Test the claim that the proportion of people who are confident is larger than 60% at the 0.01 significance level.
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A well-known brokerage firm executive claimed that 60% 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 300 people, 65% of them said they are confident of meeting their goals.
Test the claim that the proportion of people who are confident is larger than 60% at the 0.01 significance level.
The null and alternative hypothesis would be:
H1:μ<0.6H1:μ<0.6
H1:μ≠0.6H1:μ≠0.6
H1:p≠0.6H1:p≠0.6
H1:p<0.6H1:p<0.6
H1:μ>0.6H1:μ>0.6
H1:p>0.6H1:p>0.6
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
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