According to the Centers for Disease Control and Prevention , in 2008, about 11%

Question

According to the Centers for Disease Control and Prevention , in 2008, about 11% of all Americans 12 years of age and older used antidepressant medication (examples include Prozac, Paxil, Cymbalta, and Zoloft). A medical researcher wants to know if this proportion has changed since then. A random sample of 1000 people are randomly selected from this age group and it is determined that 130 of them used some kind of antidepressant medication. Conduct a hypothesis test for a proportion at the 0.05 level of significance. Select the test statistic and the conclusion (two selections). z = 2.02 Reject H0 and conclude that the true proportion of people in this age group who take antidepressants has increased since 2008. z = +/- 1.645 Fail to reject H0. The researchers conclude that the true proportion of people in this age group who take antidepressants has decreased since 2008. z = 1.75 Fail to reject H0. The researchers cannot conclude that the true proportion of people in this age group who take antidepressants has increased since 2008. z = 1.88 Reject H0 and conclude that the true proportion of people in this age group who take antidepressants has decreased since 2008.

Explanation / Answer

p = 130/1000 = 0.13

Z = 0.13 - 0.11 / srqt ( 0.11*0.89 / 1000 )

Z = 2.02

for alpha / 2 = 0.025   critcal value is 1.96

. z = 2.02 Reject H0 and conclude that the true proportion of people in this age group who take antidepressants has increased since 2008

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