A well-known brokerage firm executive claimed that 90% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over two weeks, found that in a sample of 100 people, 95% of them said they are confident of meeting their goals. Test the claim that the proportion of confident people is more significant than 90% at the 0.10 significance level. The null and alternative hypotheses would be:  H0:p=0.9H0:p=0.9 H1:p≠0.9H1:p≠0.9 H0:μ=0.9H0:μ=0.9 H1:μ≠0.9H1:μ≠0.9 H0:μ=0.9H0:μ=0.9 H1:μ>0.9H1:μ>0.9 H0:μ=0.9H0:μ=0.9 H1:μ<0.9H1:μ<0.9 H0:p=0.9H0:p=0.9 H1:p<0.9H1:p<0.9 H0:p=0.9H0:p=0.9 H1:p>0.9H1:p>0.9 The test is:  two-tailed left-tailed right-tailed What is the test statistic? (to 3 decimals) What is the p-value (to 4 decimals)   Based on this we: Fail to reject the null hypothesis Reject the null hypothesis

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Chapter11: Data Analysis And Probability
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A well-known brokerage firm executive claimed that 90% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over two weeks, found that in a sample of 100 people, 95% of them said they are confident of meeting their goals.

Test the claim that the proportion of confident people is more significant than 90% at the 0.10 significance level.

The null and alternative hypotheses would be: 

H0:p=0.9H0:p=0.9
H1:p≠0.9H1:p≠0.9
H0:μ=0.9H0:μ=0.9
H1:μ≠0.9H1:μ≠0.9
H0:μ=0.9H0:μ=0.9
H1:μ>0.9H1:μ>0.9
H0:μ=0.9H0:μ=0.9
H1:μ<0.9H1:μ<0.9
H0:p=0.9H0:p=0.9
H1:p<0.9H1:p<0.9
H0:p=0.9H0:p=0.9
H1:p>0.9H1:p>0.9

The test is: 

two-tailed
left-tailed
right-tailed
What is the test statistic? (to 3 decimals)
What is the p-value (to 4 decimals)
 
Based on this we:
  • Fail to reject the null hypothesis
  • Reject the null hypothesis
 
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