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 200 people, 96% of them said they are confident of meeting their goals.

Test the claim that the proportion of people who are confident is larger than 90% at the 0.01 significance level.

The null and alternative hypothesis would be:

• H
• 0
• :
• p
• =
• 0.9
• H0:p=0.9
• H
• 1
• :
• p
• >
• 0.9
• H1:p>0.9
• H
• 0
• :
• p
• =
• 0.9
• H0:p=0.9
• H
• 1
• :
• p
• <
• 0.9
• H1:p<0.9
• H
• 0
• :
• =
• 0.9
• H0:=0.9
• H
• 1
• :
• 0.9
• H1:0.9
• H
• 0
• :
• p
• =
• 0.9
• H0:p=0.9
• H
• 1
• :
• p
• 0.9
• H1:p0.9
• H
• 0
• :
• 0.9
• H0:0.9
• H
• 1
• :
• >
• 0.9
• H1:>0.9
• H
• 0
• :
• 0.9
• H0:0.9
• H
• 1
• :
• <
• 0.9
• H1:<0.9

The test is:two-tailed

left-tailed

right-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