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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 300 people, 9% 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 0.10 significance level.

The null and alternative hypothesis would be:

\displaystyle {H}_{{0}}:\mu={0.1}

\displaystyle {H}_{{1}}:\mu≠{0.1}

\displaystyle {H}_{{0}}:\mu\ge{0.1}

\displaystyle {H}_{{1}}:\mu<{0.1}

\displaystyle {H}_{{0}}:\mu\le{0.1}

\displaystyle {H}_{{1}}:\mu>{0.1}

\displaystyle {H}_{{0}}:{p}\ge{0.1}

\displaystyle {H}_{{1}}:{p}<{0.1}

\displaystyle {H}_{{0}}:{p}\le{0.1}

\displaystyle {H}_{{1}}:{p}>{0.1}

\displaystyle {H}_{{0}}:{p}={0.1}

\displaystyle {H}_{{1}}:{p}≠{0.1}

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:

Reject the null hypothesis
Fail to reject the null hypothesis

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