A well-known brokerage firm executive claimed that 50% 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 800 people, 47% of them said they are confident of meeting their goals. Test the claim that the proportion of people who are confident is smaller than 50% at the 0.01 significance level. The null and alternative hypothesis would be: Ho:p 2 0.5 Ho:p < 0.5 Ho:µ=0.5 Ho:µ<0.5 Ho:µ> 0.5 Ho:p=0.5 H:p< 0.5 H1:p > 0.5 H1:µ + 0.5 H:µ>0.5 H1:µ < 0.5 H1:p+0.5 The test is: right-tailed two-tailed left-tailed |(to 3 decimals) The test statistic is: The p-value is: | (to 4 decimals) Based on this we: O Fail to reject the null hypothesis O Reject the null hypothesis

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A well-known brokerage firm executive claimed that 50% 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 800 people, 47% of them said they are confident of meeting their
goals.
Test the claim that the proportion of people who are confident is smaller than 50% at the 0.01
significance level.
The null and alternative hypothesis would be:
Ho:p > 0.5 Ho:p < 0.5 Ho:µ= 0.5 Ho:µ < 0.5 Ho:µ > 0.5 Ho:p= 0.5
H1:p< 0.5 H1:p > 0.5 Hị:µ + 0.5 H:µ > 0.5 Hị:p < 0.5 H1:p+0.5
The test is:
right-tailed two-tailed left-tailed
The test statistic is:
(to 3 decimals)
The p-value is:
(to 4 decimals)
Based on this we:
O Fail to reject the null hypothesis
O Reject the null hypothesis
Transcribed Image Text:A well-known brokerage firm executive claimed that 50% 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 800 people, 47% of them said they are confident of meeting their goals. Test the claim that the proportion of people who are confident is smaller than 50% at the 0.01 significance level. The null and alternative hypothesis would be: Ho:p > 0.5 Ho:p < 0.5 Ho:µ= 0.5 Ho:µ < 0.5 Ho:µ > 0.5 Ho:p= 0.5 H1:p< 0.5 H1:p > 0.5 Hị:µ + 0.5 H:µ > 0.5 Hị:p < 0.5 H1:p+0.5 The test is: right-tailed two-tailed left-tailed The test statistic is: (to 3 decimals) The p-value is: (to 4 decimals) Based on this we: O Fail to reject the null hypothesis O Reject the null hypothesis
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