunteer and that more than 80% volunteer. Adisbeliever of this information took his own random sample of 500kids in an attempt to show that the true percentage of kids whovolunteer is less than 80%. (using a 0.01 level of significance,find the p value if 384 of the surveyed kids said they do)
a. Symbolize the null and alternative hypothesis
b. Calculate the value of the test statistic. Round to 2 placesafter the decimal point.
c. Find the p-value
d. At the 0.01 level of significance, there________ enough evidenceto suggest that the true percentage of kids who volunteer is lessthan 80%.

Explanation / Answer

H0: p_actual - .8 = 0 Ha: p_actual does not equal .8 (two tailed test). p_actual = 384 / 500 = .768 s = sqrt( p * (1-p) / n) = sqrt(.8 * (1-.8) / 500) = .0179 z = (.768 - .8) / .0179 = -1.79 --> p value of .0367 alpha = .01 --> have tail of .01/2 = .005 on either end. Since .0367 > .005, we cannot reject the null hypothesis atalpha = 1%.

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