Hypothesis Test for a Population Proportion

A well-known brokerage firm executive claimed that 10% 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 400 people, 1% of them said they are confident of meeting their goals.

Test the claim that the proportion of people who are confident is smaller than 10% at the 0.025 significance level.

The null and alternative hypothesis would be:

H0:0.1H00.1 H1:<0.1H10.1

H0:=0.1H00.1 H1:0.1H10.1

H0:p=0.1H0p0.1 H1:p0.1H1p0.1

H0:0.1H00.1 H1:>0.1H10.1

H0:p0.1H0p0.1 H1:p>0.1H1p0.1

H0:p0.1H0p0.1 H1:p<0.1H1p0.1

The test is:

two-tailed

right-tailed

left-tailed

The test statistic z is:(round to 3 decimal places)

The p-value is:(round to 3 decimal places)

Based on this we:

• Fail to reject the null hypothesis
• Reject the null hypothesis