Question 598844: A decade-old study found that the proportion, p , of high school seniors who believed that "getting rich" was an important personal goal was 75%. A researcher decides to test whether or not that percentage still stands. He finds that, among the 215 high school seniors in his random sample, 175 believe that "getting rich" is an important goal. Can he conclude, at the 0.01 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 0.01 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 stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A decade-old study found that the proportion, p , of high school seniors who believed that "getting rich" was an important personal goal was 75%. A researcher decides to test whether or not that percentage still stands. He finds that, among the 215 high school seniors in his random sample, 175 believe that "getting rich" is an important goal. Can he conclude, at the 0.01 level of significance, that the proportion has indeed changed?
Perform a two-tailed test:
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Null Hypothesis: Ho: p = 0.75 (claim)
Alternative Hypothesis: H1: p # 0.75
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Type of Test Statistic:x-bar = 175/215 = 0.8140
The Value of the Test Statistic:
z(0.814) = (0.814-0.75)/(sqrt(0.75*0.25/215)) = 2.1656
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The two critical values at the 0.01 level of significance
z = +-2.5758
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Can we conclude that the proportion of high school seniors who believe that "getting rich" is an important goal has changed?
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Conclusion: Since the test statistic is not in the reject interval,
fail to reject Ho.
Conclusion: The "getting rich" goal has not changed.
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Cheers,
Stan H.
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