question archive With this hypothesis testing question, i am confused about which hypothesis is the claim
With this hypothesis testing question, i am confused about which hypothesis is the claim
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With this hypothesis testing question, i am confused about which hypothesis is the claim.
In a 2011 National Institute on Alcohol Abuse and Alcoholism survey, 33% of American adults said that they had never consumed alcohol (USA TODAY, November 17, 2011). Suppose this result is true for the 2011 population of American adults. In a recent random sample of 2300 American adults, 35% said that they have never consumed alcohol. Using a 5% significance level, can you conclude that the current percentage of American adults who have never consumed alcohol is 33%?
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Answer:
Reject H0
Conclude that there is sufficient evidence of the current percentage of American adults who have never consumed alcohol is different than 33%.
Step-by-step explanation
H0 : P = 0.33
Ha : P ???=? 0.33
Z test for single proportion
Z criticla value = +/- 1.96 at 5% level o significance
Decision rule ; if Z stat < -1.96 or > 1.96, then reject H0
Z stat
= (p - P) / sqrt(PQ/n)
= (0.35 - 0.33) / sqrt(0.33 * 0.67 / 2300))
= 2.04
since
Z stat = 2.04 > 1.96
reject H0
Conclude that there is sufficient evidence of the current percentage of American adults who have never consumed alcohol is different than 33%.
