Test the claim that the proportion of people who are confident is smaller than 90% at the 0.025 significance level.
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 a two week period, found that in a sample of 600 people, 82% of them said they are confident of meeting their goals.
Test the claim that the proportion of people who are confident is smaller than 90% at the 0.025 significance level.
The null and alternative hypothesis would be:
- 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 - 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
The test is:
The test statistic is: (to 3 decimals)
The p-value is: (to 4 decimals)
Based on this we:
- Reject the null hypothesis
- Fail to reject the null hypothesis
![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 a two week period, found that in
a sample of 600 people, 82% of them said they are confident of meeting their goals.
Test the claim that the proportion of people who are confident is smaller than 90% at the 0.025 significance
level.
The null and alternative hypothesis would be:
O Ho:p = 0.9
H1:p > 0.9
O Ho:p = 0.9
H1:p + 0.9
O Ho: µ > 0.9
H1:µ < 0.9
0.9
%3D
H1:µ + 0.9
Ο Η: μ 0.9
H1:µ > 0.9
O Ho:p = 0.9
H1:p < 0.9
The test is:
left-tailed right-tailed two-tailed
The test statistic is:
(to 3 decimals)
The p-value is:
(to 4 decimals)
Based on this we:
O Reject the null hypothesis
O Fail to reject the null hypothesis](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff431cdf3-1e5e-47d0-a08d-476407c59ed6%2F317f622c-74c9-4f4f-a49e-93abc48fcd4f%2Feeqr48o_processed.png&w=3840&q=75)
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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 a two week period, found that in a sample of 600 people, 82% of them said they are confident of meeting their goals.
n = 600
claim: proportion of people who are confident is smaller than 90%
significance level = 0.025
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