SOLUTION: A decade-old study found that the proportion, p , of high school seniors who believed that "getting rich" was an important personal goal was 80%. A researcher decides to test wheth

Question 329775: A decade-old study found that the proportion, p , of high school seniors who believed that "getting rich" was an important personal goal was 80%. A researcher decides to test whether or not that percentage still stands. He finds that, among the 235 high school seniors in his random sample, 193 believe that "getting rich" is an important goal. Can he conclude, at the 0.05 level of significance, that the proportion has indeed changed?
Perform a two-tailed test
Null Hypothesis: Ho
Alternative Hypothesis: H1
Type of Test Statistic:
The Value of the Test Statistic:
The two critical values at the 0.05 level of significance
Can we conclude that the proportion of high school seniors who believe that "getting rich" is an important goal has changed?

Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
Perform a two-tailed test
Null Hypothesis: Ho
Alternative Hypothesis: H1
Ho: P=0.80
H1: p not 0.80
----------------------
Type of Test Statistic:
Z = (phat- P0)/sqrt(P0*(1-P0)/n) where P0=population proportion under the null
-------------------------
The Value of the Test Statistic:
Phat = 193/235=0.821 SE=sqrt(P0*(1-P0)/n)= Sqrt(0.8*0.2/235)=0.026
Z=(0.821 -0.8)/0.026=0.808
----------------------------
The two critical values at the 0.05 level of significance
a two tail .05 critical area yields critical values -1.96, +1.96
-----------------------------------
Can we conclude that the proportion of high school seniors who believe that "getting rich" is an important goal has changed?
Since the test statistic is within the critical values (ie the region in which chance variations around the Hypothsized value resides) then we cannot reject Ho and thus the population proportion has not changed from 0.80
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