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.
n = 600
claim: proportion of people who are confident is smaller than 90%
significance level = 0.025
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