A well-known brokerage firm executive claimed that 30% of investors are currentl
ID: 3058417 • Letter: A
Question
A well-known brokerage firm executive claimed that 30% 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 500 people, 26% of them said they are confident of meeting their goals.
Test the claim that the proportion of people who are confident is smaller than 30% at the 0.05 significance level.
The null and alternative hypothesis would be:
H0:=0.3H0:=0.3
H1:0.3H1:0.3
H0:p=0.3H0:p=0.3
H1:p>0.3H1:p>0.3
H0:p=0.3H0:p=0.3
H1:p0.3H1:p0.3
H0:0.3H0:0.3
H1:>0.3H1:>0.3
H0:0.3H0:0.3
H1:<0.3H1:<0.3
H0:p=0.3H0:p=0.3
H1:p<0.3H1:p<0.3
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:
Fail to reject the null hypothesis
Reject the null hypothesis
Explanation / Answer
A well-known brokerage firm executive claimed that 30% 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 500 people, 26% of them said they are confident of meeting their goals.
Test the claim that the proportion of people who are confident is smaller than 30% at the 0.05 significance level.
The null and alternative hypothesis would be:
H0:=0.3H0:=0.3
H1:0.3H1:0.3
H0:p=0.3H0:p=0.3
H1:p>0.3H1:p>0.3
H0:p=0.3H0:p=0.3
H1:p0.3H1:p0.3
H0:0.3H0:0.3
H1:>0.3H1:>0.3
H0:0.3H0:0.3
H1:<0.3H1:<0.3
H0:p=0.3H0:p=0.3
H1:p<0.3H1:p<0.3
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:
Fail to reject the null hypothesis
Reject the null hypothesis
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